View source for 2000 (number)

{{Redirect|2,000|other uses|2000 (disambiguation)}}
{{see also|millennium|2000|Y2K (disambiguation){{!}}Y2K}}

{{Infobox number
| number = 2000
| unicode = MM, mm
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Ս|lang3=[[Egyptian numerals|Egyptian hieroglyph]]|lang3 symbol=<span style="font-size:200%;">𓆽</span>}}

{{wiktionary|two thousand}}
'''2000''' ('''two thousand''') is a [[natural number]] following 1999 and preceding 2001.

It is:
:*the highest number expressible using only two unmodified characters in [[Roman numerals]] (MM)
:*an [[Achilles number]]<ref>{{cite OEIS|A052486|name=Achilles numbers - powerful but imperfect: if n = Product(p_i^e_i) then all e_i > 1 (i.e., powerful), but the highest common factor of the e_i is 1, i.e., not a perfect power}}</ref>
:*smallest four digit [[Ban number|eban number]]<ref>{{cite OEIS|A006933|'Eban' numbers (the letter 'e' is banned!)}}</ref>
:*the sum of all the [[Ban number|nban numbers]] in the sequence<ref>{{cite OEIS|A008537|Numbers that do not contain the letter 'n')}}</ref>

== Selected numbers in the range 2001–2999 ==

===2001 to 2099===
* '''2001''' – [[sphenic number]]<ref>{{cite OEIS|A007304|Sphenic numbers: products of 3 distinct primes)}}</ref>
* '''2002''' = 7<sup>4</sup> – 7<sup>3</sup> – 7<sup>2</sup> – 7. [[Palindromic number]] in [[decimal]], base 76, 90, 142, and 11 other non-trivial bases. 
* '''2003''' – [[Sophie Germain prime]] and the smallest prime number in the 2000s
* '''2004''' – Area of the 24th [https://oeis.org/A022264/a022264.jpg crystagon]<ref>{{cite OEIS|A022264|n×(7×n - 1)/2}}</ref>
* '''2005''' – A vertically symmetric number
* '''2006''' – number of subsets of {1,2,3,4,5,6,7,8,9,10,11} with relatively prime elements<ref>{{cite OEIS|A085945|Number of subsets of {1,2,...,n} with relatively prime elements}}</ref>
* '''2007''' – 2<sup>2007</sup> + 2007<sup>2</sup> is prime<ref>{{cite OEIS|A064539|Numbers n such that 2^n + n^2 is prime}}</ref>
* '''2008''' – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3<ref>{{cite OEIS|A001496|Number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to n}}</ref>
* '''2009''' = 28<sup>2</sup> + 35<sup>2</sup>, sum of two squares
* '''2010''' – number of compositions of 12 into relatively prime parts<ref>{{cite OEIS|A000740|Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement}}</ref>
* '''2011''' – [[sexy prime]] with 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211
* '''2012''' – The number 8 × 10<sup>2012</sup> − 1 is a prime number<ref>{{cite OEIS|A056721|Numbers n such that 8×10^n-1 is prime}}</ref>
* '''2013''' – [[oeis:A332337|number of widely totally strongly normal compositions of 17]]
* '''2014''' – 5 × 2<sup>2014</sup> - 1 is prime<ref>{{cite OEIS|A001770|Numbers k such that 5×2^k - 1 is prime}}</ref>
* '''2015''' – [[Lucas–Carmichael number]]<ref name=":0">{{Cite OEIS|A006972|Lucas-Carmichael numbers}}</ref>
* '''[[2016 (number)|2016]]''' – [[triangular number]], number of 5-cubes in a 9-cube, [[Erdős–Nicolas number]],<ref>{{Cite OEIS|A194472|Erdős-Nicolas numbers}}</ref> 2<sup>11</sup>-2<sup>5</sup>
* '''2017''' – [[Mertens function]] zero, [[sexy prime]] with 2011
* '''2018''' – [[oeis:A000607|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<sup>2</sup> + 11<sup>2</sup> + 43<sup>2</sup> = 7<sup>2</sup> + 17<sup>2</sup> + 41<sup>2</sup> = 13<sup>2</sup> + 13<sup>2</sup> + 41<sup>2</sup> = 11<sup>2</sup> + 23<sup>2</sup> + 37<sup>2</sup> = 17<sup>2</sup> + 19<sup>2</sup> + 37<sup>2</sup> = 23<sup>2</sup> + 23<sup>2</sup> + 31<sup>2</sup><ref>{{Cite web|date=2018-12-31|title=Can you solve it? 2019 in numbers|url=http://www.theguardian.com/science/2018/dec/31/can-you-solve-it-2019-in-numbers|access-date=2021-09-19|website=the Guardian|language=en}}</ref>
* '''2020''' – sum of the [[totient]] 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,<ref>{{cite OEIS|A294685|non-isomorphic colorings of a toroidal n × k grid using exactly three colors under translational symmetry}}</ref> beginning of a run of 4 consecutive Niven numbers<ref>{{cite OEIS|A141769|Beginning of a run of 4 consecutive Niven (or Harshad) numbers}}</ref>
* '''2023''' = 7 × 17<sup>2</sup> – multiple of 7 with digit sum equal to 7,<ref>{{cite OEIS|A063416|Multiples of 7 whose sum of digits is equal to 7}}</ref> sum of squares of digits equals 17
* '''2024''' – [[tetrahedral number]]<ref name=":1">{{Cite OEIS|A000292|Tetrahedral numbers}}</ref>
* '''2025''' = 45<sup>2</sup>, square of the sum of the first nine positive integers (and therefore sum of the cubes of the first nine positive integers, by [[Nicomachus's theorem]]), [[centered octagonal number]],<ref name=":2">{{Cite OEIS|1=A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref> lowest number with exactly 15 [[Parity (mathematics)|odd]] divisors.<ref>{{Cite OEIS |A038547 |Least number with exactly n odd divisors. }}</ref> Sum of odd numbers from 1 to 89, current year.
* '''2026''' = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices<ref>{{cite OEIS|A144959|A134955(n) - A134955(n-1). Number of hyperforests spanning n unlabeled nodes without isolated vertices.}}</ref>
* '''2027''' – [[super-prime]], [[safe prime]]<ref name=":3">{{Cite OEIS|A005385|Safe primes}}</ref>
* '''2028''' = 13<sup>3</sup> – 13<sup>2</sup>
* '''2029''' – member of the [[Mian–Chowla sequence]]<ref name=":4">{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref>
* '''2030''' = 21<sup>2</sup> + 22<sup>2</sup> + 23<sup>2</sup> + 24<sup>2</sup> = 25<sup>2</sup> + 26<sup>2</sup> + 27<sup>2</sup>
* '''2031''' – [[centered pentagonal number]]<ref name=":5">{{Cite OEIS|A005891|Centered pentagonal numbers}}</ref>
* '''2032''' – number of binary Lyndon words of length 16 with an even number of 1's<ref>{{cite OEIS|A051841|Number of binary Lyndon words with an even number of 1's}}</ref>
* '''2033''' – number of rooted trees with 9 nodes and a single labeled node<ref>{{cite OEIS|A000107|Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates}}</ref>
* '''2034''' – number of unlabeled graphs on 11 nodes whose components are unicyclic graphs<ref>{{cite OEIS|A137917|number of unlabeled graphs on n nodes whose components are unicyclic graphs}}</ref>
* '''2035''' – Wolstenholme number<ref>{{cite OEIS|A007408|Wolstenholme numbers}}</ref>
* '''2036''' – Eulerian number<ref>{{cite OEIS|A000295|Eulerian numbers}}</ref>
