2000 (number)

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 number¹
• smallest four digit eban number²
• the sum of all the nban numbers (sequence A008537 in the OEIS)³

• 2001 – sphenic number⁴
• 2002 = 7⁴ – 7³ – 7² – 7. Palindromic number in decimal, base 76, 90, 142, and 11 other non-trivial bases. A binomial coefficient, equal to ${\displaystyle {\tbinom {14}{5}}}$.
• 2003 – Sophie Germain prime and the smallest prime number in the 2000s
• 2004 – Area of the 24th crystagon⁵
• 2005 – A vertically symmetric number
• 2006 – number of subsets of {1,2,3,4,5,6,7,8,9,10,11} with relatively prime elements⁶
• 2007 – 2²⁰⁰⁷ + 2007² is prime⁷
• 2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3⁸
• 2009 = 28² + 35², sum of two squares
• 2010 – number of compositions of 12 into relatively prime parts⁹
• 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 number¹⁰
• 2013 – number of widely totally strongly normal compositions of 17
• 2014 – 5 × 2²⁰¹⁴ – 1 is prime¹¹
• 2015 – Lucas–Carmichael number¹²
• 2016 – second-smallest Erdős–Nicolas number,¹³ triangular number,¹⁴ number of 5-cubes in a 9-cube, 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 + 31²¹⁵
• 2020 – sum of the totient function for the first 81 integers; Self-descriptive number
• 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,¹⁶ beginning of a run of 4 consecutive Niven numbers¹⁷
• 2023 = 7 × 17² – multiple of 7 with digit sum equal to 7,¹⁸ sum of squares of digits equals 17
• 2024 – tetrahedral number¹⁹
• 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,²⁰ lowest number with exactly 15 odd divisors.²¹ Sum of odd numbers from 1 to 89.
• 2026 = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices²²
• 2027 – super-prime, safe prime²³
• 2028 = 13³ – 13²
• 2029 – member of the Mian–Chowla sequence²⁴
• 2030 = 21² + 22² + 23² + 24² = 25² + 26² + 27²
• 2031 – centered pentagonal number²⁵
• 2032 – number of binary Lyndon words of length 16 with an even number of 1's²⁶
• 2033 – number of rooted trees with 9 nodes and a single labeled node²⁷
• 2034 – number of unlabeled graphs on 11 nodes whose components are unicyclic graphs²⁸
• 2035 – Wolstenholme number²⁹
• 2036 – Eulerian number³⁰
• 2037 = 2¹¹ – 11³¹
• 2038 – Number of unlabeled Euler graphs with 9 nodes³²
• 2039 – Sophie Germain prime, safe prime²³
• 2040 = ${\displaystyle {\frac {15\times 16\times 17}{2}}}$ ³³
• 2041 – Number of 11-node connected graphs with at most one cycle³⁴
• 2042 = 2 × 1021. All the digits of all the prime factors are smaller than 3³⁵
• 2043 – Number of partitions of 35 in which the number of parts divides 35³⁶
• 2044 = ${\displaystyle \sigma _{3}(12)=\sum _{d|12}d^{3}}$³⁷
• 2045 – Number of partially ordered set with 7 unlabeled elements³⁸
• 2046 = 2¹¹ – 2 = the expected number of tosses of a fair coin to get 10 consecutive heads³⁹
• 2047 – super-Poulet number,⁴⁰ Woodall number,⁴¹ decagonal number,⁴² a centered octahedral number,⁴³ 2047 = 2¹¹ – 1 = 23 × 89 and is the first Mersenne number that is composite for a prime exponent
• 2048 = 2¹¹
• 2049 = 2¹¹ + 2⁰. A sum of two positive powers of two⁴⁴
• 2050 = 31² + 33². Sum of 2 consecutive odd squares
• 2051 = 1⁵ + 1⁵ + 1⁵ + 4⁵ + 4⁵. Sum of 5 positive 5th powers⁴⁵
• 2052 = 2¹¹ + 2². A sum of two positive powers of two
• 2053 – star number
• 2054 = 1⁹ + 1⁹ + 1⁹ + 1⁹ + 1⁹ + 1⁹ + 2⁹ + 2⁹ + 2⁹ + 2⁹. Sum of 10 positive 9th powers
• 2055 = 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 2¹⁰ + 2¹⁰. Sum of 9 positive 10th powers
• 2056 – magic constant of n × n normal magic square and n-queens problem for n = 16
• 2057 = 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 2¹⁰ + 2¹⁰. Sum of 11 positive 10th powers
• 2058 = ${\displaystyle 49\times \phi (49)}$⁴⁶
• 2059 = 3⁷ – 2⁷⁴⁷
• 2060 – sum of the totient function for the first 82 integers
• 2061 – Number of sets of positive integers with arithmetic mean 7⁴⁸
• 2062 = ${\displaystyle \phi (\phi (2062)+\sigma (2062))}$⁴⁹
• 2063 – Sophie Germain prime, safe prime,²³ super-prime
• 2064 = 1031 + 1033, which is a twin prime sum⁵⁰
• 2065 = Number of distinct lines through the origin in the fourdimensional lattice of side length 6⁵¹
• 2066 – Bell number⁵²
• 2067 = Number of Golomb partitions of 30⁵³
• 2068 – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed⁵⁴
• 2069 – Sophie Germain prime
• 2070 – pronic number⁵⁵
• 2071 = Number of sensed planar maps with 6 edges⁵⁶
• 2072 = 45² + 45 + 2⁵⁷
• 2073 – Genocchi number⁵⁸
• 2074 = Number of Baxter permutations of length 7⁵⁹
• 2075 = 411 + 413 + 415 + 417 + 419 = 25 + 50×41⁶⁰
• 2076 = Number of disconnected regular graphs with 17 nodes⁶¹
• 2077 = Number of canonical polygons with 16 edges having 2-fold rotational symmetry⁶²
• 2078 = Number of reversible strings with 12 beads using exactly two different colors⁶³
• 2079 = ${\displaystyle {\frac {9\cdot 10\cdot 11\cdot 12\cdot (2\cdot 9+3)}{5!}}}$, 5-dimensional pyramidal number⁶⁴
• 2080 – triangular number
• 2081 – super-prime, first member of a prime quadruplet
• 2082 = 2¹¹+2⁵+2¹⁶⁵
• 2083 – second member of a prime quadruplet
• 2084 = ${\displaystyle \lfloor 4\times \phi ^{13}\rfloor }$,⁶⁶ where ${\displaystyle \phi }$ is the golden ratio
• 2085 – average of a prime quadruplet
• 2086 = ${\displaystyle \sum _{k=1}^{19}p(k)}$,⁶⁷ where ${\displaystyle p(k)}$ = number of partions of k
• 2087 – third member of a prime quadruplet
• 2088 – The number 2088⁶ + 5 is a prime number⁶⁸
• 2089 – fourth member of a prime quadruplet
• 2093 – Mertens function zero
• 2095 – Mertens function zero
• 2096 – Mertens function zero
• 2097 – Mertens function zero
• 2099 – Mertens function zero, super-prime, safe prime,²³ highly cototient number⁶⁹

