2000 (number)

Template:Sister project 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<ref>Template:Cite OEIS</ref>
• smallest four digit eban number<ref>Template:Cite OEIS</ref>
• the sum of all the nban numbers in the sequence<ref>Template:Cite OEIS</ref>

Selected numbers in the range 2001–2999

2001 to 2099

• 2001 – sphenic number<ref>Template:Cite OEIS</ref>
• 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<ref>Template:Cite OEIS</ref>
• 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<ref>Template:Cite OEIS</ref>
• 2007 – 2²⁰⁰⁷ + 2007² is prime<ref>Template:Cite OEIS</ref>
• 2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3<ref>Template:Cite OEIS</ref>
• 2009 = 7⁴ − 7³ − 7²
• 2010 – number of compositions of 12 into relatively prime parts<ref>Template:Cite OEIS</ref>
• 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<ref>Template:Cite OEIS</ref>
• 2013 – number of widely totally strongly normal compositions of 17
• 2014 – 5 × 2²⁰¹⁴ - 1 is prime<ref>Template:Cite OEIS</ref>
• 2015 – Lucas–Carmichael number<ref name=":0">Template:Cite OEIS</ref>
• 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number,<ref>Template:Cite OEIS</ref> 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 + 31²<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 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,<ref>Template:Cite OEIS</ref> beginning of a run of 4 consecutive Niven numbers<ref>Template:Cite OEIS</ref>
• 2023 = 7 × 17² – multiple of 7 with digit sum equal to 7,<ref>Template:Cite OEIS</ref> sum of squares of digits equals 17
• 2024 – tetrahedral number<ref name=":1">Template:Cite OEIS</ref>
• 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,<ref name=":2">Template:Cite OEIS</ref> lowest number with exactly 15 odd divisors.<ref>Template:Cite OEIS</ref> Sum of odd numbers from 1 to 89, current year.
• 2026 = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices<ref>Template:Cite OEIS</ref>
• 2027 – super-prime, safe prime<ref name=":3">Template:Cite OEIS</ref>
• 2028 = 13³ – 13²
• 2029 – member of the Mian–Chowla sequence<ref name=":4">Template:Cite OEIS</ref>
• 2030 = 21² + 22² + 23² + 24² = 25² + 26² + 27²
• 2031 – centered pentagonal number<ref name=":5">Template:Cite OEIS</ref>
• 2032 = number of binary Lyndon words of length 16 with an even number of 1's<ref>Template:Cite OEIS</ref>
• 2033 = number of rooted trees with 9 nodes and a single labeled node<ref>Template:Cite OEIS</ref>
• 2034 = number of unlabeled graphs on 11 nodes whose components are unicyclic graphs<ref>Template:Cite OEIS</ref>
• 2035 – Wolstenholme number<ref>Template:Cite OEIS</ref>
• 2036 – Eulerian number<ref>Template:Cite OEIS</ref>
• 2039 – Sophie Germain prime, safe prime<ref name=":3" />
• 2045 – number of partially ordered set with 7 unlabeled elements<ref>Template:Cite OEIS</ref>
• 2047 – super-Poulet number,<ref name=":6">Template:Cite OEIS</ref> Woodall number,<ref>Template:Cite OEIS</ref> decagonal number,<ref name=":7">Template:Cite OEIS</ref> a centered octahedral number,<ref name="ReferenceA">Template:Cite OEIS</ref> 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,<ref name=":3" /> 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<ref>Template:Cite OEIS</ref>
• 2069 – Sophie Germain prime
• 2070 – pronic number<ref name=A002378>Template:Cite OEIS</ref>
• 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,<ref name=":3" /> highly cototient number<ref name=":9">Template:Cite OEIS</ref>

2100 to 2199

• 2100 – Mertens function zero
• 2101 – centered heptagonal number<ref name=":10">Template:Cite OEIS</ref>
• 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,<ref name=":11">Template:Cite OEIS</ref> 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,<ref name=":12">Template:Cite OEIS</ref> centered square number<ref name=":13">Template:Cite OEIS</ref>
• 2116 = 46²
• 2117 – Mertens function zero
• 2119 – Mertens function zero
• 2120 – Mertens function zero, Fine number<ref>Template:Cite OEIS</ref>
• 2122 – Mertens function zero
• 2125 – nonagonal number<ref name=":14">Template:Cite OEIS</ref>
• 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 22Template:Pi⁴
• 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<ref name="OEIS-A067128">Template:Cite OEIS</ref>
• 2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
• 2162 – pronic number<ref name=A002378/>
• 2166 – sum of the totient function for the first 84 integers
• 2169 – Leyland number<ref name=":15">Template:Cite OEIS</ref>
• 2171 – Mertens function zero
• 2172 – Mertens function zero
• 2175 – smallest number requiring 143 seventh powers for Waring representation
• 2176 – pentagonal pyramidal number,<ref>Template:Cite OEIS</ref> centered pentagonal number,<ref name=":5" /> number of prime knots with 12 crossings
• 2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4<ref>Template:Cite OEIS</ref>
• 2179 – Wedderburn–Etherington prime<ref>Template:Cite OEIS</ref>
• 2184 – equals both 3⁷ − 3 and 13³ − 13 and is believed to be the only such doubly strictly absurd number<ref>Template:Cite journal</ref>Template:Unreliable source?
• 2187 = 3⁷, vampire number,<ref>Template:Cite OEIS</ref> perfect totient number<ref name=":16">Template:Cite OEIS</ref>
• 2188 – Motzkin number<ref>Template:Cite OEIS</ref>
• 2197 = 13³, palindromic in base 12 (1331₁₂)
• 2199 – perfect totient number<ref name=":16" />

