1000 or one thousand is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following

999 999 or triple nine most often refers to: * 999 (emergency telephone number), a telephone number for the emergency services in several countries * 999 (number), an integer * AD 999, a year * 999 BC, a year Books * ''999'' (anthology) or ''999: T ...

and preceding 1001. In most

English-speaking countries The following is a list of English-speaking population by country, including information on both native speakers and second-language speakers. List * The European Union is a supranational union composed of 27 member states. The total Engl ...

, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000. A group of one thousand things is sometimes known, from

Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

, as a chiliad. A period of one thousand years may be known as a chiliad or, more often from

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

, as a

millennium A millennium (plural millennia or millenniums) is a period of one thousand years, sometimes called a kiloannum (ka), or kiloyear (ky). Normally, the word is used specifically for periods of a thousand years that begin at the starting point (ini ...

. The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a

long thousand Long may refer to: Measurement * Long, characteristic of something of great duration * Long, characteristic of something of great length * Longitude (abbreviation: long.), a geographic coordinate * Longa (music), note value in early music mens ...

Notation

* The decimal representation for one thousand is ** 1000—a one followed by three zeros, in the general notation ; ** 1 × 10³—in

engineering notation Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten must be divisible by three (i.e., they are powers of a thousand, but written as, for example, 106 instead of 1000 ...

, which for this number coincides with : ** 1 × 10³ exactly—in scientific normalized exponential notation ; ** 1 E+3 exactly—in scientific E notation. * The

SI prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

for a thousand units is "

kilo- Kilo is a decimal unit prefix in the metric system denoting multiplication by one thousand (103). It is used in the International System of Units, where it has the symbol k, in lowercase. The prefix ''kilo'' is derived from the Greek word (), ...

", abbreviated to "k"—for instance, a

kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...

or "kg" is a thousand

gram The gram (originally gramme; SI unit symbol g) is a Physical unit, unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure wate ...

s. This is sometimes extended to non-SI contexts, such as "ka" (

kiloannum A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hour ...

) being used as a shorthand for periods of 1000 years. In

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024). * In the SI writing style, a non-breaking space can be used as a

thousands separator A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...

, i.e., to separate the digits of a number at every power of 1000. * Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the

Y2K The year 2000 problem, also known as the Y2K problem, Y2K scare, millennium bug, Y2K bug, Y2K glitch, Y2K error, or simply Y2K refers to potential computer errors related to the formatting and storage of calendar data for dates in and after ...

computer bug of the year 2000. * A thousand units of

currency A currency, "in circulation", from la, currens, -entis, literally meaning "running" or "traversing" is a standardization of money in any form, in use or circulation as a medium of exchange, for example banknotes and coins. A more general def ...

, especially

dollar Dollar is the name of more than 20 currencies. They include the Australian dollar, Brunei dollar, Canadian dollar, Hong Kong dollar, Jamaican dollar, Liberian dollar, Namibian dollar, New Taiwan dollar, New Zealand dollar, Singapore dollar, U ...

s or pounds, are colloquially called a ''grand''. In the United States of America this is sometimes abbreviated with a "G" suffix.

Properties

There are 168 prime numbers less than 1000. 1000 is the 10th icositetragonal number, or 24-gonal number. 1000 has a reduced totient value of 100, and

totient In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ...

of 400. It is equal to the sum of

Euler's totient function In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...

over the first 57 integers, with 11 integers having a

value of 1000. 1000 is the smallest number that generates three primes in the fastest way possible by concatenation of decremented numbers: (1,000,999), (1,000,999,998,997), and (1,000,999,998,997,996,995,994,993) are all prime. The 1000th prime number is 7919. It is a difference of 1 from the order of the smallest

sporadic group In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...

, \mathrm _,

= 7920.

Selected numbers in the range 1001–1999

1001 to 1099

: 1001 =

sphenic number In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definit ...

(7 × 11 × 13),

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...

pentatope number A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row , either from left to right or from right to left. The first few numbers of this kind are: : 1, 5, 15, 35, 70, 126, 210, 330, 4 ...

:1002 = sphenic number,

Mertens function In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...

zero,

abundant number In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. Th ...

, number of

partitions Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

of 22 : 1003 = the product of some prime ''p'' and the ''p''^th prime, namely ''p'' = 17. :1004 =

heptanacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequ ...

:1005 = Mertens function zero, decagonal pyramidal number :1006 = number that is the sum of 7 positive 5th powers :1007 = number that is the sum of 8 positive 5th powers :1008 = divisible by the number of primes below it :1009 = smallest four-digit

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

palindromic A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Pana ...

in bases 11, 15, 19, 24 and 28: (838₁₁, 474₁₅, 2F2₁₉, 1I1₂₄, 181₂₈). It is also a

Lucky prime In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...

and

Chen prime A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingru ...

. :1010 = 10³ + 10, Mertens function zero :1011 = the largest ''n'' such that 2ⁿ contains 101 and doesn't contain 11011,

Harshad number In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad numbers ...

in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction :1012 =

ternary Ternary (from Latin ''ternarius'') or trinary is an adjective meaning "composed of three items". It can refer to: Mathematics and logic * Ternary numeral system, a base-3 counting system ** Balanced ternary, a positional numeral system, useful ...

number, (32₁₀) quadruple

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

(

is 253), number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction :1013 =

Sophie Germain prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

centered square number In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each cen ...

, Mertens function zero :1014 = 2¹⁰-10, Mertens function zero, sum of the nontriangular numbers between successive triangular numbers :1015 =

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broa ...

:1016 = member of the

Mian–Chowla sequence In mathematics, the Mian–Chowla sequence is an integer sequence defined recursion, recursively in the following way. The sequence starts with :a_1 = 1. Then for n>1, a_n is the smallest integer such that every pairwise sum :a_i + a_j is di ...

stella octangula number In mathematics, a stella octangula number is a figurate number based on the stella octangula, of the form .. The sequence of stella octangula numbers is :0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, ... Only two of these numbers are squar ...

, number of surface points on a cube with edge-length 14 :1017 = generalized triacontagonal number :1018 = Mertens function zero, 1018¹⁶ + 1 is prime :1019 =

safe prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

:1020 =

polydivisible number In mathematics a polydivisible number (or magic number) is a number in a given number base with digits ''abcde...'' that has the following properties: # Its first digit ''a'' is not 0. # The number formed by its first two digits ''ab'' is a mul ...

:1021 =

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

with 1019. It is also a

. :1022 =

Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, p ...

: 1023 = sum of five consecutive primes (193 + 197 + 199 + 211 + 223); the number of

three-dimensional Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...

polycube upAll 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total A puzzle involving arranging nine L tricubes into a 3×3 cube A polycube is a solid figure formed by j ...

s with 7 cells; number of elements in a

9-simplex In geometry, a 9- simplex is a self-dual regular 9-polytope. It has 10 vertices, 45 edges, 120 triangle faces, 210 tetrahedral cells, 252 5-cell 4-faces, 210 5-simplex 5-faces, 120 6-simplex 6-faces, 45 7-simplex 7-faces, and 10 8-simplex 8-fa ...

; highest number one can count to on one's fingers using binary; magic number used in

Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...

signals. : 1024 = 32² = 4⁵ = 2¹⁰, the number of

byte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...

s in a

kilobyte The kilobyte is a multiple of the unit byte for digital information. The International System of Units (SI) defines the prefix ''kilo'' as 1000 (103); per this definition, one kilobyte is 1000 bytes.International Standard IEC 80000-13 Quantiti ...

(in 1999, the

IEC The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...

coined

kibibyte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...

to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a

. :1025 =

Proth number A Proth number is a natural number ''N'' of the form N = k \times 2^n +1 where ''k'' and ''n'' are positive integers, ''k'' is odd and 2^n > k. A Proth prime is a Proth number that is prime. They are named after the French mathematician François ...

2¹⁰ + 1; member of

Moser–de Bruijn sequence In number theory, the Moser–de Bruijn sequence is an integer sequence named after Leo Moser and Nicolaas Govert de Bruijn, consisting of the sums of distinct powers of 4, or equivalently the numbers whose binary representations are nonzero o ...

, because its base-4 representation (100001₄) contains only digits 0 and 1, or it's a sum of distinct powers of 4 (4⁵ + 4⁰); Jacobsthal-Lucas number; hypotenuse of

primitive Pythagorean triangle A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A primitive Pythagorean triple is ...

