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2000 (two thousand) is a natural number following 1999 and preceding 2001. Two thousand is the highest number expressible using only two unmodified characters in Roman numerals (MM). Two thousand is also:

In the name of the products Lever 2000 and Grecian 2000, Windows 2000 In Star Trek, the registry number of the USS Excelsior, NX-2000 in Star Trek III: The Search for Spock, and NCC-2000 commanded by Hikaru Sulu in Star Trek VI: The Undiscovered Country. In the name of a broomstick from the Harry Potter series, the Nimbus 2000, in Harry Potter and the Philosopher's Stone, Harry Potter and the Chamber of Secrets, and Harry Potter and the Prisoner of Azkaban. The postal code for Antwerp (Belgium), Frederiksberg (Denmark), and Sydney (Australia) The chess rating required to achieve "Expert" level in the United States Chess Federation chess rating system.

Contents

1 Selected numbers in the range 2001–2999

1.1 2001 to 2099 1.2 2100 to 2199 1.3 2200 to 2299 1.4 2300 to 2399 1.5 2400 to 2499 1.6 2500 to 2599 1.7 2600 to 2699 1.8 2700 to 2799 1.9 2800 to 2899 1.10 2900 to 2999

2 References

Selected numbers in the range 2001–2999[edit] 2001 to 2099[edit]

2001 – sphenic number 2002 – palindromic number 2003 – Sophie Germain prime and the smallest prime number in the 2000s 2005 – A vertically symmetric number 2009 – 74 − 73 − 72 2011 – Sexy prime number. Also, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211. 2015 – Lucas–Carmichael number[1] 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number,[2] 211-25. 2017 – Mertens function zero. (2011, 2017) is a sexy prime pair. 2020 – sum of the totient function for the first 81 integers 2024 – tetrahedral number[3] 2025 – 452, sum of the cubes of the first nine integers, centered octagonal number[4] 2027 – super-prime, safe prime[5] 2029 – member of the Mian–Chowla sequence[6] 2030 – 212 + 222 + 232 + 242 = 252 + 262 + 272 2031 – centered pentagonal number[7] 2039 – Sophie Germain prime, safe prime[5] 2047 – super-Poulet number,[8] Woodall number,[9] decagonal number.[10] Also, 2047 = 211 − 1 = 23 × 89 and is the first Mersenne number that is composite for a prime exponent. 2048 – power of two 211 2053 – star number 2056 – magic constant of n × n normal magic square and n-queens problem for n = 16. 2060 – sum of the totient function for the first 82 integers 2063 – Sophie Germain prime, safe prime.[5] super-prime 2069 – Sophie Germain prime 2070 – pronic number[11] 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,[5] highly cototient number[12]

2100 to 2199[edit]

2100 – Mertens function zero 2101 – centered heptagonal number[13] 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[14] 2112 – The break-through album of the band Rush 2113 – Mertens function zero, Proth prime,[15] centered square number[16] 2116 – 462 2117 – Mertens function zero 2119 – Mertens function zero 2120 – Mertens function zero 2122 – Mertens function zero 2125 – nonagonal number[17] 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 22π4 2145 – triangular number 2162 – pronic number[11] 2166 – sum of the totient function for the first 84 integers 2169 – Leyland number[18] 2171 – Mertens function zero 2172 – Mertens function zero 2175 – smallest number requiring 143 seventh powers for Waring representation 2176 – pentagonal pyramidal number,[19] centered pentagonal number[7] 2178 – first natural integer which digits in its decimal expression get reversed when multiplied by 4.[20] 2179 – Wedderburn–Etherington number[21] 2187 – 37, vampire number,[22] perfect totient number[23] 2188 – Motzkin number[24] 2197 – 133, palindromic in base 12 (133112) 2199 – perfect totient number[23]

2200 to 2299[edit]