* '''2037''' = 2<sup>11</sup> - 11<ref>{{cite OEIS|A000325|2^n - n}}</ref>
* '''2038''' – Number of unlabeled Euler graphs with 9 nodes<ref>{{cite OEIS|A002854|Number of unlabeled Euler graphs with n nodes; number of unlabeled two-graphs with n nodes; number of unlabeled switching classes of graphs with n nodes; number of switching classes of unlabeled signed complete graphs on n nodes; number of Seidel matrices of order n}}</ref>
* '''2039''' – [[Sophie Germain prime]], [[safe prime]]<ref name=":3" />
* '''2040''' = <math>\frac{15 \times 16 \times 17}{2}</math> <ref>{{cite OEIS|A027480|n*(n+1)*(n+2)/2}}</ref>
* '''2041''' – Number of 11-node connected graphs with at most one cycle<ref>{{cite OEIS|A005703|Number of n-node connected graphs with at most one cycle}}</ref>
* '''2042''' = 2 × 1021. All the digits of all the prime factors are smaller than 3<ref>{{cite OEIS|A385344|Numbers where all the digits of all the prime factors are smaller than 3}}</ref>
* '''2043''' – Number of partitions of 35 in which the number of parts divides 35<ref>{{cite OEIS|A067538|Number of partitions of n in which the number of parts divides n}}</ref>
* '''2044''' = <math>\sigma_3(12)=\sum_{d|12}d^3</math><ref>{{cite OEIS|A001158|sigma_3(n): sum of cubes of divisors of n}}</ref>
* '''2045''' – Number of [[partially ordered set]] with 7 unlabeled elements<ref>{{cite OEIS|A000112|Number of partially ordered sets (posets) with n unlabeled elements}}</ref>
* '''2046''' = 2<sup>11</sup> - 2 = the expected number of tosses of a fair coin to get 10 consecutive heads<ref>{{cite OEIS|A000918|2^n - 2}}</ref>
* '''2047''' – [[super-Poulet number]],<ref name=":6">{{Cite OEIS|A050217|Super-Poulet numbers}}</ref> [[Woodall number]],<ref>{{Cite OEIS|A003261|Woodall numbers}}</ref> [[decagonal number]],<ref name=":7">{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref> a [[centered octahedral number]],<ref name="ReferenceA">{{cite OEIS|A001845|Centered octahedral numbers (crystal ball sequence for cubic lattice)}}</ref> 2047 = 2<sup>11</sup> - 1 = 23 × 89 and is the first [[Mersenne number]] that is composite for a prime exponent
* '''2048''' = [[power of two|2<sup>11</sup>]]
* '''2049''' = 2<sup>11</sup> + 2<sup>0</sup>. A sum of two positive [[power of two|powers of two]]<ref>{{Cite OEIS|sequencenumber=A018900|name=Sums of two distinct powers of 2}}</ref>
* '''2050''' = 31<sup>2</sup> + 33<sup>2</sup>. Sum of 2 consecutive odd squares
* '''2051''' = 1<sup>5</sup> + 1<sup>5</sup> + 1<sup>5</sup> + 4<sup>5</sup> + 4<sup>5</sup>. Sum of 5 positive 5th powers<ref>{{Cite OEIS|sequencenumber=A003350|name=Numbers that are the sum of 5 positive 5th powers}}</ref>
* '''2052''' = 2<sup>11</sup> + 2<sup>2</sup>. A sum of two positive [[power of two|powers of two]]
* '''2053''' – [[star number]]
* '''2054''' = 1<sup>9</sup> + 1<sup>9</sup> + 1<sup>9</sup> + 1<sup>9</sup> + 1<sup>9</sup> + 1<sup>9</sup> + 2<sup>9</sup> + 2<sup>9</sup> + 2<sup>9</sup> + 2<sup>9</sup>. Sum of 10 positive 9th powers
* '''2055''' = 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 2<sup>10</sup> + 2<sup>10</sup>. Sum of 9 positive 10th powers
* '''2056''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 16
* '''2057''' = 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 1<sup>10</sup> + 2<sup>10</sup> + 2<sup>10</sup>. Sum of 11 positive 10th powers
* '''2058''' = <math>49 \times \phi (49)</math><ref>{{cite OEIS|A002618|n*phi(n)}}</ref>
* '''2059''' = 3<sup>7</sup>-2<sup>7</sup><ref>{{cite OEIS|A001047|3^n - 2^n}}</ref>
* '''2060''' – sum of the [[totient function]] for the first 82 integers
* '''2061''' – Number of sets of positive integers with arithmetic mean 7<ref>{{cite OEIS|A066571|Number of sets of positive integers with arithmetic mean n}}</ref>
* '''2062''' = <math>\phi(\phi(2062) + \sigma(2062))</math><ref>{{cite OEIS|A097646|Numbers n such that n equals phi(phi(n) + sigma(n))}}</ref>
* '''2063''' – [[Sophie Germain prime]], [[safe prime]],<ref name=":3" /> [[super-prime]]
* '''2064''' = 1031 + 1033, which is a twin prime sum<ref>{{cite OEIS|A054735|Sums of twin prime pairs}}</ref>
* '''2065''' = Number of distinct lines through the origin in the fourdimensional lattice of side length 6<ref>{{cite OEIS|A090022|Number of distinct lines through the origin in the n-dimensional lattice of side length 6}}</ref>
* '''2066''' – Bell  number<ref>{{cite OEIS|A011971|Aitken's array}}</ref>
* '''2067''' = Number of Golomb partitions of 30<ref>{{cite OEIS|A325858|Number of Golomb partitions of n}}</ref>
* '''2068''' – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed<ref>{{cite OEIS|A000013|Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed}}</ref>
* '''2069''' – [[Sophie Germain prime]]
* '''2070''' – [[pronic number]]<ref name=A002378>{{Cite OEIS|A002378|Oblong (or promic, pronic, or heteromecic) numbers}}</ref>
* '''2071''' = Number of sensed planar maps with 6 edges<ref>{{Cite OEIS|A006384|Number of sensed planar maps with n edges}}</ref>
* '''2072''' = 45<sup>2</sup> + 45 + 2<ref>{{Cite OEIS|A014206|n^2 + n + 2}}</ref>
* '''2073''' – Genocchi number<ref>{{Cite OEIS|A001469|Genocchi numbers (of first kind); unsigned coefficients give expansion of x*tan(x/2)}}</ref>
* '''2074''' = Number of Baxter permutations of length 7<ref>{{Cite OEIS|A001181|Number of Baxter permutations of length n}}</ref>
* '''2075''' = 411 + 413 + 415 + 417 + 419 = 25 + 50×41<ref>
{{cite OEIS|A053742|Sum of odd numbers in range 10*n to 10*n+9}}</ref>
* '''2076''' = Number of disconnected regular graphs with 17 nodes<ref>
{{cite OEIS|A068932|Number of disconnected regular graphs with n nodes}}</ref>
* '''2077''' = Number of canonical polygons with 16 edges having 2-fold rotational symmetry<ref>
{{cite OEIS|A307454|a(n) is the number of canonical polygons with 2n edges having 2-fold rotational symmetry}}</ref>
* '''2078''' = Number of reversible strings with 12 beads using exactly two different colors<ref>
{{cite OEIS|A056309|Number of reversible strings with n beads using exactly two different colors}}</ref>
* '''2079''' = <math>\frac{9 \cdot 10 \cdot 11 \cdot 12 \cdot (2\cdot 9 + 3)}{5!}</math>, 5-dimensional pyramidal number<ref>{{cite OEIS|A005585|5-dimensional pyramidal numbers: n*(n+1)*(n+2)*(n+3)*(2n+3)/5!}}</ref>
* '''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]],<ref name=":3" /> [[highly cototient number]]<ref name=":9">{{Cite OEIS|A100827|Highly cototient numbers}}</ref>