:1026 = sum of two distinct powers of 2 ( 1024 + 2) :1027 = sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9. :1028 = sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9; number of primes <= 2¹³. :1029 = can be written from base 2 to base 18 using only the digits 0 to 9. :1030 = generalized heptagonal number :1031 = exponent and number of ones for the largest proven base-10

repunit prime In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recreat ...

super-prime Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins :3, 5, 11, 17, 31, ...

:1032 = sum of two distinct powers of 2 ( 1024 + 8) :1033 =

emirp An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as ...

with 1031 :1034 = sum of 12 positive 9th powers :1035 =

hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...

:1036 = central polygonal number :1037 = number in E-toothpick sequence :1038 =

even Even may refer to: General * Even (given name), a Norwegian male personal name * Even (surname) * Even (people), an ethnic group from Siberia and Russian Far East ** Even language, a language spoken by the Evens * Odd and Even, a solitaire game w ...

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

that is an unordered sum of two

primes A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

in exactly ''n'' ways :1039 =

of the form 8n+7, number of partitions of 30 that do not contain 1 as a part,

:1040 = 4⁵ + 4²: sum of distinct powers of 4 :1041 = sum of 11 positive 5th powers :1042 = sum of 12 positive 5th powers :1043 = number whose sum of

digits and sum of

odd Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: Acronym * ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...

digits are even :1044 = sum of distinct powers of 4 :1045 =

octagonal number An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are : 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 34 ...

:1046 = coefficient of f(q) (3rd order mock theta function) :1047 = number of ways to split a strict composition of ''n'' into contiguous subsequences that have the same sum :1048 = number of partitions of ''n'' into

squarefree In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, is square-fr ...

parts :1049 =

highly cototient number In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient fun ...

:1050 = 1050₈ to

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

becomes a

pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...

(552₁₀), number of parts in all partitions of 29 into distinct parts :1051 =

centered pentagonal number A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the ...

centered decagonal number A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for ''n'' is given by th ...

:1052 = number that is the sum of 9 positive 6th powers :1053 = triangular matchstick number :1054 =

centered triangular number A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers. The followin ...

:1055 = number that is the sum of 12 positive 6th powers :1056 =

:1057 = central polygonal number :1058 = number that is the sum of 4 positive 5th powers, area of a square with diagonal 46 :1059 = number ''n'' such that n⁴ is written in the form of a sum of four positive 4th powers :1060 = sum of the first 25 primes :1061 =

with 1063 :1062 = number that is not the sum of two

palindromes A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Panam ...

:1063 =

, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime :1064 = sum of two positive

cubes In geometry, a cube is a three-dimensional space, three-dimensional solid object bounded by six square (geometry), square faces, Facet (geometry), facets or sides, with three meeting at each vertex (geometry), vertex. Viewed from a corner it i ...

:1065 = generalized duodecagonal :1066 = number whose sum of their

divisors In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...

is a

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...

:1067 = number of strict

of ''n'' in which are empty or have smallest

part Part, parts or PART may refer to: People *Armi Pärt (born 1991), Estonian handballer * Arvo Pärt (born 1935), Estonian classical composer *Brian Part (born 1962), American child actor *Dealtry Charles Part (1882–1961), sheriff (1926–1927) a ...

not dividing the other ones :1068 = number that is the sum of 7 positive 5th powers, total number of parts in all partitions of 15 :1069 =

:1070 = number that is the sum of 9 positive 5th powers :1071 =

heptagonal number A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula :H_n=\frac. The first few heptagonal numbers are: : 0, 1, 7, 18, 34, 55, 81, 112 ...

:1072 =

centered heptagonal number A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ...

:1073 = number that is the sum of 12 positive 5th powers :1074 = number that is not the sum of two

:1075 = number non-sum of two

:1076 = number of strict trees weight ''n'' :1077 = number where 7 outnumbers every other digit in the number :1078 =

Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

transform of negative

integers An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language o ...

:1079 = every positive integer is the sum of at most 1079 tenth powers. :1080 = pentagonal number :1081 = triangular number, member of

Padovan sequence In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values :P(0)=P(1)=P(2)=1, and the recurrence relation :P(n)=P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5 ...

:1082 = central polygonal number :1083 = three-quarter

, number of partitions of 53 into prime parts :1084 =

third Third or 3rd may refer to: Numbers * 3rd, the ordinal form of the cardinal number 3 * , a fraction of one third * Second#Sexagesimal divisions of calendar time and day, 1⁄60 of a ''second'', or 1⁄3600 of a ''minute'' Places * 3rd Street (d ...

spoke of a hexagonal spiral, 1084⁶⁴ + 1 is prime :1085 = number of partitions of ''n'' into distinct parts > or = 2 :1086 =

Smith number In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-f ...

, sum of totient function for first 59 integers :1087 = super-prime,

cousin prime In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences and in O ...

lucky prime In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...

:1088 = octo-

, (

result being 136) sum of two distinct powers of 2, ( 1024 + 64) number that is divisible by exactly seven

with the inclusion of

multiplicity Multiplicity may refer to: In science and the humanities * Multiplicity (mathematics), the number of times an element is repeated in a multiset * Multiplicity (philosophy), a philosophical concept * Multiplicity (psychology), having or using mult ...

: 1089 = 33²,

nonagonal number A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns inv ...

centered octagonal number A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the od ...

, first natural number whose digits in its decimal representation get reversed when multiplied by 9. :1090 = sum of 5 positive 5th powers :1091 =

and

with 1093 :1092 = divisible by the number of primes below it : 1093 = the smallest

Wieferich prime In number theory, a Wieferich prime is a prime number ''p'' such that ''p''2 divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime ''p'' divides . Wieferich primes were first described by Ar ...

(the only other known

is 3511),

with 1091 and

star number A star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n'' − 1) + 1. The ...

:1094 = sum of 9 positive 5th powers, 1094⁶⁴ + 1 is prime :1095 = sum of 10 positive 5th powers, number that is not the sum of two

:1096 = hendecagonal number, number of strict solid partitions of 18 :1097 =

:1098 = multiple of 9 containing digit 9 in its

base-10 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

representation :1099 = number where 9 outnumbers every other digit

1100 to 1199

:1100 = number of partitions of 61 into distinct squarefree parts :1101 = pinwheel number :1102 = sum of totient function for first 60 integers :1103 =

, balanced prime :1104 =

Keith number In number theory, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n in a given number base b with k digits such that when a sequence is created such that the first k terms are the k digits of n and ...

: 1105 = 33² + 4² = 32² + 9² = 31² + 12² = 23² + 24²,

Carmichael number In number theory, a Carmichael number is a composite number n, which in modular arithmetic satisfies the congruence relation: :b^n\equiv b\pmod for all integers b. The relation may also be expressed in the form: :b^\equiv 1\pmod. for all integers ...

magic constant The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...

of ''n'' × ''n'' normal

magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...

and ''n''-queens problem for ''n'' = 13,

decagonal number A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal number ...

, centered square number,

Fermat pseudoprime In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Definition Fermat's little theorem states that if ''p'' is prime and ''a'' is coprime to ''p'', then ''a'p''− ...

:1106 = number of regions into which the plane is divided when drawing 24 ellipses :1107 = number of non-isomorphic strict T₀ multiset partitions of weight 8 :1108 = number k such that k⁶⁴ + 1 is prime :1109 = Friedlander-Iwaniec prime,

:1110 = k such that 2^k + 3 is prime :1111 =

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Example ...

:1112 = k such that 9^k - 2 is a prime :1113 = number of strict partions of 40 :1114 = number of ways to write 22 as an orderless product of orderless sums :1115 = number of partitions of 27 into a prime number of parts :1116 = divisible by the number of primes below it :1117 = number of diagonally symmetric polyominoes with 16 cells,

:1118 = number of unimodular 2 × 2 matrices having all terms in :1119 = number of bipartite graphs with 9 nodes :1120 = number k such that k⁶⁴ + 1 is prime :1121 = number of squares between 34² and 34⁴. :1122 = pronic number, divisible by the number of primes below it :1123 = balanced prime :1124 =

Leyland number In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, ...

:1125 =

Achilles number An Achilles number is a number that is powerful but not a perfect power. A positive integer is a powerful number if, for every prime factor of , is also a divisor. In other words, every prime factor appears at least squared in the factoriza ...

