2000 (number)

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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^[1]
• smallest four digit eban number^[2]
• the sum of all the nban numbers in the sequence^[3]

• 2001 – sphenic number^[4]
• 2002 – 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 crystagon^[5]
• 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^[6]
• 2007 – 2²⁰⁰⁷ + 2007² is prime^[7]
• 2008 – number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to 3^[8]
• 2009 = 7⁴ − 7³ − 7²
• 2010 – number of compositions of 12 into relatively prime parts^[9]
• 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 × 10²⁰¹² − 1 is a prime number^[10]
• 2013 – number of widely totally strongly normal compositions of 17
• 2014 – 5 × 2²⁰¹⁴ - 1 is prime^[11]
• 2015 – Lucas–Carmichael number^[12]
• 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number,^[13] 2¹¹-2⁵
• 2017 – Mertens function zero, sexy prime with 2011
• 2018 – 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 = 7² + 11² + 43² = 7² + 17² + 41² = 13² + 13² + 41² = 11² + 23² + 37² = 17² + 19² + 37² = 23² + 23² + 31^2[14]
• 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,^[15] beginning of a run of 4 consecutive Niven numbers^[16]
• 2023 = 7 * 17² – multiple of 7 with digit sum equal to 7,^[17] sum of squares of digits equals 17
• 2024 – tetrahedral number,^[18] number of the current calendar year
• 2025 = 45², sum of the cubes of the first nine positive integers (and therefore square of the sum of the first nine positive integers), centered octagonal number;^[19] least number with 15 odd divisors^[20]
• 2026 = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices^[21]
• 2027 – super-prime, safe prime^[22]
• 2028 = 13³ – 13²
• 2029 – member of the Mian–Chowla sequence^[23]
• 2030 = 21² + 22² + 23² + 24² = 25² + 26² + 27²
• 2031 – centered pentagonal number^[24]
• 2032 = number of binary Lyndon words of length 16 with an even number of 1's^[25]
• 2033 = number of rooted trees with 9 nodes and a single labeled node^[26]
• 2034 = number of unlabeled graphs on 11 nodes whose components are unicyclic graphs^[27]
• 2035 – Wolstenholme number^[28]
• 2036 – Eulerian number^[29]
• 2039 – Sophie Germain prime, safe prime^[22]
• 2045 – number of partially ordered set with 7 unlabeled elements^[30]
• 2047 – super-Poulet number,^[31] Woodall number,^[32] decagonal number,^[33] a centered octahedral number,^[34] 2047 = 2¹¹ - 1 = 23 × 89 and is the first Mersenne number that is composite for a prime exponent
• 2048 = 2¹¹
• 2050 – sum of 2 consecutive odd squares (31² + 33²)
• 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,^[22] super-prime
• 2068 – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed^[35]
• 2069 – Sophie Germain prime
• 2070 – pronic number^[36]
• 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,^[22] highly cototient number^[37]

• 2100 – Mertens function zero
• 2101 – centered heptagonal number^[38]
• 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,^[39] the sum of the third and last trio of three-digit permutable primes in decimal: 199 + 919 + 991
• 2112 – The break-through album of the band Rush
• 2113 – Mertens function zero, Proth prime,^[40] centered square number^[41]
• 2116 = 46²
• 2117 – Mertens function zero
• 2119 – Mertens function zero
• 2120 – Mertens function zero, Fine number^[42]
• 2122 – Mertens function zero
• 2125 – nonagonal number^[43]
• 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
• 2153 – with 2161, smallest consecutive primes that have the same sum of digits as each other's prime indices
• 2160 – largely composite number^[44]
• 2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
• 2162 – pronic number^[36]
• 2166 – sum of the totient function for the first 84 integers
• 2169 – Leyland number^[45]
• 2171 – Mertens function zero
• 2172 – Mertens function zero
• 2175 – smallest number requiring 143 seventh powers for Waring representation
• 2176 – pentagonal pyramidal number,^[46] centered pentagonal number,^[24] number of prime knots with 12 crossings
• 2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4^[47]
• 2179 – Wedderburn–Etherington prime^[48]
• 2184 – equals both 3⁷ − 3 and 13³ − 13 and is believed to be the only such doubly strictly absurd number^{[49][unreliable source?]}
• 2187 = 3⁷, vampire number,^[50] perfect totient number^[51]
• 2188 – Motzkin number^[52]
• 2197 = 13³, palindromic in base 12 (1331₁₂)
• 2199 – perfect totient number^[51]

• 2201 – only known non-palindromic number whose cube is palindromic; also no known fourth or higher powers are palindromic for non-palindromic numbers
• 2203 – Mersenne prime exponent
• 2205 – odd abundant number^[53]
• 2207 – safe prime,^[22] Lucas prime^[54]
• 2208 – Keith number^[55]
• 2209 = 47², palindromic in base 14 (B3B₁₄), centered octagonal number^[19]
• 2211 – triangular number
• 2221 – super-prime, happy number
• 2222 – repdigit
• 2223 – Kaprekar number^[56]
• 2230 – sum of the totient function for the first 85 integers
• 2232 – decagonal number^[33]
• 2236 – Harshad number
• 2245 – centered square number^[41]
• 2254 – member of the Mian–Chowla sequence^[23]
• 2255 – octahedral number^[57]
• 2256 – pronic number^[36]
• 2269 – super-prime, cuban prime^[58]
• 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^[38]
• 2278 – triangular number
• 2281 – star number, Mersenne prime exponent
• 2287 – balanced prime^[59]
• 2294 – Mertens function zero
• 2295 – Mertens function zero
• 2296 – Mertens function zero
• 2299 – member of a Ruth–Aaron pair with 2300 (first definition)