2200 to 2299

• 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<ref name=":17">Template:Cite OEIS</ref>
• 2207 – safe prime,<ref name=":3" /> Lucas prime<ref>Template:Cite OEIS</ref>
• 2208 – Keith number<ref name=":18">Template:Cite OEIS</ref>
• 2209 = 47², palindromic in base 14 (B3B₁₄), centered octagonal number<ref name=":2" />
• 2211 – triangular number
• 2221 – super-prime, happy number
• 2222 – repdigit
• 2223 – Kaprekar number<ref name=":19">Template:Cite OEIS</ref>
• 2230 – sum of the totient function for the first 85 integers
• 2232 – decagonal number<ref name=":7" />
• 2236 – Harshad number
• 2245 – centered square number<ref name=":13" />
• 2254 – member of the Mian–Chowla sequence<ref name=":4" />
• 2255 – octahedral number<ref name=":20">Template:Cite OEIS</ref>
• 2256 – pronic number<ref name=A002378/>
• 2269 – super-prime, cuban prime<ref name=":21">Template:Cite OEIS</ref>
• 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<ref name=":10" />
• 2278 – triangular number
• 2281 – star number, Mersenne prime exponent
• 2287 – balanced prime<ref name=":22">Template:Cite OEIS</ref>
• 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

• 2300 – tetrahedral number,<ref name=":1" /> member of a Ruth–Aaron pair with 2299 (first definition)
• 2301 – nonagonal number<ref name=":14" />
• 2304 = 48²
• 2306 – Mertens function zero
• 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number<ref name=":9" />
• 2310 – fifth primorial<ref>Template:Cite OEIS</ref>
• 2311 – primorial prime, twin prime with 2309
• 2321 – Mertens function zero
• 2322 – Mertens function zero
• 2326 – centered pentagonal number<ref name=":5" />
• 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}.</ref>

• 2331 – centered cube number<ref>Template:Cite OEIS</ref>
• 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<ref name=A002378/>
• 2357 – Smarandache–Wellin prime<ref>Template:Cite OEIS</ref>
• 2368 – sum of the totient function for the first 88 integers
• 2372 – logarithmic number<ref>Template:Cite OEIS</ref>
• 2378 – Pell number<ref>Template:Cite OEIS</ref>
• 2379 – member of the Mian–Chowla sequence<ref name=":4" />
• 2381 – super-prime, centered square number<ref name=":13" />
• 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

• 2400 – perfect score on SAT tests administered after 2005
• 2401 = 49² = 7⁴, centered octagonal number<ref name=":2" />
• 2415 – triangular number
• 2417 – super-prime, balanced prime<ref name=":22" />
• 2425 – decagonal number<ref name=":7" />
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime,<ref name=":21" /> largest right-truncatable prime in base 5
• 2447 – safe prime<ref name=":3" />
• 2450 – pronic number<ref name=A002378/>
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number<ref name=":10" />
• 2459 – Sophie Germain prime, safe prime<ref name=":3" />
• 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number<ref name=":23">Template:Cite OEIS</ref>
• 2470 – square pyramidal number<ref name=":11" />
• 2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells<ref>Template:Cite OEIS</ref>
• 2477 – super-prime, cousin prime
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number<ref name=":5" />
• 2484 – nonagonal number<ref name=":14" />
• 2485 – triangular number, number of planar partitions of 13<ref>Template:Cite OEIS</ref>
• 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 to 2599

• 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<ref name=":4" />
• 2513 – member of the Padovan sequence<ref>Template:Cite OEIS</ref>
• 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<ref name=":13" />
• 2522 – Mertens function zero
• 2523 – Mertens function zero
• 2524 – Mertens function zero
• 2525 – Mertens function zero
• 2530 – Mertens function zero, Leyland number<ref name=":15" />
• 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 number<ref name=A002378/>
• 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<ref name=":3" />
• 2580 – Keith number,<ref name=":18" /> forms a column on a telephone or PIN pad
• 2584 – Fibonacci number,<ref>Template:Cite OEIS</ref> sum of the first 37 primes
• 2592 – 3-smooth number (2⁵×3⁴)
• 2596 – sum of the totient function for the first 92 integers