===2100 to 2199===
* '''2100''' – Mertens function zero
* '''2101''' – [[centered heptagonal number]]<ref name=":10">{{Cite OEIS|1=A069099|2=Centered heptagonal numbers|access-date=2016-06-13}}</ref>
* '''2107''' – member of a [[Ruth–Aaron pair]] with 2108 (first definition)
* '''2108''' – member of a Ruth–Aaron pair with 2107 (first definition)
* '''2109''' – [[square pyramidal number]],<ref name=":11">{{Cite OEIS|1=A000330|2=Square pyramidal numbers|access-date=2016-06-13}}</ref> the sum of the third and last trio of three-digit [[permutable prime]]s in [[decimal]]: [[199 (number)|199]] + [[919 (number)|919]] + [[991 (number)|991]] 
* '''2112''' – The break-through [[2112 (album)|album]] of the band [[Rush (band)|Rush]]
* '''2113''' – Mertens function zero, [[Proth prime]],<ref name=":12">{{Cite OEIS|1=A080076|2=Proth primes|access-date=2016-06-13}}</ref> [[centered square number]]<ref name=":13">{{Cite OEIS|1=A001844|2=Centered square numbers|access-date=2016-06-13}}</ref>
* '''2116''' = 46<sup>2</sup>
* '''2117''' – Mertens function zero
* '''2119''' – Mertens function zero
* '''2120''' – Mertens function zero, Fine number<ref>{{cite OEIS|A000957|2=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}}</ref>
* '''2122''' – Mertens function zero
* '''2125''' – [[nonagonal number]]<ref name=":14">{{Cite OEIS|1=A001106|2=9-gonal (or enneagonal or nonagonal) numbers|access-date=2016-06-13}}</ref>
* '''2127''' – sum of the first 34 primes
* '''2129''' – [[Sophie Germain prime]]
* '''2135''' – Mertens function zero
* '''2136''' – Mertens function zero
* '''2137''' – prime of the form 2p-1
* '''2138''' – Mertens function zero
* '''2141''' – [[Sophie Germain prime]]
* '''2142''' – sum of the totient function for the first 83 integers
* '''2143''' – almost exactly 22{{pi}}<sup>4</sup>
* '''2145''' – triangular number
* '''2153''' – with 2161, smallest consecutive primes that have the same sum of digits as each other's prime indices
* '''2160''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''2161''' – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
* '''2162''' – pronic number<ref name=A002378/>
* '''2166''' – sum of the totient function for the first 84 integers
* '''2169''' – [[Leyland number]]<ref name=":15">{{Cite OEIS|1=A076980|2=Leyland numbers|access-date=2016-06-13}}</ref>
* '''2171''' – Mertens function zero
* '''2172''' – Mertens function zero
* '''2175''' – smallest number requiring 143 seventh powers for Waring representation
* '''2176''' – [[pentagonal pyramidal number]],<ref>{{Cite OEIS|1=A002411|2=Pentagonal pyramidal numbers|access-date=2016-06-13}}</ref> centered pentagonal number,<ref name=":5" /> number of [[prime knots]] with 12 crossings
* '''2178''' – first natural number whose digits in its decimal representation get reversed when multiplied by 4<ref>{{Cite OEIS|1=A008918|2=Numbers n such that 4*n = (n written backwards)|access-date=2016-06-14}}</ref>
* '''2179''' – [[Wedderburn–Etherington number|Wedderburn–Etherington prime]]<ref>{{Cite OEIS|1=A001190|2=Wedderburn-Etherington numbers|access-date=2016-06-13}}</ref>
* '''2184''' – equals both 3<sup>7</sup> − 3 and 13<sup>3</sup> − 13 and is believed to be the only such ''doubly strictly absurd'' number<ref>{{cite journal
| last       = Mackenzie
| first      = Dana 
| title      = 2184: An Absurd (and Adsurd) Tale
| url        = http://math.colgate.edu/~integers/s33/s33.Abstract.html
| journal    = Integers
| volume     = 18
| year       = 2018
}}</ref>{{Unreliable source?|date=July 2019}}
* '''2187''' = [[power of three|3<sup>7</sup>]], [[vampire number]],<ref>{{Cite OEIS|1=A014575|2=Vampire numbers|access-date=2016-06-13}}</ref> [[perfect totient number]]<ref name=":16">{{Cite OEIS|1=A082897|2=Perfect totient numbers|access-date=2016-06-13}}</ref>
* '''2188''' – [[Motzkin number]]<ref>{{Cite OEIS|1=A001006|2=Motzkin numbers|access-date=2016-06-13}}</ref>
* '''2197''' = 13<sup>3</sup>, palindromic in base 12 (1331<sub>12</sub>)
* '''2199''' – perfect totient number<ref name=":16" />

