600 (six hundred) 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 599 and preceding 601.

Mathematical properties

Six hundred is a

composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...

, an

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 ...

, 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 ...

and a

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 ...

Credit and cars

* In the United States, a

credit score A credit score is a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual. A credit score is primarily based on a credit report, information typically sourced from credit bu ...

of 600 or below is considered poor, limiting available credit at a normal interest rate. *

NASCAR The National Association for Stock Car Auto Racing, LLC (NASCAR) is an American auto racing sanctioning and operating company that is best known for stock car racing. The privately owned company was founded by Bill France Sr. in 1948, and hi ...

runs 600 advertised miles in the

Coca-Cola 600 The Coca-Cola 600, originally the World 600, is an annual NASCAR Cup Series points race held at the Charlotte Motor Speedway in Concord, North Carolina, on a Sunday during Memorial Day weekend. The first race, held in 1960, was also the first on ...

, its longest race. * The

Fiat 600 The Fiat 600 ( it, Seicento, ) is a rear-engine, water-cooled city car, manufactured and marketed by Fiat from 1955 to 1969 — offered in two-door fastback sedan and four-door Multipla mini MPV body styles. Measuring only long, its all-n ...

is a car, the

SEAT 600 The SEAT 600 is a city car made in Spain by SEAT from May 1957 until August 1973 under licence from Fiat. It helped to start the Spanish miracle (economic boom of 1959–1973) that came at the end of the slow recovery from the Spanish Civil War. ...

its Spanish version.

Integers from 601 to 699

600s

* 601 = prime number,

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 th ...

* 602 = 2 × 7 × 43,

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...

, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for

Phoenix, AZ Phoenix ( ; nv, Hoozdo; es, Fénix or , yuf-x-wal, Banyà:nyuwá) is the capital and most populous city of the U.S. state of Arizona Arizona ( ; nv, Hoozdo Hahoodzo ; ood, Alĭ ṣonak ) is a state in the Southwestern United Stat ...

along with 480 and

623 Year 623 (Roman numerals, DCXXIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. The denomination 623 for this year has been used since the early medieval period, when the Anno Domini calen ...

* 603 = 3² × 67,

, Riordan number,

area code A telephone numbering plan is a type of numbering scheme used in telecommunication to assign telephone numbers to subscriber telephones or other telephony endpoints. Telephone numbers are the addresses of participants in a telephone network, rea ...

for

New Hampshire New Hampshire is a U.S. state, state in the New England region of the northeastern United States. It is bordered by Massachusetts to the south, Vermont to the west, Maine and the Gulf of Maine to the east, and the Canadian province of Quebec t ...

* 604 = 2² × 151,

, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) * 605 = 5 × 11²,

, sum of the nontriangular numbers between the two successive

triangular numbers 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 i ...

55 and 66, number of non-isomorphic set-systems of weight 9. * 606 = 2 × 3 × 101,

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 ...

, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), admirable number * 607 – prime number, sum of three consecutive primes (197 + 199 + 211),

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 ...

(607) = 0, balanced prime, strictly non-palindromic number,

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 * 608 = 2⁵ × 19,

(608) = 0,

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 ...

number of regions formed by drawing the line segments connecting any two of the perimeter points of a 3 times 4 grid of squares.
* 609 = 3 × 7 × 29,

, strobogrammatic number

610s

* 610 = 2 × 5 × 61, sphenic number,

Fibonacci number In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...

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 ...

. Also a kind of telephone wall socket used in

Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, sma ...

. * 611 = 13 × 47, sum of the three standard board sizes in Go (9² + 13² + 19²), the 611th

tribonacci 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 seque ...

is prime * 612 = 2² × 3² × 17,

, Zuckerman number , area code for

Minneapolis, MN Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with list of lakes in Minneapolis, thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. ...

* 613 = prime number, first number of

prime triple In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form or . With the exceptions of and , this is the closest possible grouping of ...

(''p'', ''p'' + 4, ''p'' + 6), middle number of

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 ...

triple (''p'' − 6, ''p'', ''p'' + 6). Geometrical numbers:

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 ...

with 18 per side, circular number of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a

lucky number 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 ...

, index of prime Lucas number. ** In

Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...

the number 613 is very significant, as its metaphysics, the

Kabbalah Kabbalah ( he, קַבָּלָה ''Qabbālā'', literally "reception, tradition") is an esoteric method, discipline and Jewish theology, school of thought in Jewish mysticism. A traditional Kabbalist is called a Mekubbal ( ''Məqūbbāl'' "rece ...

, views every complete entity as divisible into 613 parts: 613 parts of every

Sefirah Sefirot (; he, סְפִירוֹת, translit=Səfīrōt, Tiberian: '), meaning '' emanations'', are the 10 attributes/emanations in Kabbalah, through which Ein Sof (The Infinite) reveals itself and continuously creates both the physical realm an ...

