2000 (number)

2,000 other uses 2000 (disambiguation) millennium 2000 Y2K (disambiguation)Y2K 2000 MM, mm Armenian Ս Egyptian hieroglyph 𓆽 two thousand 2000 (two thousand) is a natural number following 1999 and preceding 2001. In mathematics 2000 is: the highest number expressible using only two unmodified characters in Roman numerals (MM) an Achilles numberA052486 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 smallest four digit eban numberA006933 'Eban' numbers (the letter 'e' is banned!)Weisstein Eric W. Eban Number https://mathworld.wolfram.com/EbanNumber.html 2026-10-22 mathworld.wolfram.com Wolfram Research, Inc. en the sum of all the nban numbers A008537A008537 Numbers that do not contain the letter 'n') Selected numbers in the range 2001–2999 2001 to 2099 2002 2002 = 2 × 7 × 11 × 13. It is a palindromic number in decimal, base 76, 90, 142, and 11 other non-trivial bases. 2003 2003 is a Sophie Germain prime. 2005 2005 = 5 × 401. It is a vertically symmetric number. 2011 2011 is a sexy prime with 2017. It is also the sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 2015 2015 = 5 × 13 × 31. It is a Lucas–Carmichael number.A006972 Lucas-Carmichael numbersWeisstein Eric W. Lucas-Carmichael Number https://mathworld.wolfram.com/Lucas-CarmichaelNumber.html 2026-10-22 mathworld.wolfram.com Wolfram Research, Inc. en 2016 2016 = 25 × 32 × 7. It is the second-smallest Erdős–Nicolas numberA194472 Erdős-Nicolas numbersand a triangular number.A000217 Triangular numbers 2017 2017 is a sexy prime with 2011. 2024 2024 = 23 × 11 × 23. It is a tetrahedral number.A000292 Tetrahedral numbers 2025 2025 = 452, 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,A016754 Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers lowest number with exactly 15 odd divisors.A038547 Least number with exactly n odd divisors. Sum of odd numbers from 1 to 89. 2027 2027 is a super-prime and a safe prime.A005385 Safe primes 2029 2029 is a prime number and a member of the Mian–Chowla sequence.A005282 Mian-Chowla sequence 2031 2031 = 3 × 677. It is a centered pentagonal number.A005891 Centered pentagonal numbers 2035 2035 = 5 × 11 × 37. It is a Wolstenholme number.A007408 Wolstenholme numbers 2036 2036 = 22 × 509. It is an Eulerian number.A000295 Eulerian numbers 2039 2039 is a Sophie Germain prime and a safe prime. 2047 2047 = 23 × 89 = 211 − 1 and it is the first Mersenne number that is composite for a prime exponent. It is a super-Poulet number,A050217 Super-Poulet numbers a Woodall number,A003261 Woodall numbers a decagonal number,A001107 10-gonal (or decagonal) numbers and a centered octahedral number.A001845 Centered octahedral numbers (crystal ball sequence for cubic lattice) 2048 2048=2^11 2053 2053 is a prime number and a star number. 2056 2056 = 23 × 257. It is the magic constant of an n × n normal magic square and the n-queens problem for n = 16. 2063 2063 is a Sophie Germain prime, a safe prime, and a super-prime. 2066 2066 = 2 × 1033. It is a Bell number.A011971 Aitken's array 2069 2069 is a Sophie Germain prime. 2080 2080 = 25 × 5 × 13. It is a triangular number. 2081, 2083, 2087, and 2089 2081, 2083, 2087, and 2089 form a prime quadruplet. 2081 is also a super-prime. 2099 2099 is a super-prime, a safe prime, and a highly cototient number.A100827 Highly cototient numbers 2100 to 2199 2101 2101 = 11 × 191. It is a centered heptagonal number.A069099 Centered heptagonal numbers 2016-06-13 2107 and 2108 2107 and 2108 form a Ruth–Aaron pair under the first definition. 2109 2109 = 3 × 19 × 37. It is a square pyramidal number.A000330 Square pyramidal numbers 2016-06-13 2113 2113 is a Proth primeA080076 Proth primes 2016-06-13 and a centered square number.A001844 Centered square numbers 2016-06-13 2116 2116 = 462 = 22 × 232. 2125 2125 = 53 × 17. It is a nonagonal number.A001106 9-gonal (or enneagonal or nonagonal) numbers 2016-06-13 2129 2129 is a Sophie Germain prime. 2141 2141 is a Sophie Germain prime. 2145 2145 = 3 × 5 × 11 × 13. It is a triangular number. 2160 2160 = 24 × 33 × 5. It is a largely composite number.A067128 Ramanujan's largely composite numbers 2176 2176 = 27 × 17. It is a pentagonal pyramidal numberA002411 Pentagonal pyramidal numbers 2016-06-13 and a centered pentagonal number. 