===2200 to 2299===
* '''2201''' – only known non-palindromic number whose [[cube]] is [[palindromic number|palindromic]]; also no known fourth or higher powers are palindromic for non-palindromic numbers
* '''2203''' – Mersenne prime exponent
* '''2205''' – odd [[abundant number]]<ref name=":17">{{Cite OEIS|1=A005231|2=Odd abundant numbers|access-date=2016-06-13}}</ref>
* '''2207''' – [[safe prime]],<ref name=":3" /> [[Lucas prime]]<ref>{{Cite OEIS|1=A005479|2=Prime Lucas numbers|access-date=2016-06-13}}</ref>
* '''2208''' – [[Keith number]]<ref name=":18">{{Cite OEIS|1=A007629|2=Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)|access-date=2016-06-13}}</ref>
* '''2209''' = 47<sup>2</sup>, palindromic in base 14 (B3B<sub>14</sub>), centered octagonal number<ref name=":2" />
* '''2211''' – triangular number
* '''2221''' – [[super-prime]], [[happy number]]
* '''2222''' – [[repdigit]]
* '''2223''' – [[Kaprekar number]]<ref name=":19">{{Cite OEIS|1=A006886|2=Kaprekar numbers|access-date=2016-06-13}}</ref>
* '''2230''' – sum of the totient function for the first 85 integers
* '''2232''' – decagonal number<ref name=":7" />
* '''2236''' – Harshad number 
* '''2245''' – centered square number<ref name=":13" />
* '''2248''' – 2<sup>11</sup> + 200
* '''2254''' – member of the Mian–Chowla sequence<ref name=":4" />
* '''2255''' – [[octahedral number]]<ref name=":20">{{Cite OEIS|1=A005900|2=Octahedral numbers|access-date=2016-06-13}}</ref>
* '''2256''' – pronic number<ref name=A002378/>
* '''2269''' – [[super-prime]], [[cuban prime]]<ref name=":21">{{Cite OEIS|1=A002407|2=Cuban primes|access-date=2016-06-13}}</ref>
* '''2272''' – sum of the totient function for the first 86 integers
* '''2273''' – [[Sophie Germain prime]]
* '''2276''' – sum of the first 35 primes, centered heptagonal number<ref name=":10" />
* '''2278''' – triangular number
* '''2281''' – [[star number]], [[Mersenne prime|Mersenne prime exponent]]
* '''2287''' – [[balanced prime]]<ref name=":22">{{Cite OEIS|1=A006562|2=Balanced primes|access-date=2016-06-13}}</ref>
* '''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,<ref name=":1" /> member of a Ruth–Aaron pair with 2299 (first definition)
* '''2301''' – nonagonal number<ref name=":14" />
* '''2304''' = 48<sup>2</sup>
* '''2306''' – Mertens function zero
* '''2309''' – [[primorial prime]], [[twin prime]] with 2311, Mertens function zero, highly cototient number<ref name=":9" />
* '''2310''' – fifth [[primorial]]<ref>{{Cite OEIS|1=A002110|2=Primorial numbers|access-date=2016-06-13}}</ref>
* '''2311''' – primorial prime, twin prime with 2309
* '''2321''' – Mertens function zero
* '''2322''' – Mertens function zero
* '''2326''' – centered pentagonal number<ref name=":5" />
* '''2328''' – sum of the totient function for the first 87 integers, the number of groups of order 128<ref>{{cite web|url=http://www-public.tu-bs.de:8080/~beick/soft/small/small.html |title=The Small Groups library |access-date=2008-01-22 |url-status=dead |archive-url=https://web.archive.org/web/20070204070922/http://www-public.tu-bs.de:8080/~beick/soft/small/small.html |archive-date=2007-02-04 }}.</ref>
* '''2331''' – [[centered cube number]]<ref>{{Cite OEIS|1=A005898|2=Centered cube numbers|access-date=2016-06-13}}</ref>
* '''2338''' – Mertens function zero
* '''2339''' – [[Sophie Germain prime]], 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]], [[super-prime]]
* '''2352''' – pronic number<ref name=A002378/>
* '''2357''' – [[Smarandache–Wellin prime]]<ref>{{Cite OEIS|1=A069151|2=Concatenations of consecutive primes, starting with 2, that are also prime|access-date=2016-06-13}}</ref>
* '''2368''' – sum of the totient function for the first 88 integers
* '''2372''' – logarithmic number<ref>{{cite OEIS|A002104|Logarithmic numbers}}</ref>
* '''2378''' – [[Pell number]]<ref>{{Cite OEIS|1=A000129|2=Pell numbers|access-date=2016-06-13}}</ref>
* '''2379''' – member of the Mian–Chowla sequence<ref name=":4" />
* '''2381''' – [[super-prime]], centered square number<ref name=":13" />
* '''2393''' – [[Sophie Germain prime]]
* '''2397''' – sum of the squares of the first ten primes
* '''2399''' – [[Sophie Germain prime]]