:1126 = number of 2 × 2 non-singular integer matrices with entries from :1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts :1128 = triangular number, hexagonal number, divisible by the number of primes below it :1129 = number of lattice points inside a circle of radius 19 :1130 = skiponacci number :1131 = number of edges in the hexagonal triangle T(26) :1134 = divisible by the number of primes below it, triangular matchstick number :1135 =

:1136 = number o
independent vertex sets
an

in the

:1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid : 1138 = recurring number in the works of

George Lucas George Walton Lucas Jr. (born May 14, 1944) is an American filmmaker. Lucas is best known for creating the ''Star Wars'' and ''Indiana Jones'' franchises and founding Lucasfilm, LucasArts, Industrial Light & Magic and THX. He served as chairm ...

and his companies, beginning with his first feature film – ''

THX 1138 ''THX 1138'' is a 1971 American social science fiction film co-written and directed by George Lucas in his directorial debut. Produced by Francis Ford Coppola and co-written by Walter Murch, the film stars Robert Duvall and Donald Pleasence, wit ...

''; particularly, a special code for Easter eggs on ''

Star Wars ''Star Wars'' is an American epic film, epic space opera multimedia franchise created by George Lucas, which began with the Star Wars (film), eponymous 1977 film and quickly became a worldwide popular culture, pop-culture Cultural impact of S ...

'' DVDs. :1139 =

wiener index In chemical graph theory, the Wiener index (also Wiener number) introduced by Harry Wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph represen ...

of the

windmill graph In the mathematical field of graph theory, the windmill graph is an undirected graph constructed for and by joining copies of the complete graph at a shared universal vertex. That is, it is a 1-clique-sum of these complete graphs. Propert ...

D(3,17) :1140 =

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is, ...

:1141 = 7-Knödel number :1142 = n such that n³² + 1 is prime :1145 = 5- Knödel number :1151 = first prime following a

prime gap A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-th and the ''n''-th prime numbers, i.e. :g_n = p_ - p_n.\ W ...

of 22.,

:1152 =

highly totient number A highly totient number k is an integer that has more solutions to the equation \phi(x) = k, where \phi is Euler's totient function, than any integer below it. The first few highly totient numbers are 1, 2, 4, 8, 12, 24, 48, 72, 144, 240, ...

, 3-smooth number (2⁷×3²), area of a square with diagonal 48,

:1153 =

Proth prime A Proth number is a natural number ''N'' of the form N = k \times 2^n +1 where ''k'' and ''n'' are positive integers, ''k'' is odd and 2^n > k. A Proth prime is a Proth number that is prime. They are named after the French mathematician François ...

:1154 = 2 × 24² + 2 = number of points on surface of tetrahedron with edgelength 24 :1155 = number of edges in the join of two cycle graphs, both of order 33 :1156 = 34²,

octahedral number In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The ''n''th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahed ...

, centered pentagonal number, centered hendecagonal number. :1158 = number of points on surface of octahedron with edgelength 17 :1159 = member of the Mian–Chowla sequence, a

centered octahedral number A centered octahedral number or Haüy octahedral number is a figurate number that counts the number of points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases of t ...

:1160 =

:1161 = sum of the first 26 primes :1162 = pentagonal number, sum of totient function for first 61 integers :1163 = smallest prime > 34². See

Legendre's conjecture Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between n^2 and (n+1)^2 for every positive integer n. The conjecture is one of Landau's problems (1912) on prime numbers; , the conjecture has neither ...

. :1165 = 5- Knödel number :1166 = heptagonal pyramidal number :1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43 :1169 = highly cototient number :1170 = highest possible score in a

National Academic Quiz Tournaments National Academic Quiz Tournaments, LLC is a question-writing and quiz bowl tournament-organizing company founded by former players in 1996. It is unique among U.S. quiz organizations for supplying questions and hosting championships at the midd ...

(NAQT) match :1171 = super-prime :1174 = number of widely totally strongly normal compositions of 16 :1175 = maximal number of pieces that can be obtained by cutting an annulus with 47 cuts :1176 = triangular number :1177 = heptagonal number :1178 = number of surface points on a cube with edge-length 15 :1183 =

pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...

:1184 =

amicable number Amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, σ(''a'')=''b'' and σ(''b'')=''a'', where σ(''n'') is equal to the sum of positive d ...

with 1210 :1185 = number of partitions of 45 into pairwise relatively prime parts :1186 = number of diagonally symmetric

polyominoes A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in po ...

with 15 cells, number of partitions of 54 into prime parts :1187 = safe prime, Stern prime, balanced prime,

:1189 = number of squares between 35² and 35⁴. :1190 = pronic number, number of cards to build an 28-tier house of cards :1191 = 35² - 35 + 1 = H₃₅ (the 35th Hogben number) :1192 = sum of totient function for first 62 integers :1193 = a number such that 4¹¹⁹³ - 3¹¹⁹³ is prime,

:1196 =

\sum_^ \sigma(k)

:1197 = pinwheel number :1198 = centered heptagonal number :1199 = area of the 20t
conjoined trapezoid

1200 to 1299

:1200 = the

, ten "

long hundred The long hundred, also known as the great hundred or twelfty, is the number 120 (in base-10 Arabic numerals) that was referred to as "hundred" in Germanic languages prior to the 15th century, and is now known as one hundred twenty, or six score. ...

s" of 120 each, the traditional reckoning of large numbers in

Germanic languages The Germanic languages are a branch of the Indo-European language family spoken natively by a population of about 515 million people mainly in Europe, North America, Oceania and Southern Africa. The most widely spoken Germanic language, Engli ...

, the number of households the

Nielsen ratings Nielsen Media Research (NMR) is an American firm that measures media audiences, including television, radio, theatre, films (via the AMC Theatres MAP program), and newspapers. Headquartered in New York City, it is best known for the Nielsen rat ...

sample, number k such that k⁶⁴ + 1 is prime :1201 = centered square number,

:1202
number of regions
the plane is divided into by 25 ellipses :1205 = number of partitions of 28 such that the number of odd parts is a part :1207 = composite de Polignac number :1210 = amicable number with 1184 :1211 = composite de Polignac number :1213 =

:1214 = sum of first 39 composite numbers :1215 = number of edges in the hexagonal triangle T(27) :1216 = nonagonal number :1217 =

, Proth prime :1218 = triangular matchstick number :1219 =

zero,

:1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons :1222 = hexagonal pyramidal number :1223 =

, balanced prime, 200th prime number :1224 = number of edges in the join of two cycle graphs, both of order 34 :1225 = 35²,

square triangular number In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a perfect square. There are infinitely many square triangular numbers; the first few are: :0, 1, 36, , , , , , , Expl ...

, hexagonal number, centered octagonal number :1228 = sum of totient function for first 63 integers :1229 =

, number of primes between 0 and 10000 :1230 = the Mahonian number: T(9, 6) :1233 = 12² + 33² :1234 = number of parts in all partitions of 30 into distinct parts :1236 = 617 + 619: sum of twin prime pair :1237 = prime of the form 2p-1 :1238 = number of partitions of 31 that do not contain 1 as a part :1240 = square pyramidal number :1241 =

centered cube number A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equival ...

:1242 = decagonal number :1243 = composite de Polignac number :1244 = number of complete partitions of 25 :1247 = pentagonal number :1249 = emirp, trimorphic number :1250 = area of a square with diagonal 50 :1251 = 2 × 25² + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25 :1252 = 2 × 25² + 2 = number of points on surface of tetrahedron with edgelength 25 :1253 = number of partitions of 23 with at least one distinct part :1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums, number of partitions of 23 :1256 = Mertens function zero :1257 = number of lattice points inside a circle of radius 20 :1258 = Mertens function zero :1259 =

:1260 =

highly composite number __FORCETOC__ A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...

, pronic number, the smallest

vampire number In number theory, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into two natural numbers each with half as many digits as the original number, where the two factors conta ...

, sum of totient function for first 64 integers, number of strict partions of 41 and appears twice in the

Book of Revelation The Book of Revelation is the final book of the New Testament (and consequently the final book of the Christian Bible). Its title is derived from the first word of the Koine Greek text: , meaning "unveiling" or "revelation". The Book of R ...