2201 – only known non-palindromic number whose cube is palindromic; also no known fourth or higher powers are palindromic for non-palindromic numbers 2205 – odd abundant number[25] 2207 – safe prime,[5] Lucas prime[26] 2208 – Keith number[27] 2209 – 472, palindromic in base 14 (B3B14), centered octagonal number[4] 2211 – triangular number 2221 – super-prime, happy number 2222 – repdigit 2223 – Kaprekar number[28] 2230 – sum of the totient function for the first 85 integers 2232 – decagonal number[10] 2236 – Harshad Number 2245 – centered square number[16] 2254 – member of the Mian–Chowla sequence[6] 2255 – octahedral number[29] 2256 – pronic number[11] 2269 – super-prime, cuban prime[30] 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[13] 2278 – triangular number 2281 – star number 2287 – balanced prime[31] 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[edit]

2300 – tetrahedral number,[3] member of a Ruth–Aaron pair with 2299 (first definition) 2301 – nonagonal number[17] 2304 – 482 2306 – Mertens function zero 2309 – primorial prime, Mertens function zero, highly cototient number[12] 2310 – fifth primorial[32] 2311 – primorial prime 2321 – Mertens function zero 2322 – Mertens function zero 2326 – centered pentagonal number[7] 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128[33] 2331 – centered cube number[34] 2338 – Mertens function zero 2339 – Sophie Germain prime 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[11] 2357 – Smarandache–Wellin prime[35] 2368 – sum of the totient function for the first 88 integers 2378 – Pell number[36] 2379 – member of the Mian–Chowla sequence[6] 2381 – super-prime, centered square number[16] 2383 (2384) – number of delegates required to win the 2016 Democratic Party presidential primaries (out of 4051) 2393 – Sophie Germain prime 2397 – sum of the squares of the first ten primes 2399 – Sophie Germain prime

2400 to 2499[edit]

2400 – perfect score on SAT tests administered after 2005 2401 – 74, 492, centered octagonal number[4] 2415 – triangular number 2417 – super-prime, balanced prime[31] 2425 – decagonal number[10] 2427 – sum of the first 36 primes 2431 – product of three consecutive primes 2437 – cuban prime[30] 2447 – safe prime[5] 2450 – pronic number[11] 2456 – sum of the totient function for the first 89 integers 2458 – centered heptagonal number[13] 2459 – Sophie Germain prime, safe prime[5] 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number[37] 2470 – square pyramidal number[14] 2477 – super-prime, cousin prime 2480 – sum of the totient function for the first 90 integers 2481 – centered pentagonal number[7] 2484 – nonagonal number[17] 2485 – triangular number 2491 – member of Ruth–Aaron pair with 2492 under second definition 2492 – member of Ruth–Aaron pair with 2491 under second definition

2500 to 2599[edit]

2500 – 502, palindromic in base 7 (102017) 2501 – Mertens function zero 2502 – Mertens function zero 2510 – member of the Mian–Chowla sequence[6] 2513 – member of the Padovan sequence[38] 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.(sequence A072938 in the OEIS) 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 (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) 2521 – star number, centered square number[16] 2522 – Mertens function zero 2523 – Mertens function zero 2524 – Mertens function zero 2525 – Mertens function zero 2530 – Mertens function zero, Leyland number[18] 2533 – Mertens function zero 2537 – Mertens function zero 2538 – Mertens function zero 2543 – Sophie Germain prime 2549 – Sophie Germain prime, super-prime 2550 – pronic number[11] 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 of all natural numbers from 1 to 1000. 2570 – Mertens function zero 2579 – safe prime[5] 2580 – Keith number[27] 2584 – Fibonacci number,[39] sum of the first 37 primes 2596 – sum of the totient function for the first 92 integers

2600 to 2699[edit]

2600 – tetrahedral number,[3] member of a Ruth–Aaron pair with 2601 (first definition)

2600 Hz is the tone used by a blue box to defeat toll charges on long distance telephone calls. 2600: The Hacker Quarterly is a magazine named after the above. The Atari 2600 was a popular video game console.