2600 to 2699

• 2600 – tetrahedral number,<ref name=":1" /> 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<ref name="ReferenceA"/>
• 2626 – decagonal number<ref name=":7" />
• 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<ref name=":5" />
• 2647 – super-prime, centered heptagonal number<ref name=":10" />
• 2652 – pronic number<ref name=A002378/>
• 2656 – sum of the totient function for the first 93 integers
• 2665 – centered square number<ref name=":13" />
• 2674 – nonagonal number<ref name=":14" />
• 2677 – balanced prime<ref name=":22" />
• 2680 – number of 11-queens problem solutions
• 2683 – super-prime
• 2689 – Mertens function zero, Proth prime<ref name=":12" />
• 2693 – Sophie Germain prime
• 2699 – Sophie Germain prime

2700 to 2799

• 2701 – triangular number, super-Poulet number<ref name=":6" />
• 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
• Template:Vanchor – super-prime, largest known odd number which cannot be expressed in the form x² + y² + 10z² where x, y and z are integers.<ref>Template:Cite encyclopedia</ref> In 1997 it was conjectured that this is also the largest such odd number.<ref name=Ono>Template:Cite journal</ref> It is nowTemplate:When known this is true if the generalized Riemann hypothesis is true.<ref name=Ken>Template:Cite journal</ref>
• 2728 – Kaprekar number<ref name=":19" />
• 2729 – highly cototient number<ref name=":9" />
• 2731 – the only Wagstaff prime with four digits,<ref>Template:Cite OEIS</ref> Jacobsthal prime
• 2736 – octahedral number<ref name=":20" />
• 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<ref name=":12" />
• 2756 – pronic number<ref name=A002378/>
• 2763 - Factors of 2763 are 1, 3, 9, 307, 921. There are 5 integers that are factors of 2763. The biggest factor of 2763 is 921.
• 2774 – sum of the totient function for the first 95 integers
• 2775 – triangular number
• 2780 – member of the Mian–Chowla sequence<ref name=":4" />
• 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<ref name=":21" />

2800 to 2899

• 2801 – first base 7 repunit prime
• 2803 – super-prime
• 2806 – centered pentagonal number,<ref name=":5" /> sum of the totient function for the first 96 integers
• 2809 = 53², centered octagonal number<ref name=":2" />
• 2813 – centered square number<ref name=":13" />
• 2816 – number of parts in all compositions of 10<ref>Template:Cite OEIS</ref>
• 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)<ref name=":3" />
• 2821 – Carmichael number<ref name=":23" />
• 2835 – odd abundant number,<ref name=":17" /> decagonal number<ref name=":7" />
• 2843 – centered heptagonal prime<ref>Template:Cite OEIS</ref>
• 2850 – triangular number
• 2862 – pronic number<ref name=A002378/>
• 2870 – square pyramidal number<ref name=":11" />
• 2871 – nonagonal number<ref name=":14" />
• 2872 – tetranacci number<ref>Template:Cite OEIS</ref>
• 2875 — number of lines on a quintic threefold<ref>Template:Citation</ref>
• 2879 – safe prime<ref name=":3" />
• 2897 – super-prime, Markov prime<ref>Template:Cite OEIS</ref>

2900 to 2999

• 2902 – sum of the totient function for the first 97 integers
• 2903 – Sophie Germain prime, safe prime,<ref name=":3" /> balanced prime<ref name=":22" />
• 2909 – super-prime
• 2914 – sum of the first 39 primes
• 2915 – Lucas–Carmichael number<ref name=":0" />
• 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,<ref name=":1" /> member of the Mian-Chowla sequence<ref name=":4" />
• 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<ref name=":22" />
• 2964 – number of parallelogram polyominoes with 11 cells<ref>Template:Cite OEIS</ref>
• 2965 – greater of second pair of Smith brothers, centered square number<ref name=":13" />
• 2969 – Sophie Germain prime
• 2970 – harmonic divisor number,<ref>Template:Cite OEIS</ref> pronic number<ref name=A002378/>
• 2976 – centered pentagonal number<ref name=":5" />
• 2988 – number of reduced trees with 20 nodes<ref>Template:Cite OEIS</ref>
• 2989 – in hexadecimal, reads as "BAD"
• 2997 – 1000-gonal number<ref>Template:Cite OEIS</ref>
• 2999 – safe prime

Prime numbers

There are 127 prime numbers between 2000 and 3000:<ref>Template:Cite OEIS</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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