:1261 = star number, Mertens function zero :1262 = maximal number of regions the plane is divided into by drawing 36 circles :1263 = rounded total surface area of a regular tetrahedron with edge length 27 :1264 = sum of the first 27 primes :1265 = number of rooted trees with 43 vertices in which vertices at the same level have the same degree :1266 = centered pentagonal number, Mertens function zero :1267 = 7-Knödel number :1268 = number of partitions of 37 into prime power parts :1270 = Mertens function zero :1271 = sum of first 40 composite numbers :1274 = sum of the nontriangular numbers between successive triangular numbers :1275 = triangular number, sum of the first 50 natural numbers :1276 = number of irredundant sets in the 25-cocktail party graph :1278 = number of Narayana's cows and calves after 20 years :1279 = Mertens function zero,

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17t ...

exponent :1280 = Mertens function zero, number of parts in all compositions of 9 :1281 =

:1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts :1283 = safe prime :1284 = 641 + 643: sum of twin prime pair :1285 = Mertens function zero, number of free

nonomino A nonomino (or enneomino or 9-omino) is a polyomino of order 9, that is, a polygon in the plane made of 9 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix non(a)-. When rotations and reflectio ...

es, number of parallelogram polyominoes with 10 cells. :1288 = heptagonal number : 1289 = Sophie Germain prime, Mertens function zero :1291 = Mertens function zero :1292 = Mertens function zero :1294 = rounded volume of a regular octahedron with edge length 14 :1295 = number of edges in the join of two cycle graphs, both of order 35 :1296 = 36² = 6⁴, sum of the cubes of the first eight positive integers, the number of

rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containi ...

s on a normal 8 × 8

chessboard A chessboard is a used to play chess. It consists of 64 squares, 8 rows by 8 columns, on which the chess pieces are placed. It is square in shape and uses two colours of squares, one light and one dark, in a chequered pattern. During play, the bo ...

, also the maximum font size allowed in Adobe InDesign :1297 =

, Mertens function zero, pinwheel number :1298 = number of partitions of 55 into prime parts :1299 = Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts

1300 to 1399

:1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an

NAQT National Academic Quiz Tournaments, LLC is a question-writing and quiz bowl tournament-organizing company founded by former players in 1996. It is unique among U.S. quiz organizations for supplying questions and hosting championships at the midd ...

match :1301 = centered square number, Honaker prime :1302 = Mertens function zero, number of edges in the hexagonal triangle T(28) :1305 = triangular matchstick number :1306 = Mertens function zero. In

base 10 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numer ...

, raising the digits of 1306 to powers of successive integers equals itself:

135 135 may refer to: * 135 (number) * AD 135 * 135 BC * 135 film, better known as 35 mm film, is a format of photographic film used for still photography *135 (New Jersey bus) 135 may refer to: * 135 (number) * AD 135 * 135 BC * 135 film, better know ...

, 175, 518, and

598 __NOTOC__ Year 598 ( DXCVIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. The denomination 598 for this year has been used since the early medieval period, when the Anno Domini calendar ...

also have this property.

Centered triangular number A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers. The followin ...

. :1307 = safe prime :1308 = sum of totient function for first 65 integers :1309 = the first

followed by two consecutive such number :1311 = number of integer partitions of 32 with no part dividing all the others :1312 = member of the Mian-Chowla sequence; code for "

ACAB ACAB (All Cops Are Bastards) is an acronym used as a political slogan associated with dissidents who are opposed to the police. It is typically written as a catchphrase in graffiti, tattoos or other imagery in public spaces. It is sometimes num ...

" itself an acronym for "all cops are bastards" :1314 = number of integer partitions of 41 whose distinct parts are connected :1318 = Mertens function zero :1319 = safe prime :1320 = 659 + 661: sum of twin prime pair :1321 = Friedlander-Iwaniec prime :1322 = area of the 21t
conjoined trapezoid
:1323 =

:1325 =

Markov number A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are : 1, 2, 5, 13, 29, 34, 89 ...

, centered tetrahedral number :1326 = triangular number, hexagonal number, Mertens function zero :1327 = first prime followed by 33 consecutive composite numbers :1328 = sum of totient function for first 66 integers :1329 = Mertens function zero, sum of first 41 composite numbers :1330 = tetrahedral number, forms a

Ruth–Aaron pair In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: :714 = 2 × 3 × 7 × 17, :715 = 5 × 11 × 13, and : 2 + 3 + 7 + 17 = 5 + 11 + 13 ...

with 1331 under second definition :1331 = 11³, centered heptagonal number, forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form ''x''² + ''x'' − 1, for ''x'' = 36. :1332 = pronic number :1333 = 37² - 37 + 1 = H₃₇ (the 37th Hogben number) :1334 = maximal number of regions the plane is divided into by drawing 37 circles :1335 = pentagonal number, Mertens function zero :1336 = Mertens function zero :1337 = Used in the novel form of spelling called

leet Leet (or "1337"), also known as eleet or leetspeak, is a system of modified spellings used primarily on the Internet. It often uses character replacements in ways that play on the similarity of their glyphs via reflection or other resemblance. ...

. Approximate melting point of

gold Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...

kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...

s. :1338 = Mertens function zero :1340 = k such that 5 × 2^k - 1 is prime :1342 =

\sum_^ \sigma(k)

, Mertens function zero :1343
cropped hexagone
:1344 = 37² - 5², the only way to express 1344 as a difference of prime squares :1345 = k such that k, k+1 and k+2 are products of two primes :1349 = Stern-Jacobsthal number :1350 = nonagonal number :1351 = number of partitions of 28 into a prime number of parts :1352 = number of surface points on a cube with edge-length 16,

:1353 = 2 × 26² + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26 :1354 = 2 × 26² + 2 = number of points on surface of tetrahedron with edgelength 26 :1357 = number of nonnegative solutions to x² + y² ≤ 41² :1358 = rounded total surface area of a regular tetrahedron with edge length 28 :1360 = 37² - 3², the only way to express 1360 as a difference of prime squares :1361 = first prime following a

of 34,

, Honaker prime :1362 = number of achiral integer partitions of 48 :1365 = pentatope number :1367 = safe prime, balanced prime, sum of three, nine, and eleven consecutive primes (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151), :1368 = number of edges in the join of two cycle graphs, both of order 36 :1369 = 37², centered octagonal number :1370 = σ₂(37): sum of squares of divisors of 37 :1371 = sum of the first 28 primes :1372 =

:1373 = number of lattice points inside a circle of radius 21 :1374 = number of unimodular 2 × 2 matrices having all terms in :1375 = decagonal pyramidal number :1376 = primitive abundant number (

all of whose proper divisors are deficient numbers) :1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts :1378 = triangular number :1379 =

of ''n'' × ''n'' normal

and ''n''-queens problem for ''n'' = 14. :1380 = number of 8-step mappings with 4 inputs :1381 = centered pentagonal numberMertens function zero :1384 =

\sum_^ \sigma(k)

:1385 = up/down number :1386 = octagonal pyramidal number :1387 = 5th

of base 2, 22nd

centered hexagonal number In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following ...

and the 19th

, second

Super-Poulet number A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides :2''d'' − 2. For example, 341 is a super-Poulet number: it has positive divisors and we have: :(211 - 2) / 11 = 2046 / 11 = 186 :(231 - 2) ...

. :1389 = sum of first 42 composite numbers :1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47 :1392 = number of edges in the hexagonal triangle T(29) :1393 = 7-Knödel number :1394 = sum of totient function for first 67 integers :1395 =

, member of the Mian–Chowla sequence triangular matchstick number :1396 =

:1398 = number of integer partitions of 40 whose distinct parts are connected

1400 to 1499

:1400 = number of sum-free subsets of :1401 = pinwheel number :1402 = number of integer partitions of 48 whose augmented differences are distinct :1404 = heptagonal number :1405 = 26² + 27², 7² + 8² + ... + 16², centered square number :1406 = pronic number,

semi-meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges. Meander Given a fixed oriented li ...

:1407 = 38² - 38 + 1 = H₃₈ (the 38th Hogben number) :1408 = maximal number of regions the plane is divided into by drawing 38 circles :1409 =

, Sophie Germain prime, smallest number whose eighth power is the sum of 8 eighth powers, Proth prime :1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations :1415 = the Mahonian number: T(8, 8) :1417 = number of partitions of 32 in which the number of parts divides 32 :1419 =

Zeisel number A Zeisel number, named after Helmut Zeisel, is a square-free integer ''k'' with at least three prime factors which fall into the pattern :p_x = ap_ + b where ''a'' and ''b'' are some integer constants and ''x'' is the index number of each prime f ...

:1420 = Number of partitions of 56 into prime parts :1423 = 200 + 1223 and the 200th prime is 1223 :1424 = number of nonnegative solutions to x² + y² ≤ 42² :1425 =

self-descriptive number In mathematics, a self-descriptive number is an integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inver ...

in base 5 :1426 = sum of totient function for first 68 integers, pentagonal number, number of strict partions of 42 :1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts :1430 =

Catalan number In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Ca ...