===2400 to 2499===
* '''2400''' – perfect score on [[SAT]] tests administered after 2005
* '''2401''' = 49<sup>2</sup> = 7<sup>4</sup>, centered octagonal number<ref name=":2" />
* '''2415''' – triangular number
* '''2417''' – [[super-prime]], balanced prime<ref name=":22" />
* '''2425''' – decagonal number<ref name=":7" />
* '''2427''' – sum of the first 36 primes
* '''2431''' – product of three consecutive primes
* '''2437''' – cuban prime,<ref name=":21" /> largest [[right-truncatable prime]] in base 5
* '''2447''' – [[safe prime]]<ref name=":3" />
* '''2450''' – pronic number<ref name=A002378/>
* '''2456''' – sum of the totient function for the first 89 integers
* '''2458''' – centered heptagonal number<ref name=":10" />
* '''2459''' – [[Sophie Germain prime]], [[safe prime]]<ref name=":3" />
* '''2465''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 17, [[Carmichael number]]<ref name=":23">{{Cite OEIS|1=A002997|2=Carmichael numbers|access-date=2016-06-13}}</ref>
* '''2470''' – square pyramidal number<ref name=":11" />
* '''2471''' – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells<ref>{{cite OEIS|A000258|Expansion of e.g.f. exp(exp(exp(x)-1)-1)}}</ref>
* '''2477''' – [[super-prime]], [[cousin prime]]
* '''2480''' – sum of the totient function for the first 90 integers
* '''2481''' – centered pentagonal number<ref name=":5" />
* '''2484''' – nonagonal number<ref name=":14" />
* '''2485''' – triangular number, number of planar partitions of 13<ref>{{cite OEIS|A000219|Number of planar partitions (or plane partitions) of n}}</ref>
* '''2491''' = 47 * 53, consecutive [[prime numbers]], member of [[Ruth–Aaron pair]] with 2492 under second definition
* '''2492''' – member of Ruth–Aaron pair with 2491 under second definition