2601 – 512, member of a Ruth–Aaron pair with 2600 (first definition) 2609 – super-prime 2620 – amicable number with 2924 2626 – decagonal number[10] 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[7] 2647 – super-prime, centered heptagonal number[13] 2652 – pronic number 2656 – sum of the totient function for the first 93 integers 2665 – centered square number[16] 2674 – nonagonal number[17] 2677 – balanced prime[31] 2680 – number of 11-queens problem solutions 2683 – super-prime 2689 – Mertens function zero, Proth prime[15] 2693 – Sophie Germain prime 2699 – Sophie Germain prime

2700 to 2799[edit]

2701 – triangular number, super-Poulet number[8] 2702 – sum of the totient function for the first 94 integers 2704 – 522 2719 – super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.[40] In 1997 it was conjectured that this is also the largest such odd number.[41] It is now known this is true if the generalized Riemann hypothesis is true.[42] 2728 – Kaprekar number[28] 2729 – highly cototient number[12] 2731 – Wagstaff prime[43] 2736 – octahedral number[29] 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[15] 2756 – pronic number 2774 – sum of the totient function for the first 95 integers 2775 – triangular number 2780 – member of the Mian–Chowla sequence[6] 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[30]

2800 to 2899[edit]

2801 – first base 7 repunit prime 2803 – super-prime 2806 – centered pentagonal number,[7] sum of the totient function for the first 96 integers 2809 – 532, centered octagonal number[4] 2813 – centered square number[16] 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)[5] 2821 – Carmichael number[37] 2835 – odd abundant number,[25] decagonal number[10] 2843 – centered heptagonal prime[44] 2850 – triangular number 2862 – pronic number 2870 – square pyramidal number[14] 2871 – nonagonal number[17] 2872 – tetranacci number[45] 2879 – safe prime[5] 2897 – super-prime, Markov number[46]

2900 to 2999[edit]

2902 – sum of the totient function for the first 97 integers 2903 – Sophie Germain prime, safe prime,[5] balanced prime[31] 2909 – super-prime 2914 – sum of the first 39 primes 2915 – Lucas–Carmichael number[1] 2916 – 542 2924 – amicable number with 2620 2925 – magic constant of n × n normal magic square and n-queens problem for n = 18, tetrahedral number,[3] member of the Mian-Chowla sequence[6] 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[31] 2965 – greater of second pair of Smith brothers, centered square number[16] 2969 – Sophie Germain prime 2970 – harmonic divisor number,[47] pronic number 2976 – centered pentagonal number[7] 2997 – chiliagonal number[48] 2999 – safe prime

References[edit]

^ a b Sloane, N.J.A. (ed.). "Sequence A006972 (Lucas-Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A194472 (Erdős-Nicolas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ a b c d Sloane, N.J.A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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. Retrieved 2016-06-13.  ^ 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. Retrieved 2016-06-13.  ^ 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. Retrieved 2016-06-13.  ^ 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. Retrieved 2016-06-13.  ^ a b Sloane, N.J.A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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. Retrieved 2016-06-13.  ^ a b c d e f Sloane, N.J.A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ a b c Sloane, N.J.A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ 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.  ^ 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.  ^ 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.  ^ 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.  ^ a b Sloane, N.J.A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ Sloane, N.J.A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A014575 (Vampire numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ Sloane, N.J.A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ Sloane, N.J.A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ a b Sloane, N.J.A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ a b Sloane, N.J.A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ 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.  ^ Sloane, N.J.A. (ed.). "Sequence A002110 (Primorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ "Archived copy". Archived from the original on 2007-02-04. Retrieved 2008-01-22. . ^ Sloane, N.J.A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ 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.  ^ Sloane, N.J.A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ a b Sloane, N.J.A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ "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.  ^ Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists" (PDF). American Mathematical Monthly. 104 (10): 912–917. doi:10.2307/2974471. Retrieved 11 November 2012.  ^ Ono, Ken; K Soundararajan (1997). "Ramanujan's ternary quadratic forms" (PDF). Inventiones Mathematicae. 130 (3): 415–454. doi:10.1007/s002220050191. Retrieved 12 November 2012.  ^ Sloane, N.J.A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A144974 (Centered heptagonal prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.  ^ Sloane, N.J.A. (ed.). "Sequence A195163 (1000-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-

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