:1431 = triangular number, hexagonal number :1432 = member of Padovan sequence :1433 =

, Honaker prime, typical port used for remote connections to

Microsoft SQL Server Microsoft SQL Server is a relational database management system developed by Microsoft. As a database server, it is a software product with the primary function of storing and retrieving data as requested by other software applications—which ma ...

database In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases sp ...

s :1434 = rounded volume of a regular tetrahedron with edge length 23 :1435 =

; the standard railway gauge in millimetres, equivalent to :1437 = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^ :1438 = k such that 5 × 2^k - 1 is prime :1439 = Sophie Germain prime, safe prime :1440 = a

and a 481- gonal number. Also, the number of

minute The minute is a unit of time usually equal to (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a nega ...

s in one day, the blocksize of a standard

floppy disk A floppy disk or floppy diskette (casually referred to as a floppy, or a diskette) is an obsolescent type of disk storage composed of a thin and flexible disk of a magnetic storage medium in a square or nearly square plastic enclosure lined w ...

, and the horizontal resolution of WXGA(II) computer displays :1441 = star number :1442 = number of parts in all partitions of 31 into distinct parts :1443 = the sum of the second trio of three-digit

permutable prime A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to study th ...

s in

: 337, 373, and

733 __NOTOC__ Year 733 ( DCCXXXIII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. The denomination 733 for this year has been used since the early medieval period, when the Anno Domini calend ...

. Also the number of edges in the join of two cycle graphs, both of order 37 :1444 = 38², smallest

pandigital number In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 (one billion two hundred thirty four million five hundred sixty seven tho ...

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

:1446 = number of points on surface of octahedron with edgelength 19 :1447 =

happy number In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...

:1448 = number k such that phi(prime(k)) is a square :1449 =

Stella octangula number In mathematics, a stella octangula number is a figurate number based on the stella octangula, of the form .. The sequence of stella octangula numbers is :0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, ... Only two of these numbers are squar ...

:1450 = σ₂(34): sum of squares of divisors of 34 :1451 = Sophie Germain prime :1452 = first Zagreb index of the complete graph K₁₂ :1453 =

Sexy prime In number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and . The term "sexy prime" is a pun stemming from the Latin word for six: . If o ...

with 1459 :1454 = 3 × 22² + 2 = number of points on surface of square pyramid of side-length 22 :1455 = k such that geometric mean of phi(k) and sigma(k) is an integer :1457 = 2 × 27² − 1 =
twin square
: 1458 = maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×3⁶) :1459 = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181),

pierpont prime In number theory, a Pierpont prime is a prime number of the form 2^u\cdot 3^v + 1\, for some nonnegative integers and . That is, they are the prime numbers for which is 3-smooth. They are named after the mathematician James Pierpont, who use ...

:1460 = Nickname of the original " Doc Marten's" boots, released 1 April 1960 :1461 = number of partitions of 38 into prime power parts :1462 = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices :1463 = total number of parts in all partitions of 16 :1464 = rounded total surface area of a regular icosahedron with edge length 13 :1465 = 5- Knödel number :1469 = octahedral number, highly cototient number :1470 =

, sum of totient function for first 69 integers :1471 =

, centered heptagonal number :1473
cropped hexagone
:1476 = coreful perfect number :1477 = 7-Knödel number :1479 = number of planar partitions of 12 :1480 = sum of the first 29 primes :1481 = Sophie Germain prime :1482 = pronic number, number of unimodal compositions of 15 where the maximal part appears once :1483 = 39² - 39 + 1 = H₃₉ (the 39th Hogben number) :1484 = maximal number of regions the plane is divided into by drawing 39 circles :1485 = triangular number :1486 = number of strict solid partitions of 19 :1487 = safe prime :1488 = triangular matchstick number :1489 =

:1490 = tetranacci number :1491 = nonagonal number, Mertens function zero :1492 = Mertens function zero :1493 = Stern prime :1494 = sum of totient function for first 70 integers :1496 = square pyramidal number :1497 = skiponacci number :1498 = number of flat partitions of 41 :1499 = Sophie Germain prime,

1500 to 1599

:1500 = hypotenuse in three different Pythagorean triangles :1501 = centered pentagonal number :1502 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47 :1504 = primitive abundant number (

all of whose proper divisors are deficient numbers) :1507 = number of partitions of 32 that do not contain 1 as a part :1508 = heptagonal pyramidal number :1509 = pinwheel number : 1510 =

deficient number In number theory, a deficient number or defective number is a number ''n'' for which the sum of divisors of ''n'' is less than 2''n''. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than ''n''. For ex ...

odious number In number theory, an odious number is a positive integer that has an odd number of 1s in its binary expansion. In computer science, an odious number is said to have odd parity. Examples The first odious numbers are: Properties If a(n) denotes ...

:1511 = Sophie Germain prime, balanced prime :1512 = k such that geometric mean of phi(k) and sigma(k) is an integer :1513 = centered square number :1514 = sum of first 44 composite numbers :1517 = number of lattice points inside a circle of radius 22 :1518 = Mertens function zero :1519 = Mertens function zero :1520 = pentagonal number, Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition :1521 = 39², Mertens function zero, centered octagonal number, forms a Ruth–Aaron pair with 1520 under second definition :1522 = k such that 5 × 2^k - 1 is prime :1523 =

, Mertens function zero, safe prime, member of the Mian–Chowla sequence :1524 = Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer :1525 = heptagonal number, Mertens function zero :1526 = number of conjugacy classes in the alternating group A₂₇ :1527 = Mertens function zero :1528 = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21 :1529 = composite de Polignac number :1530 =

:1531 = prime number,

, Mertens function zero :1532 = Mertens function zero :1534 = number of achiral integer partitions of 50 :1535 =

Thabit number In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 \cdot 2^n - 1 for a non-negative integer ''n''. The first few Thabit numbers are: : 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 61 ...

:1536 = a common size of

microplate A microplate, also known as a microtiter plate (''Microtiter'' is a registered trademark in the United States, therefore it should not be used generically without attribution), microwell plate or multiwell, is a flat plate with multiple "wells" ...

, 3-smooth number (2⁹×3), number of threshold functions of exactly 4 variables :1537 = Keith number, Mertens function zero :1538 = number of surface points on a cube with edge-length 17 :1539 = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts :1540 = triangular number, hexagonal number, decagonal number, tetrahedral number :1541 =

:1543 = Mertens function zero :1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length :1546 = Mertens function zero :1547 = hexagonal pyramidal number :1548 = coreful perfect number :1549 = de Polignac prime :1552 = Number of partitions of 57 into prime parts :1556 = sum of the squares of the first nine primes :1557 = number of graphs with 8 nodes and 13 edges :1558 = number k such that k⁶⁴ + 1 is prime :1559 = Sophie Germain prime :1560 = pronic number :1561 = a

, number of series-reduced trees with 19 nodes :1562 = maximal number of regions the plane is divided into by drawing 40 circles :1564 = sum of totient function for first 71 integers :1565 =

\sqrt

and

1036+1173=47^2

:1566 = number k such that k⁶⁴ + 1 is prime :1567 = number of partitions of 24 with at least one distinct part :1568 =

:1569 = 2 × 28² + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28 :1570 = 2 × 28² + 2 = number of points on surface of tetrahedron with edgelength 28 :1571 = Honaker prime :1572 = member of the Mian–Chowla sequence :1575 = odd

, sum of the nontriangular numbers between successive triangular numbers, number of partitions of 24 :1578 = sum of first 45 composite numbers :1579 = number of partitions of 54 such that the smallest part is greater than or equal to number of parts :1580 = number of achiral integer partitions of 51 :1581 = number of edges in the hexagonal triangle T(31) :1583 = Sophie Germain prime :1584 = triangular matchstick number :1585 = Riordan number,

:1586 = area of the 23t
conjoined trapezoid
:1588 = sum of totient function for first 72 integers :1589 = composite de Polignac number :1590 = rounded volume of a regular icosahedron with edge length 9 :1591 = rounded volume of a regular octahedron with edge length 15 :1593 = sum of the first 30 primes :1595 = number of non-isomorphic set-systems of weight 10 :1596 = triangular number :1597 =

Fibonacci prime A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime. The first Fibonacci primes are : : 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, .... Known Fibonacci primes It is not known whet ...