; 613 mitzvot, or divine Commandments in the

Torah The Torah (; hbo, ''Tōrā'', "Instruction", "Teaching" or "Law") is the compilation of the first five books of the Hebrew Bible, namely the books of Genesis, Exodus, Leviticus, Numbers and Deuteronomy. In that sense, Torah means the s ...

; 613 parts of the human body. ** The number 613 hangs from the rafters at

Madison Square Garden Madison Square Garden, colloquially known as The Garden or by its initials MSG, is a multi-purpose indoor arena in New York City. It is located in Midtown Manhattan between Seventh and Eighth avenues from 31st to 33rd Street, above Pennsylva ...

in honor of

New York Knicks The New York Knickerbockers, shortened and more commonly referred to as the New York Knicks, are an American professional basketball team based in the New York City borough of Manhattan. The Knicks compete in the National Basketball Associat ...

coach

Red Holzman William "Red" Holzman (August 10, 1920 – November 13, 1998) was an American professional basketball player and coach. He is best known as the head coach of the New York Knicks of the National Basketball Association (NBA) from 1967 to ...

's 613 victories. * 614 = 2 × 307,

, 2-Knödel number. According to Rabbi

Emil Fackenheim Emil Ludwig Fackenheim (22 June 1916 – 18 September 2003) was a Jewish philosopher and Reform rabbi. Born in Halle, Germany, he was arrested by Nazis on the night of 9 November 1938, known as Kristallnacht. Briefly interned at the Sachsenhause ...

, the number of Commandments in Judaism should be 614 rather than the traditional 613. * 615 = 3 × 5 × 41,

* 616 = 2³ × 7 × 11,

Padovan number 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 ...

, balanced number, an alternative value for the Number of the Beast (more commonly accepted to be

666 666 may refer to: * 666 (number) * 666 BC, a year * AD 666, a year * The number of the beast, a reference in the Book of Revelation in the New Testament Places * 666 Desdemona, a minor planet in the asteroid belt * U.S. Route 666, an America ...

). * 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137),

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 ...

Eisenstein prime In mathematics, an Eisenstein prime is an Eisenstein integer : z = a + b\,\omega, \quad \text \quad \omega = e^, that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...

with no imaginary part, number of compositions of 17 into distinct parts, prime index prime, index of prime Lucas number **

Area code 617 Area codes 617 and 857 are the North American area codes serving Boston and several surrounding communities in Massachusetts—such as Brookline, Cambridge, Newton and Quincy ( LATA code 128). The main area code, 617, was one of the orig ...

, a telephone area code covering the metropolitan Boston area. * 618 = 2 × 3 × 103,

, admirable number. * 619 = prime number, strobogrammatic prime, alternating factorial

620s

* 620 = 2² × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97). The sum of the first 620 primes is itself prime. * 621 = 3³ × 23, Harshad number, the discriminant of a totally real cubic field * 622 = 2 × 311,

, Fine number. Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree It is also the standard diameter of modern road

bicycle wheel A bicycle wheel is a wheel, most commonly a wire wheel, designed for a bicycle. A pair is often called a wheelset, especially in the context of ready built "off the shelf" performance-oriented wheels. Bicycle wheels are typically designed ...

s (622 mm, from hook bead to hook bead) * 623 = 7 × 89, number of partitions of 23 into an even number of parts * 624 = 2⁴ × 3 × 13 = J₄(5), sum of a twin prime (311 + 313), Harshad number, Zuckerman number * 625 = 25² = 5⁴, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103),

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 ...

, 1-

automorphic number In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself. Definition and properties Given a number base b, a natura ...

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 ...

since 625 = 5⁶⁻² * 626 = 2 × 313,

, 2-Knödel number. Stitch's experiment number. * 627 = 3 × 11 × 19, sphenic number, number of integer

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 20,

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 ...

* 628 = 2² × 157,

, totient sum for first 45 integers * 629 = 17 × 37,

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 ...

, number of diagonals in a 37-gon

630s

* 630 = 2 × 3² × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113),

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 ...

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 ...

sparsely totient number In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, ''n'', is sparsely totient if for all ''m'' > ''n'', :\varphi(m)>\varphi(n) where \varphi is Euler's totient function. The first few sparsely toti ...

, Harshad number, balanced number * 631 =

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 = ...

number,

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 ...

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 ...

, Chen prime, lazy caterer number * 632 = 2³ × 79,

refactorable number A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as : 1, 2, 8, 9, 12, 18, ...

, number of 13-bead necklaces with 2 colors * 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223),

Blum integer In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/tal ...