===2500 to 2599===
* '''2500''' = 50<sup>2</sup>, [[palindromic]] in base 7 (10201<sub>7</sub>)
* '''2501''' – Mertens function zero
* '''2502''' – Mertens function zero
* '''2503''' – Friedman prime
* '''2510''' – member of the Mian–Chowla sequence<ref name=":4" />
* '''2513''' – member of the [[Padovan sequence]]<ref>{{Cite OEIS|1=A000931|2=Padovan sequence|access-date=2016-06-13}}</ref>
* '''2517''' – Mertens function zero
* '''2519''' – the smallest number congruent to 1 (mod 2), 2 (mod 3), 3 (mod 4), ..., 9 (mod 10)
* '''[[2520 (number)|2520]]''' – [[superior highly composite number]]; smallest number divisible by numbers [[1 (number)|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 {{OEIS|id=A072938}}. Not only it is the 7th (and last) number with more divisors than any number double itself but is also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 {{OEIS|id=A095921}} which is a property the previous number with this pattern of divisors does not have ([[360 (number)|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 (number)|60]] is) and is not divisible by 1 to 7 (which [[420 (number)|420]] is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number {{OEIS|id=A106037}}.
* '''2521''' – [[star prime]], centered square number<ref name=":13" />
* '''2522''' – Mertens function zero
* '''2523''' – Mertens function zero
* '''2524''' – Mertens function zero
* '''2525''' – Mertens function zero
* '''2530''' – Mertens function zero, Leyland number<ref name=":15" />
* '''2533''' – Mertens function zero
* '''2537''' – Mertens function zero
* '''2538''' – Mertens function zero
* '''2543''' – [[Sophie Germain prime]], sexy prime with 2549
* '''2548''' = 14<sup>3</sup> - 14<sup>2</sup>
* '''2549''' – [[Sophie Germain prime]], [[super-prime]], sexy prime with 2543
* '''2550''' – pronic number<ref name=A002378/>
* '''2552''' – sum of the totient function for the first 91 integers
* '''2556''' – triangular number
* '''2567''' – Mertens function zero
* '''2568''' – Mertens function zero, number of digits in the [[decimal]] expansion of 1000[[factorial|!]], or the [[product (mathematics)|product]] of all [[natural number]]s from 1 to 1000
* '''2570''' – Mertens function zero
* '''2579''' – [[safe prime]]<ref name=":3" />
* '''2580''' – [[Keith number]],<ref name=":18" /> forms a column on a telephone or [[PIN pad]]
* '''2584''' – [[Fibonacci number]],<ref>{{Cite OEIS|1=A000045|2=Fibonacci numbers|access-date=2016-06-13}}</ref> sum of the first 37 primes
* '''2592''' – [[3-smooth]] number (2<sup>5</sup>×3<sup>4</sup>)
* '''2596''' – sum of the totient function for the first 92 integers