, Markov prime,

:1598 = number of unimodular 2 × 2 matrices having all terms in :1599 = number of edges in the join of two cycle graphs, both of order 39

1600 to 1699

:1600 = 40², structured great rhombicosidodecahedral number, repdigit in base 7 (4444₇), street number on Pennsylvania Avenue of the

White House The White House is the official residence and workplace of the president of the United States. It is located at 1600 Pennsylvania Avenue NW in Washington, D.C., and has been the residence of every U.S. president since John Adams in 1800. ...

, length in meters of a common High School Track Event, perfect score on

SAT The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Schol ...

(except from 2005-2015) :1601 = Sophie Germain prime, Proth prime, the novel '' 1601 (Mark Twain)'' :1602 = number of points on surface of octahedron with edgelength 20 :1603 = number of partitions of 27 with nonnegative rank :1606 = enneagonal pyramidal number :1608 =

\sum_^ \sigma(k)

:1609
cropped hexagone
:1610 = number of strict partions of 43 :1611 = number of rational numbers which can be constructed from the set of integers between 1 and 51 :1617 = pentagonal number :1618 = centered heptagonal number :1619 =

palindromic prime In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such ...

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...

, safe prime :1620 = 809 + 811: sum of twin prime pair :1621 =

, pinwheel number :1624 = number of squares in the

Aztec diamond In combinatorial mathematics, an Aztec diamond of order ''n'' consists of all squares of a square lattice whose centers (''x'',''y'') satisfy , ''x'', + , ''y'', ≤ ''n''. Here ''n'' is a fixed integer, and the square lattice consists of unit s ...

of order 28 :1625 = centered square number :1626 = centered pentagonal number :1629 = rounded volume of a regular tetrahedron with edge length 24 :1630 = number k such that k^64 + 1 is prime :1633 = star number :1634 =

Narcissistic number In number theory, a narcissistic number 1 F_ : \mathbb \rightarrow \mathbb to be the following: : F_(n) = \sum_^ d_i^k. where k = \lfloor \log_ \rfloor + 1 is the number of digits in the number in base b, and : d_i = \frac is the value of each d ...

in base 10 :1636 = number of nonnegative solutions to x² + y² ≤ 45² :1637 = prime island: least prime whose adjacent primes are exactly 30 apart :1638 =

harmonic divisor number In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are: : 1, 6, 2 ...

, 5 × 2¹⁶³⁸ - 1 is prime :1639 = nonagonal number :1640 = pronic number :1641 = 41² - 41 + 1 = H₄₁ (the 41st Hogben number) :1642 = maximal number of regions the plane is divided into by drawing 41 circles :1643 = sum of first 46 composite numbers :1644 = 821 + 823: sum of twin prime pair :1645 = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection :1646 = number of graphs with 8 nodes and 14 edges :1647 and 1648 are both divisible by cubes :1648 = number of partitions of 34³ into distinct cubes :1649 = highly cototient number, Leyland number :1650 = number of cards to build an 33-tier house of cards :1651 = heptagonal number :1652 = number of partitions of 29 into a prime number of parts :1653 = triangular number, hexagonal number, number of lattice points inside a circle of radius 23 :1654 = number of partitions of 42 into divisors of 42 :1655 = rounded volume of a regular dodecahedron with edge length 6 :1656 = 827 + 829: sum of twin prime pair :1657 =

cuban prime A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''. First series This is the first of these equations: :p = \frac,\ x = ...

, prime of the form 2p-1 :1658 = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations :1659 = number of rational numbers which can be constructed from the set of integers between 1 and 52 :1660 = sum of totient function for first 73 integers :1661 = a number with only palindromic divisors :1662 = number of partitions of 49 into pairwise relatively prime parts :1663 = a prime number and 5¹⁶⁶³ - 4¹⁶⁶³ is a 1163-digit prime number :1664 = k such that k, k+1 and k+2 are sums of 2 squares :1665 = centered tetrahedral number :1666 = largest efficient

(each symbol occurs exactly once) :1667 = 228 + 1439 and the 228th prime is 1439 :1668 = number of partitions of 33 into parts all relatively prime to 33 :1669 =

, smallest prime with a gap of exactly 24 to the next prime :1670 = number of compositions of 12 such that at least two adjacent parts are equal :1671 divides the sum of the first 1671 composite numbers :1672 = 41² - 2², the only way to express 1672 as a difference of prime squares :1673 = RMS number :1674 = k such that geometric mean of phi(k) and sigma(k) is an integer :1675 = Kin number :1676 = number of partitions of 34 into parts each of which is used a different number of times :1677 = 41² - 3², the only way to express 1677 as a difference of prime squares :1678 = n such that n³² + 1 is prime :1679 = highly cototient number, semiprime (23 × 73, see also Arecibo message), number of parts in all partitions of 32 into distinct parts :1680 = highly composite number, number of edges in the join of two cycle graphs, both of order 40 :1681 = 41², smallest number yielded by the formula ''n''² + ''n'' + 41 that is not a prime; centered octagonal number :1682 = and 1683 is a member of a Ruth–Aaron pair (first definition) :1683 = triangular matchstick number :1684 =

:1685 = 5- Knödel number :1686 =

\sum_^ \sigma(k)

:1687 = 7-Knödel number :1688 = number of finite connected sets of positive integers greater than one with least common multiple 72 :1689 =

9!!\sum_^ \frac

:1690 = number of compositions of 14 into powers of 2 :1691 = the same upside down, which makes it a strobogrammatic number :1692 = coreful perfect number :1693 = smallest prime > 41². :1694 = number of unimodular 2 × 2 matrices having all terms in :1695 =

of ''n'' × ''n'' normal

and ''n''-queens problem for ''n'' = 15. Number of partitions of 58 into prime parts :1696 = sum of totient function for first 74 integers :1697 = Friedlander-Iwaniec prime :1698 = number of rooted trees with 47 vertices in which vertices at the same level have the same degree :1699 = number of rooted trees with 48 vertices in which vertices at the same level have the same degree

1700 to 1799

:1700 = σ₂(39): sum of squares of divisors of 39 : 1701 =

\left\

, decagonal number, hull number of the U.S.S. Enterprise on ''

Star Trek ''Star Trek'' is an American science fiction media franchise created by Gene Roddenberry, which began with the eponymous 1960s television series and quickly became a worldwide pop-culture phenomenon. The franchise has expanded into vari ...

'' :1702 = palindromic in 3 consecutive bases: 898₁₄, 787₁₅, 6A6₁₆ :1703 = 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1 :1704 = sum of the squares of the parts in the partitions of 18 into two distinct parts :1705 =

tribonacci number In mathematics, the Fibonacci numbers form a sequence defined recursion, recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibo ...

:1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4 :1707 = number of partitions of 30 in which the number of parts divides 30 :1708 = 2² × 7 × 61 a number whose product of prime indices 1 × 1 × 4 × 18 is divisible by its sum of prime factors 2 + 2 + 7 + 61 :1709 = first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773 :1710 = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts :1711 = triangular number,

:1712 = number of irredundant sets in the 29-cocktail party graph :1713 = number of aperiodic rooted trees with 12 nodes :1714 = number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of a
3 × 6 grid of squares
:1715 = k such that geometric mean of phi(k) and sigma(k) is an integer :1716 = 857 + 859: sum of twin prime pair :1717 = pentagonal number :1718 =

\sum_ \binom

:1719 = composite de Polignac number :1720 = sum of the first 31 primes :1721 = twin prime; number of squares between 42² and 42⁴. :1722 = Giuga number, pronic number :1723 =

:1724 = maximal number of regions the plane is divided into by drawing 42 circles :1725 = 47² - 22² = (prime(15))² - (nonprime(15))² :1726 = number of partitions of 44 into distinct and relatively prime parts :1727 = area of the 24t
conjoined trapezoid
: 1728 = the quantity expressed as 1000 in

duodecimal The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead wri ...

, that is, the cube of twelve (called a

great gross 1728 is the natural number following 1727 and preceding 1729. 1728 is a dozen gross, one great gross (or grand gross). It is the number of cubic inches in a cubic foot. It is also the number of daily chants of the Hare Krishna mantra by a Hare ...

), and so, the number of cubic inches in a cubic

foot The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg made ...

, palindromic in base 11 (1331₁₁) and 23 (363₂₃) : 1729 =

taxicab number In mathematics, the ''n''th taxicab number, typically denoted Ta(''n'') or Taxicab(''n''), also called the ''n''th Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two ''positive'' integer cubes in ...

, Carmichael number, Zeisel number, centered cube number,

Hardy–Ramanujan number 1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian ma ...