• 2100 – Mertens function zero
• 2101 – centered heptagonal number⁷⁰
• 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,⁷¹ 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,⁷² centered square number⁷³
• 2116 = 46²
• 2117 – Mertens function zero
• 2119 – Mertens function zero
• 2120 – Mertens function zero, Fine number⁷⁴
• 2122 – Mertens function zero
• 2125 – nonagonal number⁷⁵
• 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 number⁷⁶
• 2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
• 2162 – pronic number⁵⁵
• 2166 – sum of the totient function for the first 84 integers
• 2169 – Leyland number⁷⁷
• 2171 – Mertens function zero
• 2172 – Mertens function zero
• 2175 – smallest number requiring 143 seventh powers for Waring representation
• 2176 – pentagonal pyramidal number,⁷⁸ centered pentagonal number,²⁵ number of prime knots with 12 crossings
• 2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4⁷⁹
• 2179 – Wedderburn–Etherington prime⁸⁰
• 2184 – equals both 3⁷ − 3 and 13³ − 13 and is believed to be the only such doubly strictly absurd number⁸¹
• 2187 = 3⁷, vampire number,⁸² perfect totient number⁸³
• 2188 – Motzkin number⁸⁴
• 2197 = 13³, palindromic in base 12 (1331₁₂)
• 2199 – perfect totient number⁸³

