2000 (number)

← 1999 2000 2001 →
Cardinaltwo thousand
Ordinal2000th
(two thousandth)
Factorization24 × 53
Greek numeral,Β´
Roman numeralMM, mm
Unicode symbol(s)MM, mm
Binary111110100002
Ternary22020023
Senary131326
Octal37208
Duodecimal11A812
Hexadecimal7D016
ArmenianՍ
Egyptian hieroglyph𓆽

2000 (two thousand) is a natural number following 1999 and preceding 2001.

In mathematics

2000 is:

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.

2016

2016 = 25 × 32 × 7. It is the second-smallest Erdős–Nicolas numberand a triangular number.

2017

2017 is a sexy prime with 2011.

2024

2024 = 23 × 11 × 23. It is a tetrahedral number.

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, lowest number with exactly 15 odd divisors. Sum of odd numbers from 1 to 89.

2027

2027 is a super-prime and a safe prime.

2029

2029 is a prime number and a member of the Mian–Chowla sequence.

2031

2031 = 3 × 677. It is a centered pentagonal number.

2035

2035 = 5 × 11 × 37. It is a Wolstenholme number.

2036

2036 = 22 × 509. It is an Eulerian number.

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, a Woodall number, a decagonal number, and a centered octahedral number.

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.

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.

2100 to 2199

2101

2101 = 11 × 191. It is a centered heptagonal number.

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.

2113

2113 is a Proth prime and a centered square number.

2116

2116 = 462 = 22 × 232.

2125

2125 = 53 × 17. It is a nonagonal number.

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.

2176

2176 = 27 × 17. It is a pentagonal pyramidal number and a centered pentagonal number.

2179

2179 is a prime number and a Wedderburn–Etherington number.

2187

2187 = 37. It is a vampire number and a perfect totient number.

2188

2188 = 22 × 547. It is a Motzkin number.

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 prime

2208

2208 – Keith number

2209

2209 = 472, palindromic in base 14 (B3B14), centered octagonal number

2211

2211 – triangular number

2221

2221 – super-prime, happy number

2223

2223 – Kaprekar number

2232

2232 – decagonal number

2245

2245 – centered square number

2254

2254 – member of the Mian–Chowla sequence

2255

2255 – octahedral number

2269

2269 – super-prime, cuban prime

2273

2273 – Sophie Germain prime

2276

2276 _ centered heptagonal number

2278

2278 – triangular number

2281

2281 – star number,

2287

2287 – balanced prime

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 primorial

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 128

2331

2331 – centered cube number

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 number

2357

2357 – Smarandache–Wellin prime

2378

2378 – Pell number

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 number

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 13

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

2600 to 2699

2700 to 2799

2800 to 2899

2900 to 2999

Prime numbers

There are 127 prime numbers 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

  1. ↑ Sloane, N. J. A. (ed.). "Sequence A052486 (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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "Sequence A006933 ('Eban' numbers (the letter 'e' is banned!))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "Sequence A008537 (Numbers that do not contain the letter 'n'))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. 1 2 Sloane, N. J. A. (ed.). "Sequence A006972 (Lucas-Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "Sequence A194472 (Erdős-Nicolas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ↑ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. 1 2 3 4 Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. 1 2 3 4 Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ↑ Sloane, N. J. A. (ed.). "Sequence A038547 (Least number with exactly n odd divisors.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. 1 2 3 4 5 6 7 8 9 10 11 Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. 1 2 3 4 5 6 Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. 1 2 3 4 5 6 7 Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ↑ Sloane, N. J. A. (ed.). "Sequence A007408 (Wolstenholme numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ↑ Sloane, N. J. A. (ed.). "Sequence A000295 (Eulerian numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. 1 2 Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ↑ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. 1 2 3 4 5 Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. 1 2 Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ↑ Sloane, N. J. A. (ed.). "Sequence A011971 (Aitken's array)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. 1 2 3 Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. 1 2 3 4 Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  22. 1 2 3 Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  23. 1 2 3 Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  24. 1 2 3 4 5 6 7 Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  25. 1 2 3 4 5 Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  26. ↑ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. ↑ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  28. ↑ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  29. ↑ Sloane, N. J. A. (ed.). "Sequence A014575 (Vampire numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  30. 1 2 Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  31. ↑ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  32. ↑ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  33. 1 2 Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  34. 1 2 Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  35. 1 2 Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  36. 1 2 3 Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  37. 1 2 3 4 5 Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  38. ↑ Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  39. ↑ "The Small Groups library". Archived from the original on 2007-02-04. Retrieved 2008-01-22..
  40. ↑ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  41. 1 2 3 4 5 6 7 Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  42. ↑ Sloane, N. J. A. (ed.). "Sequence A069151 (Concatenations of consecutive primes, starting with 2, that are also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  43. ↑ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  44. 1 2 Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  45. ↑ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  46. ↑ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  47. ↑ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  48. ↑ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  49. ↑ "Odd numbers that are not of the form x^2+y^2+10*z^2.". The Online Encyclopedia of Integer Sequences. The OEIS Foundation, Inc. Retrieved 13 November 2012.
  50. ↑ Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists" (PDF). American Mathematical Monthly. 104 (10): 912–917. doi:10.2307/2974471. JSTOR 2974471. Archived from the original (PDF) on 15 October 2015. Retrieved 11 November 2012.
  51. ↑ Ono, Ken; K Soundararajan (1997). "Ramanujan's ternary quadratic forms" (PDF). Inventiones Mathematicae. 130 (3): 415–454. Bibcode:1997InMat.130..415O. doi:10.1007/s002220050191. S2CID 122314044. Archived from the original (PDF) on 18 July 2019. Retrieved 12 November 2012.
  52. ↑ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  53. ↑ Sloane, N. J. A. (ed.). "Sequence A144974 (Centered heptagonal prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  54. ↑ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  55. ↑ Pandharipande, Rahul (1998), "Rational curves on hypersurfaces (after A. Givental)", Astérisque, 1997/98 (252): 307–340, arXiv:math/9806133, Bibcode:1998math......6133P, MR 1685628
  56. ↑ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  57. ↑ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  58. ↑ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  59. ↑ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.