2000 (two thousand) is a
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 ...
following 1999 and preceding
2001.
It is:
:*the highest number expressible using only two unmodified characters in
Roman numerals (MM)
:*an
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 ...
:*smallest four digit
eban number
Selected numbers in the range 2001–2999
2001 to 2099
* 2001 –
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 ...
* 2002 –
palindromic number
* 2003 –
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 +  ...
and the smallest prime number in the 2000s
* 2004 – Area of the 24t
crystagon* 2005 – A vertically symmetric number
* 2006 – number of subsets of with relatively prime elements
* 2007 – 2
2007 + 2007
2 is prime
* 2008 – number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to 3
* 2009 = 7
4 − 7
3 − 7
2
* 2010 – number of compositions of 12 into relatively prime parts
* 2011 –
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 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211
* 2012 – The number 8 × 10
2012 − 1 is a prime number
* 2013 –
number of widely totally strongly normal compositions of 17
* 2014 – 5 × 2
2014 - 1 is prime
* 2015 –
Lucas–Carmichael number
*
2016
File:2016 Events Collage.png, From top left, clockwise: Bombed-out buildings in Ankara following the 2016 Turkish coup d'état attempt; the Impeachment of Dilma Rousseff, impeachment trial of Brazilian President Dilma Rousseff; Damaged houses duri ...
–
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 i ...
, number of 5-cubes in a 9-cube,
Erdős–Nicolas number
In number theory, an Erdős–Nicolas number is a number that is not perfect, but that equals one of the partial sums of its divisors.
That is, a number is Erdős–Nicolas number when there exists another number such that
: \sum_d=n.
The fir ...
, 2
11-2
5.
* 2017 –
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,
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 2011
* 2018 –
Number of partitions of 60 into prime parts
* 2019 – smallest number that can be represented as the sum of 3 prime squares 6 different ways: 2019 = 7
2 + 11
2 + 43
2 = 7
2 + 17
2 + 41
2 = 13
2 + 13
2 + 41
2 = 11
2 + 23
2 + 37
2 = 17
2 + 19
2 + 37
2 = 23
2 + 23
2 + 31
2.
* 2020 – sum of the
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 ...
function for the first 81 integers
* 2021 = 43 * 47, consecutive
prime numbers, next is 2491
* 2022 – non-isomorphic colorings of a toroidal 3 × 3 grid using exactly three colors under translational symmetry, beginning of a run of 4 consecutive Niven numbers
* 2023 – multiple of 7 with digit sum equal to 7
* 2024 –
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,
...
* 2025 = 45
2, sum of the cubes of the first nine integers,
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 ...
* 2027 –
super-prime,
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 +  ...
* 2029 – member of the
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 ...
* 2030 = 21
2 + 22
2 + 23
2 + 24
2 = 25
2 + 26
2 + 27
2
* 2031 –
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 ...
* 2039 –
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 +  ...
,
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 +  ...
* 2045 – number of
partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a bina ...
with 7 unlabeled elements
* 2047 –
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) ...
,
Woodall number
In number theory, a Woodall number (''W'n'') is any natural number of the form
:W_n = n \cdot 2^n - 1
for some natural number ''n''. The first few Woodall numbers are:
:1, 7, 23, 63, 159, 383, 895, … .
History
Woodall numbers were first st ...
,
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 ...
,
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 ...
. Also, 2047 = 2
11 - 1 = 23 × 89 and is the first
Mersenne number
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 17th ...
that is composite for a prime exponent.
* 2048 =
211
* 2053 –
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 ...
* 2056 –
magic constant of ''n'' × ''n'' normal
magic square and
''n''-queens problem for ''n'' = 16.
* 2060 – sum of the
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 ...
for the first 82 integers
* 2063 –
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 +  ...
,
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 +  ...
.
super-prime
* 2069 –
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 +  ...
* 2070 –
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 ...
* 2080 – triangular number
* 2081 –
super-prime
* 2093 – Mertens function zero
* 2095 – Mertens function zero
* 2096 – Mertens function zero
* 2097 – Mertens function zero
* 2099 – Mertens function zero,
super-prime,
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 +  ...
,
highly cototient number
2100 to 2199
* 2100 – Mertens function zero
* 2101 –
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 ...
* 2107 – member of 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 2108 (first definition)
* 2108 – member of a Ruth–Aaron pair with 2107 (first definition)
* 2109 –
square pyramidal number,
the sum of the third and last 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 the ...
s in
decimal:
199
Year 199 ( CXCIX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was sometimes known as year 952 '' Ab urbe condita''. The denomination 199 for this year has been used since the ...
+
919 +
991.
* 2112 – The break-through album of the band
Rush
* 2113 – Mertens function zero,
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 ...
,
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 ...