; also, in the title of the movie ''

633 Squadron ''633 Squadron'' is a 1964 British / American war film directed by Walter Grauman and starring Cliff Robertson, George Chakiris, and Maria Perschy. The plot, which involves the exploits of a fictional World War II British bomber squadron, wa ...

'' * 634 = 2 × 317,

, Smith number * 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts ** "Project 635", the Irtysh River diversion project in China involving a

dam A dam is a barrier that stops or restricts the flow of surface water or underground streams. Reservoirs created by dams not only suppress floods but also provide water for activities such as irrigation, human consumption, industrial use ...

and a

canal Canals or artificial waterways are waterways or engineered channels built for drainage management (e.g. flood control and irrigation) or for conveyancing water transport vehicles (e.g. water taxi). They carry free, calm surface flow un ...

. * 636 = 2² × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number, Mertens function(636) = 0 * 637 = 7² × 13, Mertens function(637) = 0,

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 ...

* 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167),

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 ...

* 639 = 3² × 71, sum of the first twenty primes, also

ISO 639 ISO 639 is a set of standards by the International Organization for Standardization that is concerned with representation of names for languages and language groups. It was also the name of the original standard, approved in 1967 (as ''ISO 639/R ...

is the

ISO ISO is the most common abbreviation for the International Organization for Standardization. ISO or Iso may also refer to: Business and finance * Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007 * Iso ...

's standard for codes for the representation of

language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of met ...

640s

* 640 = 2⁷ × 5,

, hexadecagonal number, number of 1's in all partitions of 24 into odd parts, number of acres in a square mile * 641 = prime number,

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 + ...

, factor of 4294967297 (the smallest nonprime

Fermat number In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 42949672 ...

), Chen prime, Eisenstein prime with no imaginary part,

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 ...

* 642 = 2 × 3 × 107 = 1⁴ + 2⁴ + 5⁴,

, admirable number * 643 = prime number, largest prime factor of 123456 * 644 = 2² × 7 × 23,

Perrin number In mathematics, the Perrin numbers are defined by the recurrence relation : for , with initial values :. The sequence of Perrin numbers starts with : 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, ... The number of different maxima ...

, Harshad number, common

umask In computing, umask is a command that determines the settings of a mask that controls how file permissions are set for newly created files. It may also affect how the file permissions are changed explicitly. is also a function that sets the ma ...

, admirable number * 645 = 3 × 5 × 43, sphenic number,

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 ...

, Smith 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''− ...

to base 2, Harshad number * 646 = 2 × 17 × 19, sphenic number, also

ISO 646 ISO/IEC 646 is a set of ISO/IEC standards, described as ''Information technology — ISO 7-bit coded character set for information interchange'' and developed in cooperation with ASCII at least since 1964. Since its first edition in ...

is the ISO's standard for international 7-bit variants of

ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...

, number of permutations of length 7 without rising or falling successions * 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3⁶⁴⁷ - 2⁶⁴⁷ is prime * 648 = 2³ × 3⁴
A331452(7, 1)
Harshad number,

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 ...

, area of a square with diagonal 36 * 649 = 11 × 59,

650s

* 650 = 2 × 5² × 13, primitive abundant number, square pyramidal number, pronic number,

, totient sum for first 46 integers; (other fields) the number of seats in the

House of Commons of the United Kingdom The House of Commons is the lower house of the Parliament of the United Kingdom. Like the upper house, the House of Lords, it meets in the Palace of Westminster in London, England. The House of Commons is an elected body consisting of 650 me ...

, admirable number * 651 = 3 × 7 × 31, sphenic number,

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 ...

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

* 652 = 2² × 163, maximal number of regions by drawing 26 circles * 653 = prime number, Sophie Germain prime, balanced prime, Chen prime, Eisenstein prime with no imaginary part * 654 = 2 × 3 × 109, sphenic number,

, Smith number, admirable number * 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid * 656 = 2⁴ × 41 =

\lfloor \frac \rfloor

. In

, 656 is the number of times that

Jerusalem Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...

is mentioned in the

Hebrew Bible The Hebrew Bible or Tanakh (;"Tanach"
''Random House Webster's Unabridged Dictionary''. Hebrew: ''Tān ...

Old Testament The Old Testament (often abbreviated OT) is the first division of the Christian biblical canon, which is based primarily upon the 24 books of the Hebrew Bible or Tanakh, a collection of ancient religious Hebrew writings by the Israelites. The ...

. * 657 = 3² × 73, the largest known number not of the form ''a''²+''s'' with ''s'' a

semiprime In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime nu ...

* 658 = 2 × 7 × 47,

untouchable number An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...

