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2000 (number)

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

It is:

Selected numbers in the range 2001–2999

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2001 to 2099

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2100 to 2199

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2200 to 2299

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2300 to 2399

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2400 to 2499

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2500 to 2599

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  • 2500 = 502, palindromic in base 7 (102017)
  • 2501 – Mertens function zero
  • 2502 – Mertens function zero
  • 2503 – Friedman prime
  • 2510 – member of the Mian–Chowla sequence[23]
  • 2513 – member of the Padovan sequence[65]
  • 2517 – Mertens function zero
  • 2519 – the smallest number congruent to 1 (mod 2), 2 (mod 3), 3 (mod 4), ..., 9 (mod 10)
  • 2520superior 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 (sequence A072938 in the OEIS). 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 (sequence A095921 in the OEIS) 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 (sequence A106037 in the OEIS).
  • 2521star prime, centered square number[37]
  • 2522 – Mertens function zero
  • 2523 – Mertens function zero
  • 2524 – Mertens function zero
  • 2525 – Mertens function zero
  • 2530 – Mertens function zero, Leyland number[41]
  • 2533 – Mertens function zero
  • 2537 – Mertens function zero
  • 2538 – Mertens function zero
  • 2543Sophie Germain prime, sexy prime with 2549
  • 2549Sophie Germain prime, super-prime, sexy prime with 2543
  • 2550 – pronic number[32]
  • 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!, or the product of all natural numbers from 1 to 1000
  • 2570 – Mertens function zero
  • 2579safe prime[22]
  • 2580Keith number,[51] forms a column on a telephone or PIN pad
  • 2584Fibonacci number,[66] sum of the first 37 primes
  • 25923-smooth number (25×34)
  • 2596 – sum of the totient function for the first 92 integers

2600 to 2699

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2700 to 2799

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  • 2701 – triangular number, super-Poulet number[27]
  • 2702 – sum of the totient function for the first 94 integers
  • 2704 = 522
  • 2707strong prime, model number for the concept supersonic airliner Boeing 2707
  • 2719super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.[67] In 1997 it was conjectured that this is also the largest such odd number.[68] It is now[when?] known this is true if the generalized Riemann hypothesis is true.[69]
  • 2728Kaprekar number[52]
  • 2729 – highly cototient number[33]
  • 2731 – the only Wagstaff prime with four digits,[70] Jacobsthal prime
  • 2736 – octahedral number[53]
  • 2741Sophie Germain prime, 400th prime number
  • 2744 = 143, palindromic in base 13 (133113)
  • 2747 – sum of the first 38 primes
  • 2749super-prime, cousin prime with 2753
  • 2753Sophie Germain prime, Proth prime[36]
  • 2756 – pronic number[32]
  • 2774 – sum of the totient function for the first 95 integers
  • 2775 – triangular number
  • 2780 – member of the Mian–Chowla sequence[23]
  • 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[54]

2800 to 2899

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2900 to 2999

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Prime numbers

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There are 127 prime numbers between 2000 and 3000:[80][81]

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

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  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. ^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A022264 (n*(7*n - 1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A085945 (Number of subsets of {1,2,...,n} with relatively prime elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A064539 (Numbers n such that 2^n + n^2 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A001496 (Number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A000740 (Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A056721 (Numbers n such that 8*10^n-1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ a b Sloane, N. J. A. (ed.). "Sequence A006972 (Lucas-Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A194472 (Erdős-Nicolas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ "Can you solve it? 2019 in numbers". the Guardian. 2018-12-31. Retrieved 2021-09-19.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A294685 (non-isomorphic colorings of a toroidal n X k grid using exactly three colors under translational symmetry)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A141769 (Beginning of a run of 4 consecutive Niven (or Harshad) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A063416 (Multiples of 7 whose sum of digits is equal to 7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^ a b c d 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.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A038547 (Least number with exactly n odd divisors.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A144959 (A134955(n) - A134955(n-1). Number of hyperforests spanning n unlabeled nodes without isolated vertices.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A051841 (Number of binary Lyndon words with an even number of 1's)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. ^ a b Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  30. ^ a b 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.
  31. ^ Sloane, N. J. A. (ed.). "Sequence 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^ a b c Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  35. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  36. ^ a b c Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  37. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A000957 (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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  39. ^ a b c d e 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.
  40. ^ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ^ a b Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  42. ^ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A008918 (Numbers n such that 4*n = (n written backwards))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-14.
  44. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  45. ^ Mackenzie, Dana (2018). "2184: An Absurd (and Adsurd) Tale". Integers. 18.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A014575 (Vampire numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  47. ^ a b Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  49. ^ a b Sloane, N. J. A. (ed.). "Sequence A005231 (Odd abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  51. ^ a b 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.
  52. ^ a b Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  53. ^ a b Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  54. ^ a b c Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  55. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  57. ^ "The Small Groups library". Archived from the original on 2007-02-04. Retrieved 2008-01-22..
  58. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  59. ^ 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.
  60. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  61. ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  62. ^ a b Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  63. ^ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  64. ^ 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.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  66. ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  67. ^ "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.
  68. ^ Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists" (PDF). American Mathematical Monthly. 104 (10): 912–917. CiteSeerX 10.1.1.514.8070. doi:10.2307/2974471. JSTOR 2974471. Archived from the original (PDF) on 15 October 2015. Retrieved 11 November 2012.
  69. ^ Ono, Ken; K Soundararajan (1997). "Ramanujan's ternary quadratic forms" (PDF). Inventiones Mathematicae. 130 (3): 415–454. Bibcode:1997InMat.130..415O. CiteSeerX 10.1.1.585.8840. doi:10.1007/s002220050191. S2CID 122314044. Archived from the original (PDF) on 18 July 2019. Retrieved 12 November 2012.
  70. ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  71. ^ Sloane, N. J. A. (ed.). "Sequence A001792 (a(n) = (n+2)*2^(n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  72. ^ Sloane, N. J. A. (ed.). "Sequence A144974 (Centered heptagonal prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  73. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  74. ^ Pandharipande, Rahul (1998), "Rational curves on hypersurfaces (after A. Givental)", Astérisque, 1997/98 (252): 307–340, arXiv:math/9806133, Bibcode:1998math......6133P, MR 1685628
  75. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  76. ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  77. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  78. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  79. ^ Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  80. ^ 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.
  81. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.