* 2116 = 46
2
* 2117 – Mertens function zero
* 2119 – Mertens function zero
* 2120 – Mertens function zero, Fine number.
* 2122 – Mertens function zero
* 2125 –
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 ...
* 2127 – sum of the first 34 primes
* 2129 –
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 +  ...
* 2135 – Mertens function zero
* 2136 – Mertens function zero
* 2137 – prime of the form 2p-1
* 2138 – Mertens function zero
* 2141 –
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 +  ...
* 2142 – sum of the totient function for the first 83 integers
* 2143 – almost exactly 22
4
* 2145 – triangular number
* 2153 – with 2161, smallest consecutive primes that have the same sum of digits as each other's prime indices
* 2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
* 2162 – pronic number
* 2166 – sum of the totient function for the first 84 integers
* 2169 –
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, ...
* 2171 – Mertens function zero
* 2172 – Mertens function zero
* 2175 – smallest number requiring 143 seventh powers for Waring representation
* 2176 –
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. ...
, centered pentagonal number
* 2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4.
* 2179 –
Wedderburn–Etherington prime
* 2184 – equals both 3
7 − 3 and 13
3 − 13 and is believed to be the only such ''doubly strictly absurd'' number.
* 2187 =
37,
vampire number,
perfect totient number
* 2188 –
Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have d ...
* 2197 = 13
3, palindromic in base 12 (1331
12)
* 2199 – perfect totient number
2200 to 2299
* 2201 – only known non-palindromic number whose
cube is
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 ...
; also no known fourth or higher powers are palindromic for non-palindromic numbers
* 2203 – Mersenne prime exponent
* 2205 – odd
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 ...
* 2207 –
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 +  ...
,
Lucas prime
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 ...
* 2208 –
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 ...
* 2209 = 47
2, palindromic in base 14 (B3B
14), centered octagonal number
* 2211 – triangular number
* 2221 –
super-prime,
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 ...
* 2222 –
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 ...
* 2223 –
Kaprekar number
In mathematics, a natural number in a given number base is a p-Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p digits, that add up to the original number. The numbers are n ...
* 2230 – sum of the totient function for the first 85 integers
* 2232 – decagonal number
* 2236 – Harshad number
* 2245 – centered square number
* 2254 – member of the Mian–Chowla sequence
* 2255 –
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 ...
* 2256 – pronic number
* 2269 –
super-prime,
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 = ...
* 2272 – sum of the totient function for the first 86 integers
* 2273 –
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 +  ...
* 2276 – sum of the first 35 primes, centered heptagonal number
* 2278 – triangular number
* 2281 –
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 ...
,
Mersenne prime exponent
* 2287 –
balanced prime
* 2294 – Mertens function zero
* 2295 – Mertens function zero
* 2296 – Mertens function zero
* 2299 – member of a Ruth–Aaron pair with 2300 (first definition)
2300 to 2399
* 2300 – tetrahedral number,
member of a Ruth–Aaron pair with 2299 (first definition)
* 2301 – nonagonal number
* 2304 = 48
2
* 2306 – Mertens function zero
* 2309 –
primorial prime In mathematics, a primorial prime is a prime number of the form ''pn''# ± 1, where ''pn''# is the primorial of ''pn'' (i.e. the product of the first ''n'' primes).
Primality tests show that
: ''pn''# − 1 is prime for ''n ...
,
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 p ...
with 2311, Mertens function zero, highly cototient number
* 2310 – fifth
primorial
* 2311 – primorial prime, twin prime with 2309
* 2321 – Mertens function zero
* 2322 – Mertens function zero
* 2326 – centered pentagonal number
* 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128
* 2331 –
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 ...
* 2338 – Mertens function zero
* 2339 –
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 +  ...
, twin prime with 2341
* 2341 –
super-prime, twin prime with 2339
* 2346 – triangular number
* 2347 – sum of seven consecutive primes (313 + 317 + 331 + 337 + 347 + 349 + 353)
* 2351 –
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 +  ...
,
super-prime
* 2352 – pronic number
* 2357 –
Smarandache–Wellin prime
* 2368 – sum of the totient function for the first 88 integers
* 2372 – logarithmic number
* 2378 –
Pell number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , an ...
* 2379 – member of the Mian–Chowla sequence
* 2381 –
super-prime, centered square number
* 2383 (2384) – number of delegates required to win the
2016 Democratic Party presidential primaries
Presidential primaries and caucuses were organized by the Democratic Party to select the 4,051 delegates to the 2016 Democratic National Convention held July 25–28 and determine the nominee for president in the 2016 United States presidential ...
(out of 4051)
* 2393 –
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 +  ...
* 2397 – sum of the squares of the first ten primes
* 2399 –
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 +  ...