* 659 = prime number, Sophie Germain prime, sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Chen prime, Mertens function sets new low of −10 which stands until 661, highly cototient number, Eisenstein prime with no imaginary part, strictly non-palindromic number

660s

* 660 = 2² × 3 × 5 × 11 **Sum of four consecutive primes (157 + 163 + 167 + 173). **Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127). **Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101). **Sparsely totient number. **Sum of 11th row when writing the natural numbers as a triangle. **

. * 661 = prime number **Sum of three consecutive primes (211 + 223 + 227). **Mertens function sets new low of −11 which stands until 665. **

Pentagram A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle arou ...

number of the form

5n^-5n+1

. **

Hexagram , can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram ( Greek language, Greek) or sexagram (Latin) is a six-pointed ...

number of the form

6n^-6n+1

i.e. a

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 ...

. * 662 = 2 × 331,

, member of

Mian–Chowla sequence In mathematics, the Mian–Chowla sequence is an integer sequence defined 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 distinct, for ...

* 663 = 3 × 13 × 17,

, Smith number * 664 = 2³ × 83,

, number of knapsack partitions of 33 **Telephone area code for Montserrat. ** Area code for Tijuana within Mexico. **Model number for the Amstrad CPC664 home computer. * 665 = 5 × 7 × 19,

, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon *

= 2 × 3² × 37,

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 ...

* 667 = 23 × 29, lazy caterer number * 668 = 2² × 167,

* 669 = 3 × 223,

blum integer In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/tal ...

670s

* 670 = 2 × 5 × 67, sphenic number,

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 ...

* 671 = 11 × 61. This number is the

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'' = 11. * 672 = 2⁵ × 3 × 7,

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 ...

, Zuckerman number, admirable number * 673 = prime number, Proth prime * 674 = 2 × 337,

, 2-Knödel number * 675 = 3³ × 5²,

* 676 = 2² × 13² = 26², palindromic square * 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10 * 678 = 2 × 3 × 113, sphenic number,

, number of surface points of an octahedron with side length 13, admirable number * 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5

680s

* 680 = 2³ × 5 × 17,

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, ...

* 681 = 3 × 227, centered pentagonal number * 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzl
strikketoy
* 683 = prime number, Sophie Germain prime, sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part,

Wagstaff prime In number theory, a Wagstaff prime is a prime number of the form : where ''p'' is an odd prime. Wagstaff primes are named after the mathematician Samuel S. Wagstaff Jr.; the prime pages credit François Morain for naming them in a lecture at the ...

* 684 = 2² × 3² × 19, Harshad number, number of graphical forest partitions of 32 * 685 = 5 × 137, centered square number * 686 = 2 × 7³,

, number of multigraphs on infinite set of nodes with 7 edges * 687 = 3 × 229, 687 days to orbit the sun (

Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...

) D-number * 688 = 2⁴ × 43, Friedman number since 688 = 8 × 86, 2-

* 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). Strobogrammatic number

690s

* 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number, Smith number, Harshad number **

ISO 690 ISO 690 is an ISO standard governing bibliographic references in different kinds of documents, including electronic documents. This international standard specifies the bibliographic elements that need to be included in references to published ...

is the ISO's standard for bibliographic references * 691 = prime number, (negative) numerator of the

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, ...

''B''₁₂ = -691/2730.

Ramanujan's tau function The Ramanujan tau function, studied by , is the function \tau : \mathbb \rarr\mathbb defined by the following identity: :\sum_\tau(n)q^n=q\prod_\left(1-q^n\right)^ = q\phi(q)^ = \eta(z)^=\Delta(z), where with , \phi is the Euler function, is the ...

τ and the

divisor function In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (including ...

σ₁₁ are related by the remarkable congruence τ(''n'') ≡ σ₁₁(''n'') (mod 691). ** In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved. * 692 = 2² × 173, number of partitions of 48 into powers of 2 * 693 = 3² × 7 × 11, triangular matchstick number, the number of sections in

Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...

's ''

Philosophical Investigations ''Philosophical Investigations'' (german: Philosophische Untersuchungen) is a work by the philosopher Ludwig Wittgenstein, published posthumously in 1953. ''Philosophical Investigations'' is divided into two parts, consisting of what Wittgens ...

''. * 694 = 2 × 347, centered triangular number,

* 695 = 5 × 139, 695!! + 2 is prime. * 696 = 2³ × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice * 697 = 17 × 41,

cake number In mathematics, the cake number, denoted by ''Cn'', is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly ''n'' planes. The cake number is so-called because one may imagine each partition of the cu ...

; the number of sides of Colorado * 698 = 2 × 349,

, sum of squares of two primes * 699 = 3 × 233, D-number

References

{{Integers, 6 Integers