2179 2179 is a prime number and a Wedderburn–Etherington number.A001190 Wedderburn-Etherington numbers 2016-06-13 2187 2187 = 37. It is a vampire numberA014575 Vampire numbers 2016-06-13 and a perfect totient number.A082897 Perfect totient numbers 2016-06-13 2188 2188 = 22 × 547. It is a Motzkin number.A001006 Motzkin numbers 2016-06-13 2199 2199 = 3 × 733. It is a perfect totient number. 2200 to 2299 2201 2201 – only known non-palindromic number whose cube is palindromic; also no known fourth or higher powers are palindromic for non-palindromic numbers 2207 2207 – safe prime, Lucas primeA005479 Prime Lucas numbers 2016-06-13 2208 2208 – Keith numberA007629 Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers) 2016-06-13 2209 2209 = 472, palindromic in base 14 (B3B14), centered octagonal number 2211 2211 – triangular number 2221 2221 – super-prime, happy number 2223 2223 – Kaprekar numberA006886 Kaprekar numbers 2016-06-13 2232 2232 – decagonal number 2245 2245 – centered square number 2254 2254 – member of the Mian–Chowla sequence 2255 2255 – octahedral numberA005900 Octahedral numbers 2016-06-13 2269 2269 – super-prime, cuban primeA002407 Cuban primes 2016-06-13 2273 2273 – Sophie Germain prime 2276 2276 _ centered heptagonal number 2278 2278 – triangular number 2281 2281 – star number, 2287 2287 – balanced primeA006562 Balanced primes 2016-06-13 2299 2299 – member of a Ruth–Aaron pair with 2300 (first definition) 2300 to 2399 2300 2300 – tetrahedral number, member of a Ruth–Aaron pair with 2299 (first definition) 2301 2301 – nonagonal number 2309 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number 2310 2310 – fifth primorialA002110 Primorial numbers 2016-06-13 2311 2311 – primorial prime, twin prime with 2309 2326 2326 – centered pentagonal number 2328 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128http://www-public.tu-bs.de:8080/~beick/soft/small/small.html The Small Groups library 2008-01-22 dead https://web.archive.org/web/20070204070922/http://www-public.tu-bs.de:8080/~beick/soft/small/small.html 2007-02-04 . 2331 2331 – centered cube numberA005898 Centered cube numbers 2016-06-13 2339 2339 – Sophie Germain prime, twin prime with 2341 2341 2341 – super-prime, twin prime with 2339 2346 2346 – triangular number 2351 2351 – Sophie Germain prime, super-prime 2352 2352 – pronic numberA002378 Oblong (or promic, pronic, or heteromecic) numbers 2357 2357 – Smarandache–Wellin primeA069151 Concatenations of consecutive primes, starting with 2, that are also prime 2016-06-13 2378 2378 – Pell numberA000129 Pell numbers 2016-06-13 2379 2379 – member of the Mian–Chowla sequence 2381 2381 – super-prime, centered square number 2393 2393 – Sophie Germain prime 2399 2399 – Sophie Germain prime 2400 to 2499 2401 2401 = 492 = 74, centered octagonal number 2415 2415 – triangular number 2417 2417 – super-prime, balanced prime 2425 2425 – decagonal number 2437 2437 – cuban prime, largest right-truncatable prime in base 5 2447 2447 – safe prime 2450 2450 – pronic number 2458 2458 – centered heptagonal number 2459 2459 – Sophie Germain prime, safe prime 2465 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael numberA002997 Carmichael numbers 2016-06-13 2470 2470 – square pyramidal number 2477 2477 – super-prime, cousin prime 2481 2481 – centered pentagonal number 2484 2484 – nonagonal number 2485 2485 – triangular number, number of planar partitions of 13A000219 Number of planar partitions (or plane partitions) of n 2491 2491 = member of Ruth–Aaron pair with 2492 under second definition 2492 2492 – member of Ruth–Aaron pair with 2491 under second definition 2500 to 2599 2510 – member of the Mian–Chowla sequence 2513 – member of the Padovan sequenceA000931 Padovan sequence 2016-06-13 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 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 A095921 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 is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number A106037. 