2400 to 2499
* 2400 – 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 ...
tests administered after 2005
* 2401 = 7
4, 49
2, centered octagonal number
* 2415 – triangular number
* 2417 –
super-prime, balanced prime
* 2425 – decagonal number
* 2427 – sum of the first 36 primes
* 2431 – product of three consecutive primes
* 2437 – cuban prime,
largest
right-truncatable prime in base 5
* 2447 –
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 +  ...
* 2450 – pronic number
* 2456 – sum of the totient function for the first 89 integers
* 2458 – centered heptagonal number
* 2459 –
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 +  ...
,
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 +  ...
* 2465 –
magic constant of ''n'' × ''n'' normal
magic square and
''n''-queens problem for ''n'' = 17,
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 ...
* 2470 – square pyramidal number
* 2471 – number of ways to partition and then partition each cell (block) into subcells.
* 2477 –
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 ...
* 2480 – sum of the totient function for the first 90 integers
* 2481 – centered pentagonal number
* 2484 – nonagonal number
* 2485 – triangular number, number of planar partitions of 13
* 2491 = 47 * 53, consecutive
prime numbers, member of
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 2492 under second definition
* 2492 – member of Ruth–Aaron pair with 2491 under second definition
2500 to 2599
* 2500 = 50
2, palindromic in base 7 (10201
7)
* 2501 – Mertens function zero
* 2502 – Mertens function zero
* 2503 – Friedman prime
* 2510 – member of the Mian–Chowla sequence
* 2513 – member of the
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 ...
* 2517 – Mertens function zero
* 2519 – the smallest number congruent to 1 (mod 2), 2 (mod 3), 3 (mod 4), ..., 9 (mod 10)
*
2520 –
superior highly composite number; smallest number divisible by numbers
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 12 ;
colossally abundant number;
Harshad number in several bases. It is also the highest number with more divisors than any number less than double itself . Not only is it the 7th (and last) number with more divisors than any number double itself but it also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 which is a property the previous number with this pattern of divisors does not have (
360). That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which
60 is) and is not divisible by 1 to 7 (which
420
420 may refer to:
* 420 (number)
*420 (cannabis culture), informal reference to cannabis use and celebrations on April 20
** California Senate Bill 420 or the Medical Marijuana Program Act
*AD 420, a year in the 5th century of the Julian calendar
* ...
is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number.
* 2521 –
star prime, centered square number
* 2522 – Mertens function zero
* 2523 – Mertens function zero
* 2524 – Mertens function zero
* 2525 – Mertens function zero
* 2530 – Mertens function zero, Leyland number
* 2533 – Mertens function zero
* 2537 – Mertens function zero
* 2538 – Mertens function zero
* 2543 –
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 +  ...
, sexy prime with 2549
* 2549 –
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 +  ...
,
super-prime, sexy prime with 2543
* 2550 – pronic number
* 2552 – sum of the totient function for the first 91 integers
* 2556 – triangular number
* 2567 – Mertens function zero
* 2568 – Mertens function zero. Also number of digits in the
decimal expansion of 1000
!, or the
product
Product may refer to:
Business
* Product (business), an item that serves as a solution to a specific consumer problem.
* Product (project management), a deliverable or set of deliverables that contribute to a business solution
Mathematics
* Produ ...
of all
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 ...
s from 1 to 1000.
* 2570 – Mertens function zero
* 2579 –
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 +  ...
* 2580 –
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 ...
,
forms a column on a telephone or
PIN pad
A PIN pad or PIN entry device (PED) is an electronic device used in a debit, credit or smart card-based transaction to accept and encrypt the cardholder's personal identification number (PIN).
PIN pads are normally used with payment terminals ...
* 2584 –
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 ...
, sum of the first 37 primes
* 2592 –
3-smooth
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × ...
number (2
5×3
4)
* 2596 – sum of the totient function for the first 92 integers
2600 to 2699
* 2600 – tetrahedral number,
member of 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 2601 (first definition)
** 2600
Hz is the tone used by a
blue box
A blue box is an electronic device that produces tones used to generate the in-band signaling tones formerly used within the North American long-distance telephone network to send line status and called number information over voice circuits. ...
to defeat toll charges on
long distance telephone calls.
**
2600: The Hacker Quarterly is a magazine named after the above.
** The
Atari 2600
The Atari 2600, initially branded as the Atari Video Computer System (Atari VCS) from its release until November 1982, is a home video game console developed and produced by Atari, Inc. Released in September 1977, it popularized microprocesso ...
was a popular
video game console
A video game console is an electronic device that outputs a video signal or image to display a video game that can be played with a game controller. These may be home consoles, which are generally placed in a permanent location connected to ...
.
* 2601 = 51
2, member of 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 2600 (first definition)
* 2609 –
super-prime
* 2620 –
telephone number
A telephone number is a sequence of digits assigned to a landline telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices f ...