. In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical ''

Hair Hair is a protein filament that grows from follicles found in the dermis. Hair is one of the defining characteristics of mammals. The human body, apart from areas of glabrous skin, is covered in follicles which produce thick terminal and f ...

'' closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36. :1730 = 3 × 24² + 2 = number of points on surface of square pyramid of side-length 24 :1731 = k such that geometric mean of phi(k) and sigma(k) is an integer :1732 =

\sum_^5 \binom^k

:1733 =

, palindromic in bases 3, 18, 19. :1734 = surface area of a cube of edge length 17 :1735 = number of partitions of 55 such that the smallest part is greater than or equal to number of parts :1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18 :1737 = pinwheel number :1738 = number of achiral integer partitions of 52 :1739 = number of 1s in all partitions of 30 into odd parts :1740 = number of squares in the

of order 29 :1741 =

, centered square number :1742
number of regions
the plane is divided into by 30 ellipses :1743 =

of the

D(3,21) :1744 = k such that k, k+1 and k+2 are sums of 2 squares :1745 = 5- Knödel number :1746 = number of unit-distance graphs on 8 nodes :1747 = balanced prime :1748 = number of partitions of 55 into distinct parts in which the number of parts divides 55 :1749 = number of integer partitions of 33 with no part dividing all the others :1750 = hypotenuse in three different Pythagorean triangles :1751
cropped hexagone
:1752 = 79² - 67², the only way to express 1752 as a difference of prime squares :1753 = balanced prime :1754 = k such that 5*2^k - 1 is prime :1755 = number of integer partitions of 50 whose augmented differences are distinct :1756 = centered pentagonal number :1758 =

\sum_^ \sigma(k)

:1759 = de Polignac prime :1760 = the number of

yard The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactly 0.914 ...

s in a mile :1761 = k such that k, k+1 and k+2 are products of two primes :1762 = number of binary sequences of length 12 an
curling number 2
:1763 = number of edges in the join of two cycle graphs, both of order 41 :1764 = 42² :1765 = number of stacks, or planar partitions of 15 :1766 = number of points on surface of octahedron with edgelength 21 :1767 = σ(28²) = σ(35²) :1768 = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation :1769 = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts :1770 = triangular number, hexagonal number, Seventeen Seventy, town in Australia :1771 = tetrahedral number :1772 = centered heptagonal number, sum of totient function for first 76 integers :1773 = number of words of length 5 over the alphabet such that no two even numbers appear consecutively :1774 = number of rooted identity trees with 15 nodes and 5 leaves :1775 =

\sum_prime(i)\cdot(2\cdot i-1)

: sum of piles of first 10 primes :1776
square star number
:1777 = smallest prime > 42². :1778 = least k >= 1 such that the remainder when 6^k is divided by k is 22 :1779 = number of achiral integer partitions of 53 :1780 = number of lattice paths from (0, 0) to (7, 7) using E (1, 0) and N (0, 1) as steps that horizontally cross the diagonal y = x with even many times :1781 = the first 1781 digits of e form a prime :1782 = heptagonal number :1783 = de Polignac prime :1784 = number of subsets of such that every pair of distinct elements has a different quotient :1785 = square pyramidal number, triangular matchstick number :1786 =

:1787 =

, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191) :1788 = Euler transform of -1, -2, ..., -34 :1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa) :1790 = number of partitions of 50 into pairwise relatively prime parts :1791 = largest natural number that cannot be expressed as a sum of at most four

s. :1792 =

Granville number In mathematics, specifically number theory, Granville numbers, also known as \mathcal-perfect numbers, are an extension of the perfect numbers. The Granville set In 1996, Andrew Granville proposed the following construction of a set \mathcal: :Le ...

:1793 = number of lattice points inside a circle of radius 24 :1794 = nonagonal number, number of partitions of 33 that do not contain 1 as a part :1795 = number of heptagons with perimeter 38 :1796 = k such that geometric mean of phi(k) and sigma(k) is an integer :1797 = number k such that phi(prime(k)) is a square :1798 = 2 × 29 × 31 = 10₂ × 11101₂ × 11111₂, which yield zero when the prime factors are xored together :1799 = 2 × 30² − 1 =
twin square

1800 to 1899

:1800 = pentagonal pyramidal number,

, also, in da Ponte's ''

Don Giovanni ''Don Giovanni'' (; K. 527; Vienna (1788) title: , literally ''The Rake Punished, or Don Giovanni'') is an opera in two acts with music by Wolfgang Amadeus Mozart to an Italian libretto by Lorenzo Da Ponte. Its subject is a centuries-old Spanis ...

'', the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally :1801 =

, sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227) :1802 = 2 × 30² + 2 = number of points on surface of tetrahedron with edgelength 30, number of partitions of 30 such that the number of odd parts is a part :1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion) :1804 = number k such that k^64 + 1 is prime :1805 = number of squares between 43² and 43⁴. :1806 = pronic number, product of first four terms of

Sylvester's sequence In number theory, Sylvester's sequence is an integer sequence in which each term of the sequence is the product of the previous terms, plus one. The first few terms of the sequence are :2, 3, 7, 43, 1807, 3263443, 10650056950807, 11342371305542184 ...

primary pseudoperfect number In mathematics, and particularly in number theory, ''N'' is a primary pseudoperfect number if it satisfies the Egyptian fraction equation :\frac + \sum_\frac = 1, where the sum is over only the prime divisors of ''N''. Properties Equivalentl ...

, only number for which ''n'' equals the denominator of the ''n''th

Bernoulli number In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...

Schröder number In mathematics, the Schröder number S_n, also called a ''large Schröder number'' or ''big Schröder number'', describes the number of lattice paths from the southwest corner (0,0) of an n \times n grid to the northeast corner (n,n), using only ...

:1807 = fifth term of Sylvester's sequence :1808 = maximal number of regions the plane is divided into by drawing 43 circles :1809 = sum of first 17

s :1810 =

\sum_^4 \binom^4

:1811 = Sophie Germain prime :1812 = n such that n³² + 1 is prime :1813 = number of

with 26 cells, symmetric about two orthogonal axes :1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six :1815 = polygonal chain number

\#(P^3_)

:1816 = number of strict partions of 44 :1817 = total number of prime parts in all partitions of 20 :1818 = n such that n³² + 1 is prime :1819 = sum of the first 32 primes, minus 32 :1820 = pentagonal number, pentatope number, number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing :1821 = member of the Mian–Chowla sequence :1822 = number of integer partitions of 43 whose distinct parts are connected :1823 =

, safe prime :1824 = 43² - 5², the only way to express 1824 as a difference of prime squares :1825 =

:1826 = decagonal pyramidal number :1827 =

:1828 =

meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges. Meander Given a fixed oriented lin ...

open meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges. Meander Given a fixed oriented li ...

, appears twice in the first 10 decimal digits of '' e'' :1829 = composite de Polignac number :1830 = triangular number :1831 = smallest prime with a gap of exactly 16 to next prime (1847) :1832 = sum of totient function for first 77 integers :1833 = number of atoms in a decahedron with 13 shells :1834 = octahedral number, sum of the cubes of the first five primes :1835 = absolute value of numerator of

D_6^

:1836 = factor by which a

proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

is more massive than an

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...

:1837 = star number :1838 = number of unimodular 2 × 2 matrices having all terms in :1839 =

\rfloor

:1840 = 43² - 3², the only way to express 1840 as a difference of prime squares :1841 = Mertens function zero :1842 = number of unlabeled rooted trees with 11 nodes :1843 = Mertens function zero :1844 = Mertens function zero :1845 = Mertens function zero :1846 = sum of first 49 composite numbers :1847 =

:1848 = number of edges in the join of two cycle graphs, both of order 42 :1849 = 43², palindromic in base 6 (= 12321₆), centered octagonal number :1850 = Number of partitions of 59 into prime parts :1851 = sum of the first 32 primes :1852 = number of quantales on 5 elements, up to isomorphism :1853 = Mertens function zero :1854 = Mertens function zero :1855 = rencontres number: number of permutations of with exactly one fixed point :1856 = sum of totient function for first 78 integers :1857 = Mertens function zero, pinwheel number :1858 = number of 14-carbon alkanes C₁₄H₃₀ ignoring stereoisomers :1859 = composite de Polignac number :1860 = number of squares in the

of order 30 :1861 = centered square number, Mertens function zero :1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition :1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition :1864 = Mertens function zero,

\frac

is a prime :1865 = 12345₆: Largest

senary A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two con ...

metadrome (number with digits in strict ascending order in base 6) :1866 = Mertens function zero, number of plane partitions of 16 with at most two rows :1867 = prime de Polignac number :1868 = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^ :1869 = Hultman number: S_H(7, 4) :1870 = decagonal number :1871 = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879) :1872 = first Zagreb index of the complete graph K₁₃ :1873 = number of Narayana's cows and calves after 21 years :1874 = area of the 25t
conjoined trapezoid
:1875 = 50² - 25² :1876 = number k such that k^64 + 1 is prime :1877 = number of partitions of 39 where 39 divides the product of the parts :1878 = n such that n³² + 1 is prime :1879 = a prime with square index :1880 = the 10th element of the self convolution of

Lucas numbers The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci nu ...