• 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 number⁸⁵
• 2207 – safe prime,²³ Lucas prime⁸⁶
• 2208 – Keith number⁸⁷
• 2209 = 47², palindromic in base 14 (B3B₁₄), centered octagonal number²⁰
• 2211 – triangular number
• 2221 – super-prime, happy number
• 2222 – repdigit
• 2223 – Kaprekar number⁸⁸
• 2230 – sum of the totient function for the first 85 integers
• 2232 – decagonal number⁴²
• 2236 – Harshad number
• 2245 – centered square number⁷³
• 2248 – 2¹¹ + 200
• 2254 – member of the Mian–Chowla sequence²⁴
• 2255 – octahedral number⁸⁹
• 2256 – pronic number⁵⁵
• 2269 – super-prime, cuban prime⁹⁰
• 2272 – sum of the totient function for the first 86 integers
• 2273 – Sophie Germain prime
• 2276 – sum of the first 35 primes, centered heptagonal number⁷⁰
• 2278 – triangular number
• 2281 – star number, Mersenne prime exponent
• 2287 – balanced prime⁹¹
• 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,¹⁹ member of a Ruth–Aaron pair with 2299 (first definition)
• 2301 – nonagonal number⁷⁵
• 2304 = 48²
• 2306 – Mertens function zero
• 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number⁶⁹
• 2310 – fifth primorial⁹²
• 2311 – primorial prime, twin prime with 2309
• 2321 – Mertens function zero
• 2322 – Mertens function zero
• 2326 – centered pentagonal number²⁵
• 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128⁹³
• 2331 – centered cube number⁹⁴
• 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 number⁵⁵
• 2357 – Smarandache–Wellin prime⁹⁵
• 2368 – sum of the totient function for the first 88 integers
• 2372 – logarithmic number⁹⁶
• 2378 – Pell number⁹⁷
• 2379 – member of the Mian–Chowla sequence²⁴
• 2381 – super-prime, centered square number⁷³
• 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 number²⁰
• 2402 – 7⁴ + 1
• 2406 appears for the first time in the Recamán's sequence at n = 394,178,473,633,984. Or in other words A057167(2406) = 394,178,473,633,984
• 2415 – triangular number
• 2417 – super-prime, balanced prime⁹¹
• 2425 – decagonal number⁴²
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime,⁹⁰ largest right-truncatable prime in base 5
• 2447 – safe prime²³
• 2450 – pronic number⁵⁵
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number⁷⁰
• 2459 – Sophie Germain prime, safe prime²³
• 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number⁹⁸
• 2470 – square pyramidal number⁷¹
• 2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells⁹⁹
• 2477 – super-prime, cousin prime
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number²⁵
• 2484 – nonagonal number⁷⁵
• 2485 – triangular number, number of planar partitions of 13¹⁰⁰
• 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
• 2504 – Friedman number
• 2505 – Friedman number
• 2506 – Friedman number
• 2507 – Friedman number
• 2508 – Friedman number
• 2509 – Friedman number
• 2510 – member of the Mian–Chowla sequence²⁴
• 2513 – member of the Padovan sequence¹⁰¹
• 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 number⁷³
• 2522 – Mertens function zero
• 2523 – Mertens function zero
• 2524 – Mertens function zero
• 2525 – Mertens function zero
• 2526 - Mertens function zero
• 2530 – Mertens function zero, Leyland number⁷⁷
• 2533 – Mertens function zero
• 2537 – Mertens function zero
• 2538 – Mertens function zero
• 2543 – Sophie Germain prime, sexy prime with 2549
• 2548 = 14³ - 14²
• 2549 – Sophie Germain prime, super-prime, sexy prime with 2543
• 2550 – pronic number⁵⁵
• 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 prime²³, palindromic prime in bases 5, 25, and 28: 2579 = 40304₅ = 434₂₅ = 383₂₈
• 2580 – Keith number,⁸⁷ forms a column on a telephone or PIN pad
• 2584 – Fibonacci number,¹⁰² 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,¹⁹ 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 number⁴³
• 2626 – decagonal number⁴²
• 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 number²⁵
• 2647 – super-prime, centered heptagonal number⁷⁰
• 2652 – pronic number⁵⁵
• 2656 – sum of the totient function for the first 93 integers
• 2659 – palindromic prime in base 5: 2659 = 41114₅
• 2665 – centered square number⁷³
• 2674 – nonagonal number⁷⁵
• 2677 – balanced prime⁹¹
• 2680 – number of 11-queens problem solutions
• 2683 – super-prime
• 2689 – Mertens function zero, Proth prime⁷²
• 2693 – Sophie Germain prime
• 2699 – Sophie Germain prime