,
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 2924
* 2625 = 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 ...
* 2626 – decagonal number
* 2628 – triangular number
* 2632 – number of consecutive baseball games played by
Cal Ripken Jr.
Calvin Edwin Ripken Jr. (born August 24, 1960), nicknamed " The Iron Man", is an American former baseball shortstop and third baseman who played 21 seasons in Major League Baseball (MLB) for the Baltimore Orioles (1981–2001). One of his posit ...
* 2633 – sum of twenty-five consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167)
* 2641 – centered pentagonal number
* 2647 –
super-prime, centered heptagonal number
* 2652 – pronic number
* 2656 – sum of the totient function for the first 93 integers
* 2665 – centered square number
* 2674 – nonagonal number
* 2677 – balanced prime
* 2680 – number of
11-queens problem solutions
* 2683 –
super-prime
* 2689 – Mertens function zero, Proth prime
* 2693 –
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 +  ...
* 2699 –
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 +  ...
2700 to 2799
* 2701 – triangular number, super-Poulet number
* 2702 – sum of the totient function for the first 94 integers
* 2704 = 52
2
* 2707 – model number for the concept supersonic airliner
Boeing 2707
The Boeing 2707 was an American supersonic passenger airliner project during the 1960s. After winning a competition for a government-funded contract to build an American supersonic airliner, Boeing began development at its facilities in Seattl ...
* –
super-prime, largest known odd number which cannot be expressed in the form
''x''2 + ''y''2 + 10''z''2 where ''x'', ''y'' and ''z'' are integers. In 1997 it was conjectured that this is also the largest such odd number.
It is now known this is true if the
generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global ''L''-functions, whic ...
is true.
* 2728 –
Kaprekar number
In mathematics, a natural number in a given number base is a p-Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p digits, that add up to the original number. The numbers are n ...
* 2729 – highly cototient number
* 2731 – the only
Wagstaff prime with four digits,
Jacobsthal prime
* 2736 – octahedral number
* 2741 –
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 +  ...
, 400th prime number
* 2744 = 14
3, palindromic in base 13 (1331
13)
* 2747 – sum of the first 38 primes
* 2749 –
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 ...
with 2753
* 2753 –
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 +  ...
, Proth prime
* 2756 – pronic number
* 2774 – sum of the totient function for the first 95 integers
* 2775 – triangular number
* 2780 – member of the Mian–Chowla sequence
* 2783 – member of a Ruth–Aaron pair with 2784 (first definition)
* 2784 – member of a Ruth–Aaron pair with 2783 (first definition)
* 2791 – cuban prime
2800 to 2899
* 2801 – first base 7
repunit
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 ...
prime
* 2803 –
super-prime
* 2806 – centered pentagonal number,
sum of the totient function for the first 96 integers
* 2809 = 53
2, centered octagonal number
* 2813 – centered square number
* 2816 – number of parts in all compositions of 10.
* 2819 –
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 +  ...
,
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 +  ...
, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)
* 2821 – Carmichael number
* 2835 – odd abundant number,
decagonal number
* 2843 – centered heptagonal prime
* 2850 – triangular number
* 2862 – pronic number
* 2870 – square pyramidal number
* 2871 – nonagonal number
* 2872 –
tetranacci number
* 2879 –
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 +  ...
* 2897 –
super-prime,
Markov prime
2900 to 2999
* 2902 – sum of the totient function for the first 97 integers
* 2903 –
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 +  ...
,
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 +  ...
,
balanced prime
* 2909 –
super-prime
* 2914 – sum of the first 39 primes
* 2915 – Lucas–Carmichael number
* 2916 = 54
2
* 2924 – amicable number with 2620
* 2925 –
magic constant of ''n'' × ''n'' normal
magic square and
''n''-queens problem for ''n'' = 18, tetrahedral number,
member of the Mian-Chowla sequence
* 2926 – triangular number
* 2939 –
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 +  ...
* 2944 – sum of the totient function for the first 98 integers
* 2963 –
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 +  ...
,
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 +  ...
, balanced prime
* 2964 – number of parallelogram polyominoes with 11 cells
* 2965 – greater of second pair of
Smith brothers
The Smith Brothers were makers of the first cough drops produced and advertised in the United States, becoming one of the most famous brands in the country in its day.
History
William Wallace Smith I (1830–1913) and Andrew Smith (1836–1895 ...
, centered square number
* 2969 –
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 +  ...
* 2970 –
harmonic divisor number, pronic number
* 2976 – centered pentagonal number
* 2989 – in
hexadecimal, reads as "
BAD"
* 2997 – 1000-gonal number
* 2999 –
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 +  ...
Prime numbers
There are 127
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 ...
s between 2000 and 3000:
:2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999
References
{{Integers, 10
Integers