:1881 = tricapped prism number :1882 = number of

linearly separable In Euclidean geometry, linear separability is a property of two sets of point (geometry), points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of poi ...

boolean functions In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

in 4 variables :1883 = number of conjugacy classes in the alternating group A₂₈ :1884 = k such that 5*2^k - 1 is prime :1885 = Zeisel number :1886 = number of partitions of 6⁴ into fourth powers :1887 = number of edges in the hexagonal triangle T(34) :1888 = primitive abundant number (

all of whose proper divisors are deficient numbers) :1889 = Sophie Germain prime, highly cototient number :1890 = triangular matchstick number :1891 = triangular number, hexagonal number, centered pentagonal number,

:1892 = pronic number :1893 = 44² - 44 + 1 = H₄₄ (the 44th Hogben number) :1894 = maximal number of regions the plane is divided into by drawing 44 circles :1895 = Stern-Jacobsthal number :1896 = member of the Mian-Chowla sequence :1897 = member of Padovan sequence, number of triangle-free graphs on 9 vertices :1898 = smallest multiple of n whose digits sum to 26 :1899
cropped hexagone

1900 to 1999

:1900 = number of primes <= 2¹⁴. Also ''1900'' (film) or ''Novecento'', 1976 movie.

1900 As of March 1 ( O.S. February 17), when the Julian calendar acknowledged a leap day and the Gregorian calendar did not, the Julian calendar fell one day further behind, bringing the difference to 13 days until February 28 ( O.S. February 15), 2 ...

was the year

Thorold Gosset John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher, and ...

introduced his list of

semiregular polytope In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-transitive and has all its facets being regular polytopes. E.L. Elte compiled a longer list in 1912 as ''The Semiregular Polyt ...

s; it is also the year

Max Brückner Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German geometer, known for his collection of polyhedral models. Education and career Brückner was born in Hartau, in the Kingdom of Saxony, a town that is now part of Zittau, ...

published his study of polyhedral models, including stellations of the

icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...

, such as the novel

final stellation of the icosahedron In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three inter ...

. :1901 = Sophie Germain prime,

:1902 = number of symmetric plane partitions of 27 :1903 = generalized catalan number :1904 = number of flat partitions of 43 :1905 =

:1906 = number n such that 3ⁿ - 8 is prime :1907 = safe prime, balanced prime :1908 = coreful perfect number :1909 =

hyperperfect number In mathematics, a ''k''-hyperperfect number is a natural number ''n'' for which the equality ''n'' = 1 + ''k''(''σ''(''n'') − ''n'' − 1) holds, where ''σ''(''n'') is the divisor function (i.e., the sum of all positive divisors of ''n ...

:1910 = number of compositions of 13 having exactly one fixed point :1911 = heptagonal pyramidal number :1912 = size of 6th maximum raising after one blind in pot-limit poker :1913 =

, Honaker prime :1914 = number of bipartite partitions of 12 white objects and 3 black ones :1915 = number of nonisomorphic semigroups of order 5 :1916 = sum of first 50 composite numbers :1917 = number of partitions of 51 into pairwise relatively prime parts :1918 = heptagonal number :1919 = smallest number with reciprocal of period length 36 in base 10 :1920 = sum of the nontriangular numbers between successive triangular numbers :1921 = 4-dimensional centered cube number :1922 = Area of a square with diagonal 62 :1923 = 2 × 31² + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31 :1924 = 2 × 31² + 2 = number of points on surface of tetrahedron with edgelength 31 :1925 = number of ways to write 24 as an orderless product of orderless sums :1926 = pentagonal number :1927 = 2¹¹ - 11² :1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways) :1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected :1930 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53 :1931 = Sophie Germain prime :1932 = number of partitions of 40 into prime power parts :1933 = centered heptagonal number, Honaker prime :1934 = sum of totient function for first 79 integers :1935 = number of edges in the join of two cycle graphs, both of order 43 :1936 = 44², 18-gonal number, 324-gonal number. :1937 = number of chiral n-ominoes in 12-space, one cell labeled :1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22 :1939 = 7-Knödel number :1940 = the Mahonian number: T(8, 9) :1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines :1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes :1943 = largest number not the sum of distinct tetradecagonal numbers :1944 = 3-smooth number (2³×3⁵),

:1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime :1946 = number of surface points on a cube with edge-length 19 :1947 = k such that 5·2^k + 1 is a prime factor of a Fermat number 2^{2^m} + 1 for some m :1948 = number of strict solid partitions of 20 :1949 = smallest prime > 44². :1950 =

1 \cdot 2 \cdot 3 + 4 \cdot 5 \cdot 6 + 7 \cdot 8 \cdot 9 + 10 \cdot 11 \cdot 12

, largest number not the sum of distinct pentadecagonal numbers :1951 = cuban prime :1952 = number of covers of :1953 = triangular number :1956 = number of sum-free subsets of :1955 = number of partitions of 25 with at least one distinct part :1956 = nonagonal number :1957 =

\sum_^ \frac

= total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set :1958 = number of partitions of 25 :1959 = Heptanacci-Lucas number :1960 = number of parts in all partitions of 33 into distinct parts :1961 = number of lattice points inside a circle of radius 25 :1962 = number of edges in the join of the complete graph K₃₆ and the cycle graph C₃₆ :1963! - 1 is prime :1964 = number of linear forests of planted planar trees with 8 nodes :1965 = total number of parts in all partitions of 17 :1966 = sum of totient function for first 80 integers :1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem :σ(1968) = σ(1967) + σ(1966) :1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize :1970 = number of compositions of two types of 9 having no even parts :1971 =

3^7-6^3

:1972 = n such that

\frac

is prime : 1973 = Sophie Germain prime, Leonardo prime :1974 = number of binary vectors of length 17 containing no singletons :1975 = number of partitions of 28 with nonnegative rank :1976 =

:1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons :1978 = n such that n , (3ⁿ + 5) :1979 = number of squares between 45² and 45⁴. :1980 = pronic number :1981 = pinwheel number :1982 = maximal number of regions the plane is divided into by drawing 45 circles :1983 = skiponacci number :1984 = 11111000000 in

, see also:

1984 (disambiguation) 1984 was a leap year starting on Sunday of the Gregorian calendar, the 1984th year of the Common Era (CE) and Anno Domini (AD) designations, the 984th year of the 2nd millennium, the 84th year of the 20th century, and the 5th year of the 1980s de ...

:1985 =

:1986 = number of ways to write 25 as an orderless product of orderless sums :

1987 File:1987 Events Collage.png, From top left, clockwise: The MS Herald of Free Enterprise capsizes after leaving the Port of Zeebrugge in Belgium, killing 193; Northwest Airlines Flight 255 crashes after takeoff from Detroit Metropolitan Airport, k ...

= 300th

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

:1988 = sum of the first 33 primes :1989 = number of 9-step mappings with 4 inputs :1990 =

:1991 = the 46th Gullwing number, palindromic composite number with only palindromic prime factors :1992 = number of nonisomorphic sets of nonempty subsets of a 4-set :1993 = a number with the property that 4¹⁹⁹³ - 3¹⁹⁹³ is prime, number of partitions of 30 into a prime number of parts :1994 = Glaisher's function W(37) :1995 = number of unlabeled graphs on 9 vertices with independence number 6 :1996 = a number with the property that (1996! + 3)/3 is prime :1997 =

\sum_^

:1998 = triangular matchstick number :1999 =

number of regular forms in a

myriagram The myriagram (french: myriagramme) is a former France, French and International System of Units, metric unit of mass equal to 10,000 grams (''myriad'' being the Greek word for ten thousand). Although never as widely used as the kilogram, the myri ...

Prime numbers

There are 135

s between 1000 and 2000: :1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999

References

{{Authority control Integers