===2600 to 2699===
* '''2600''' – tetrahedral number,<ref name=":1" /> member of a [[Ruth–Aaron pair]] with 2601 (first definition)
** 2600 [[Hertz|Hz]] is the tone used by a [[blue box]] to defeat toll charges on [[long distance telephone call]]s
** ''[[2600: The Hacker Quarterly]]'' is a magazine named after the above
** The [[Atari 2600]] was a popular [[video game console]]
* '''2601''' = 51<sup>2</sup>, member of a [[Ruth–Aaron pair]] with 2600 (first definition)
* '''2609''' – [[super-prime]]
* '''2620''' – [[telephone number (mathematics)|telephone number]], [[amicable number]] with 2924
* '''2625''' = a [[centered octahedral number]]<ref name="ReferenceA"/>
* '''2626''' – decagonal number<ref name=":7" />
* '''2628''' – triangular number
* '''2632''' – number of consecutive baseball games played by [[Cal Ripken Jr.]]
* '''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<ref name=":5" />
* '''2647''' – [[super-prime]], centered heptagonal number<ref name=":10" />
* '''2652''' – pronic number<ref name=A002378/>
* '''2656''' – sum of the totient function for the first 93 integers
* '''2665''' – centered square number<ref name=":13" />
* '''2674''' – nonagonal number<ref name=":14" />
* '''2677''' – balanced prime<ref name=":22" />
* '''2680''' – number of [[Eight queens puzzle|11-queens problem]] solutions
* '''2683''' – [[super-prime]]
* '''2689''' – Mertens function zero, Proth prime<ref name=":12" />
* '''2693''' – [[Sophie Germain prime]]
* '''2699''' – [[Sophie Germain prime]]

===2700 to 2799===
* '''2701''' – triangular number, [[super-Poulet number]]<ref name=":6" />
* '''2702''' – sum of the totient function for the first 94 integers
* '''2704''' = 52<sup>2</sup>
* '''2707''' – [[strong prime]], model number for the concept supersonic airliner [[Boeing 2707]]
* '''{{Vanchor|2719}}''' – [[super-prime]], largest known odd number which cannot be expressed in the form [[Ramanujan's ternary quadratic form|''x''<sup>2</sup> + ''y''<sup>2</sup> + 10''z''<sup>2</sup>]] where ''x'', ''y'' and ''z'' are integers.<ref>{{cite encyclopedia|title=Odd numbers that are not of the form x^2+y^2+10*z^2.|url=http://oeis.org/search?q=3%2C+7%2C+21%2C+31%2C+33%2C+43%2C&language=english&go=Search|encyclopedia=The Online Encyclopedia of Integer Sequences|publisher=The OEIS Foundation, Inc.|access-date=13 November 2012}}</ref> In 1997 it was conjectured that this is also the largest such odd number.<ref name=Ono>{{cite journal|last=Ono|first=Ken|title=Ramanujan, taxicabs, birthdates, zipcodes and twists|journal=American Mathematical Monthly|year=1997|volume=104|issue=10|pages=912–917|url=http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/023.pdf|access-date=11 November 2012|doi=10.2307/2974471|jstor=2974471|citeseerx=10.1.1.514.8070|archive-date=15 October 2015|archive-url=https://web.archive.org/web/20151015193211/http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/023.pdf|url-status=dead}}</ref> It is now{{When|date=April 2024|reason=When is "now"?}} known this is true if the [[generalized Riemann hypothesis]] is true.<ref name=Ken>{{cite journal|last=Ono|first=Ken|author2=K Soundararajan|title=Ramanujan's ternary quadratic forms|journal=Inventiones Mathematicae|year=1997|volume=130|issue=3|pages=415–454|url=http://mathcs.emory.edu/~ono/publications-cv/pdfs/025.pdf|access-date=12 November 2012|doi=10.1007/s002220050191|bibcode=1997InMat.130..415O|citeseerx=10.1.1.585.8840|s2cid=122314044|archive-url=https://web.archive.org/web/20190718155256/http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/025.pdf|archive-date=18 July 2019|url-status=dead}}</ref>
* '''2728''' – [[Kaprekar number]]<ref name=":19" />
* '''2729''' – highly cototient number<ref name=":9" />
* '''2731''' – the only [[Wagstaff prime]] with four digits,<ref>{{Cite OEIS|1=A000979|2=Wagstaff primes|access-date=2016-06-13}}</ref> [[Jacobsthal prime]]
* '''2736''' – octahedral number<ref name=":20" />
* '''2741''' – [[Sophie Germain prime]], 400th prime number
* '''2744''' = 14<sup>3</sup>, palindromic in base 13 (1331<sub>13</sub>)
* '''2747''' – sum of the first 38 primes
* '''2749''' – [[super-prime]], [[cousin prime]] with 2753
* '''2753''' – [[Sophie Germain prime]], Proth prime<ref name=":12" />
* '''2756''' – pronic number<ref name=A002378/>
* '''2774''' – sum of the totient function for the first 95 integers
* '''2775''' – triangular number
* '''2780''' – member of the Mian–Chowla sequence<ref name=":4" />
* '''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<ref name=":21" />