2521 – star prime, centered square number 2530 – Leyland numberA076980 Leyland numbers 2016-06-13 2543 – Sophie Germain prime, sexy prime with 2549 2549 – Sophie Germain prime, super-prime, sexy prime with 2543 2550 – pronic number 2556 – triangular number 2579 – safe prime, palindromic prime in bases 5, 25, and 28: 2579 = 403045 = 43425 = 38328 2580 – Keith number, 2584 – Fibonacci number,A000045 Fibonacci numbers 2016-06-13 2600 to 2699 2600 – tetrahedral number, member of a Ruth–Aaron pair with 2601 (first definition) 2601 = 512, member of a Ruth–Aaron pair with 2600 (first definition) 2609 – super-prime 2620 – telephone number, amicable number with 2924 2625 = a centered octahedral number 2626 – decagonal number 2628 – triangular number 2641 – centered pentagonal number 2647 – super-prime, centered heptagonal number 2652 – pronic number 2665 – centered square number 2674 – nonagonal number 2677 – balanced prime 2680 – number of 11-queens problem solutions 2683 – super-prime 2689 – Proth prime 2693 – Sophie Germain prime 2699 – Sophie Germain prime 2700 to 2799 2701 – triangular number, super-Poulet number 2702 – sum of the totient function for the first 94 integers 2707 – strong prime 2719 – super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.Odd numbers that are not of the form x^2+y^2+10*z^2. http://oeis.org/search?q=3%2C+7%2C+21%2C+31%2C+33%2C+43%2C&language=english&go=Search The Online Encyclopedia of Integer Sequences The OEIS Foundation, Inc. 13 November 2012 In 1997 it was conjectured that this is also the largest such odd number.Ono Ken Ramanujan, taxicabs, birthdates, zipcodes and twists American Mathematical Monthly 1997 104 10 912–917 http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/023.pdf 11 November 2012 10.2307/2974471 2974471 15 October 2015 https://web.archive.org/web/20151015193211/http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/023.pdf dead It is nowApril 2024 When is "now"? known this is true if the generalized Riemann hypothesis is true.Ono Ken K Soundararajan Ramanujan's ternary quadratic forms Inventiones Mathematicae 1997 130 3 415–454 http://mathcs.emory.edu/~ono/publications-cv/pdfs/025.pdf 12 November 2012 10.1007/s002220050191 1997InMat.130..415O 122314044 https://web.archive.org/web/20190718155256/http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/025.pdf 18 July 2019 dead 2728 – Kaprekar number 2729 – highly cototient number 2731 – the only Wagstaff prime with four digits,A000979 Wagstaff primes 2016-06-13 Jacobsthal prime 2736 – octahedral number 2741 – Sophie Germain prime, 400th prime number 2744 = 143, palindromic in base 13 (133113) 2747 – sum of the first 38 primes 2749 – super-prime, cousin prime with 2753 2753 – Sophie Germain prime, 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 prime 2803 – super-prime 2806 – centered pentagonal number, sum of the totient function for the first 96 integers 2809 = 532, centered octagonal number 2813 – centered square number 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421) 2821 – Carmichael number 2835 – decagonal number 2843 – centered heptagonal primeA144974 Centered heptagonal prime numbers 2016-06-13 2850 – triangular number 2862 – pronic number 2870 – square pyramidal number 2871 – nonagonal number 2872 – tetranacci numberA000078 Tetranacci numbers 2016-06-13 2875 – number of lines on a quintic threefoldPandharipande Rahul Rational curves on hypersurfaces (after A. Givental) http://www.numdam.org/item?id=SB_1997-1998__40__307_0 1685628 1998 Astérisque 1997/98 252 307–340 math/9806133 1998math......6133P 2879 – safe prime 2897 – super-prime, Markov primeA002559 Markoff (or Markov) numbers 2016-06-13 2900 to 2999 2903 – Sophie Germain prime, safe prime, balanced prime 2909 – super-prime 2915 – Lucas–Carmichael number 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 2963 – Sophie Germain prime, safe prime, balanced prime 2965 – greater of second pair of Smith brothers, centered square number 2969 – Sophie Germain prime 2970 – harmonic divisor number,A001599 Harmonic or Ore numbers 2016-06-13 pronic number 2976 – centered pentagonal number 2999 – safe prime Prime numbers There are 127 prime numbers between 2000 and 3000:A038823 Number of primes between n*1000 and (n+1)*1000Stein William A. William A. Stein The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/ wstein.org 10 February 2017 6 February 2021 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 10 Category:Integers