• 2701 – triangular number, super-Poulet number⁴⁰
• 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.¹⁰³ In 1997 it was conjectured that this is also the largest such odd number.¹⁰⁴ It is now known this is true if the generalized Riemann hypothesis is true.¹⁰⁵
• 2728 – Kaprekar number⁸⁸
• 2729 – highly cototient number⁶⁹
• 2731 – the only Wagstaff prime with four digits,¹⁰⁶ Jacobsthal prime
• 2736 – octahedral number⁸⁹
• 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 prime⁷²
• 2756 – pronic number⁵⁵
• 2774 – sum of the totient function for the first 95 integers
• 2775 – triangular number
• 2780 – member of the Mian–Chowla sequence²⁴
• 2783 – member of a Ruth–Aaron pair with 2784 (first definition)
• 2784 – member of a Ruth–Aaron pair with 2783 (first definition)
• 2791 – cuban prime⁹⁰

• 2801 – first base 7 repunit prime
• 2803 – super-prime
• 2806 – centered pentagonal number,²⁵ sum of the totient function for the first 96 integers
• 2809 = 53², centered octagonal number²⁰
• 2813 – centered square number⁷³
• 2816 – number of parts in all compositions of 10¹⁰⁷
• 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)²³
• 2821 – Carmichael number⁹⁸
• 2835 – odd abundant number,⁸⁵ decagonal number⁴²
• 2843 – centered heptagonal prime¹⁰⁸
• 2850 – triangular number
• 2862 – pronic number⁵⁵
• 2870 – square pyramidal number⁷¹
• 2871 – nonagonal number⁷⁵
• 2872 – tetranacci number¹⁰⁹
• 2875 – number of lines on a quintic threefold¹¹⁰
• 2879 – safe prime²³
• 2897 – super-prime, Markov prime¹¹¹

• 2902 – sum of the totient function for the first 97 integers
• 2903 – Sophie Germain prime, safe prime,²³ balanced prime⁹¹
• 2909 – super-prime
• 2914 – sum of the first 39 primes
• 2915 – Lucas–Carmichael number¹²
• 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,¹⁹ member of the Mian-Chowla sequence²⁴
• 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 prime⁹¹
• 2964 – number of parallelogram polyominoes with 11 cells¹¹²
• 2965 – greater of second pair of Smith brothers, centered square number⁷³
• 2969 – Sophie Germain prime
• 2970 – harmonic divisor number,¹¹³ pronic number⁵⁵
• 2976 – centered pentagonal number²⁵
• 2988 – number of reduced trees with 20 nodes¹¹⁴
• 2989 – in hexadecimal, reads as "BAD"
• 2997 – 1000-gonal number¹¹⁵
• 2999 – safe prime

There are 127 prime numbers between 2000 and 3000:¹¹⁶¹¹⁷

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