===2800 to 2899===
* '''2801''' – first base 7 [[repunit]] prime
* '''2803''' – [[super-prime]]
* '''2806''' – [[centered pentagonal number]],<ref name=":5" /> sum of the totient function for the first 96 integers
* '''2809''' = 53<sup>2</sup>, centered octagonal number<ref name=":2" />
* '''2813''' – centered square number<ref name=":13" />
* '''2816''' – number of parts in all compositions of 10<ref>{{cite OEIS|A001792|2=a(n) = (n+2)*2^(n-1)}}</ref>
* '''2819''' – [[Sophie Germain prime]], [[safe prime]], sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)<ref name=":3" />
* '''2821''' – Carmichael number<ref name=":23" />
* '''2835''' – odd abundant number,<ref name=":17" /> decagonal number<ref name=":7" />
* '''2843''' – centered heptagonal prime<ref>{{Cite OEIS|1=A144974|2=Centered heptagonal prime numbers|access-date=2016-06-13}}</ref>
* '''2850''' – triangular number
* '''2862''' – pronic number<ref name=A002378/>
* '''2870''' – square pyramidal number<ref name=":11" />
* '''2871''' – nonagonal number<ref name=":14" />
* '''2872''' – [[tetranacci number]]<ref>{{Cite OEIS|1=A000078|2=Tetranacci numbers|access-date=2016-06-13}}</ref>
* '''2875''' – number of lines on a [[quintic threefold]]<ref>{{Citation | last1=Pandharipande | first1=Rahul | title=Rational curves on hypersurfaces (after A. Givental) | url=http://www.numdam.org/item?id=SB_1997-1998__40__307_0 | mr=1685628  | year=1998 | journal=Astérisque |volume=1997/98 |issue=252 | pages=307–340| arxiv=math/9806133 | bibcode=1998math......6133P }}</ref>
* '''2879''' – [[safe prime]]<ref name=":3" />
* '''2897''' – [[super-prime]], [[Markov prime]]<ref>{{Cite OEIS|1=A002559|2=Markoff (or Markov) numbers|access-date=2016-06-13}}</ref>

===2900 to 2999===
* '''2902''' – sum of the [[totient function]] for the first 97 integers
* '''2903''' – [[Sophie Germain prime]], [[safe prime]],<ref name=":3" /> balanced prime<ref name=":22" />
* '''2909''' – [[super-prime]]
* '''2914''' – sum of the first 39 primes
* '''2915''' – Lucas–Carmichael number<ref name=":0" />
* '''2916''' = 54<sup>2</sup>
* '''2924''' – amicable number with 2620
* '''2925''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 18, tetrahedral number,<ref name=":1" /> member of the Mian-Chowla sequence<ref name=":4" />
* '''2926''' – triangular number
* '''2939''' – [[Sophie Germain prime]]
* '''2944''' – sum of the totient function for the first 98 integers
* '''2963''' – [[Sophie Germain prime]], [[safe prime]], balanced prime<ref name=":22" />
* '''2964''' – number of parallelogram polyominoes with 11 cells<ref>{{cite OEIS|A006958|Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused)}}</ref>
* '''2965''' – greater of second pair of [[Smith number|Smith brothers]], centered square number<ref name=":13" />
* '''2969''' – [[Sophie Germain prime]]
* '''2970''' – [[harmonic divisor number]],<ref>{{Cite OEIS|1=A001599|2=Harmonic or Ore numbers|access-date=2016-06-13}}</ref> pronic number<ref name=A002378/>
* '''2976''' – centered pentagonal number<ref name=":5" />
* '''2988''' – number of reduced trees with 20 nodes<ref>{{cite OEIS|A000014|Number of series-reduced trees with n nodes}}</ref>
* '''2989''' – in [[hexadecimal]], reads as "[[evil|BAD]]"
* '''2997''' – 1000-gonal number<ref>{{Cite OEIS|1=A195163|2=1000-gonal numbers|access-date=2016-06-13}}</ref>
* '''2999''' – [[safe prime]]

===Prime numbers===
There are 127 [[prime number]]s between 2000 and 3000:<ref>{{Cite OEIS|A038823|Number of primes between n*1000 and (n+1)*1000}}</ref><ref>{{cite web |last=Stein |first=William A. |author-link=William A. Stein |title=The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture |url=https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/ |website=wstein.org |date=10 February 2017 |access-date=6 February 2021}}</ref>
: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 ==
{{reflist}}

{{Integers|10}}

[[Category:Integers]]