• 2300 – tetrahedral number,^[18] member of a Ruth–Aaron pair with 2299 (first definition)
• 2301 – nonagonal number^[43]
• 2304 = 48²
• 2306 – Mertens function zero
• 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number^[37]
• 2310 – fifth primorial^[60]
• 2311 – primorial prime, twin prime with 2309
• 2321 – Mertens function zero
• 2322 – Mertens function zero
• 2326 – centered pentagonal number^[24]
• 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128^[61]
• 2331 – centered cube number^[62]
• 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^[36]
• 2357 – Smarandache–Wellin prime^[63]
• 2368 – sum of the totient function for the first 88 integers
• 2372 – logarithmic number^[64]
• 2378 – Pell number^[65]
• 2379 – member of the Mian–Chowla sequence^[23]
• 2381 – super-prime, centered square number^[41]
• 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 – perfect score on SAT tests administered after 2005
• 2401 = 49² = 7⁴, centered octagonal number^[19]
• 2415 – triangular number
• 2417 – super-prime, balanced prime^[59]
• 2425 – decagonal number^[33]
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime,^[58] largest right-truncatable prime in base 5
• 2447 – safe prime^[22]
• 2450 – pronic number^[36]
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number^[38]
• 2459 – Sophie Germain prime, safe prime^[22]
• 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number^[66]
• 2470 – square pyramidal number^[39]
• 2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells^[67]
• 2477 – super-prime, cousin prime
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number^[24]
• 2484 – nonagonal number^[43]
• 2485 – triangular number, number of planar partitions of 13^[68]
• 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 = 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^[69]
• 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 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).
• 2521 – star prime, centered square number^[41]
• 2522 – Mertens function zero
• 2523 – Mertens function zero
• 2524 – Mertens function zero
• 2525 – Mertens function zero
• 2530 – Mertens function zero, Leyland number^[45]
• 2533 – Mertens function zero
• 2537 – Mertens function zero
• 2538 – Mertens function zero
• 2543 – Sophie Germain prime, sexy prime with 2549
• 2549 – Sophie Germain prime, super-prime, sexy prime with 2543
• 2550 – pronic number^[36]
• 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
• 2579 – safe prime^[22]
• 2580 – Keith number,^[55] forms a column on a telephone or PIN pad
• 2584 – Fibonacci number,^[70] sum of the first 37 primes
• 2592 – 3-smooth number (2⁵×3⁴)
• 2596 – sum of the totient function for the first 92 integers

• 2600 – tetrahedral number,^[18] 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 – telephone number, amicable number with 2924
• 2625 = a centered octahedral number^[34]
• 2626 – decagonal number^[33]
• 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^[24]
• 2647 – super-prime, centered heptagonal number^[38]
• 2652 – pronic number^[36]
• 2656 – sum of the totient function for the first 93 integers
• 2665 – centered square number^[41]
• 2674 – nonagonal number^[43]
• 2677 – balanced prime^[59]
• 2680 – number of 11-queens problem solutions
• 2683 – super-prime
• 2689 – Mertens function zero, Proth prime^[40]
• 2693 – Sophie Germain prime
• 2699 – Sophie Germain prime

• 2701 – triangular number, super-Poulet number^[31]
• 2702 – sum of the totient function for the first 94 integers
• 2704 = 52²
• 2707 – strong prime, model number for the concept supersonic airliner Boeing 2707
• 2719 – super-prime, largest known odd number which cannot be expressed in the form x² + y² + 10z² where x, y and z are integers.^[71] In 1997 it was conjectured that this is also the largest such odd number.^[72] It is now^[when?] known this is true if the generalized Riemann hypothesis is true.^[73]
• 2728 – Kaprekar number^[56]
• 2729 – highly cototient number^[37]
• 2731 – the only Wagstaff prime with four digits,^[74] Jacobsthal prime
• 2736 – octahedral number^[57]
• 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^[40]
• 2756 – pronic number^[36]
• 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^[58]

• 2801 – first base 7 repunit prime
• 2803 – super-prime
• 2806 – centered pentagonal number,^[24] sum of the totient function for the first 96 integers
• 2809 = 53², centered octagonal number^[19]
• 2813 – centered square number^[41]
• 2816 – number of parts in all compositions of 10^[75]
• 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)^[22]
• 2821 – Carmichael number^[66]
• 2835 – odd abundant number,^[53] decagonal number^[33]
• 2843 – centered heptagonal prime^[76]
• 2850 – triangular number
• 2862 – pronic number^[36]
• 2870 – square pyramidal number^[39]
• 2871 – nonagonal number^[43]
• 2872 – tetranacci number^[77]
• 2875 — number of lines on a quintic threefold^[78]
• 2879 – safe prime^[22]
• 2897 – super-prime, Markov prime^[79]

• 2902 – sum of the totient function for the first 97 integers
• 2903 – Sophie Germain prime, safe prime,^[22] balanced prime^[59]
• 2909 – super-prime
• 2914 – sum of the first 39 primes
• 2915 – Lucas–Carmichael number^[12]
• 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,^[18] member of the Mian-Chowla sequence^[23]
• 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^[59]
• 2964 – number of parallelogram polyominoes with 11 cells^[80]
• 2965 – greater of second pair of Smith brothers, centered square number^[41]
• 2969 – Sophie Germain prime
• 2970 – harmonic divisor number,^[81] pronic number^[36]
• 2976 – centered pentagonal number^[24]
• 2988 – number of reduced trees with 20 nodes^[82]
• 2989 – in hexadecimal, reads as "BAD"
• 2997 – 1000-gonal number^[83]
• 2999 – safe prime

There are 127 prime numbers between 2000 and 3000:^[84][85]

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