2001 to 2099 •
2001 –
sphenic number •
2002 = 74 – 73 – 72 – 7.
Palindromic number in
decimal, base 76, 90, 142, and 11 other non-trivial bases. A
binomial coefficient, equal to \tbinom{14}{5}. •
2003 –
Sophie Germain prime and the smallest prime number in the 2000s •
2004 – Area of the 24th crystagon •
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 •
2007 – 22007 + 20072 is prime •
2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3 •
2009 = 282 + 352, sum of two squares •
2010 – number of compositions of 12 into relatively prime parts •
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 •
2013 –
number of widely totally strongly normal compositions of 17 •
2014 – 5 × 22014 – 1 is prime •
2015 –
Lucas–Carmichael number •
2016 – second-smallest
Erdős–Nicolas number,
triangular number, 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 + 312 •
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, beginning of a run of 4 consecutive Niven numbers •
2023 = 7 × 172 – multiple of 7 with digit sum equal to 7, sum of squares of digits equals 17 •
2024 –
tetrahedral number •
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, lowest number with exactly 15
odd divisors. Sum of odd numbers from 1 to 89. •
2026 = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices •
2027 –
super-prime,
safe prime •
2028 = 133 – 132 •
2029 – member of the
Mian–Chowla sequence •
2030 = 212 + 222 + 232 + 242 = 252 + 262 + 272 •
2031 –
centered pentagonal number •
2032 – number of binary Lyndon words of length 16 with an even number of 1's •
2033 – number of rooted trees with 9 nodes and a single labeled node •
2034 – number of unlabeled graphs on 11 nodes whose components are unicyclic graphs •
2035 – Wolstenholme number •
2036 – Eulerian number •
2037 = 211 – 11 •
2038 – Number of unlabeled Euler graphs with 9 nodes •
2039 –
Sophie Germain prime,
safe prime •
2041 – Number of 11-node connected graphs with at most one cycle •
2042 = 2 × 1021. All the digits of all the prime factors are smaller than 3 •
2043 – Number of partitions of 35 in which the number of parts divides 35 •
2044 = \sigma_3(12)=\sum_{d|12}d^3 •
2045 – Number of
partially ordered set with 7 unlabeled elements •
2046 = 211 – 2 = the expected number of tosses of a fair coin to get 10 consecutive heads •
2047 –
super-Poulet number,
Woodall number,
decagonal number, a
centered octahedral number, 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 two •
2050 = 312 + 332. Sum of 2 consecutive odd squares •
2051 = 15 + 15 + 15 + 45 + 45. Sum of 5 positive 5th powers •
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 = 49 \times \phi (49) •
2059 = 37 – 27 •
2060 – sum of the
totient function for the first 82 integers •
2061 – Number of sets of positive integers with arithmetic mean 7 •
2062 = \phi(\phi(2062) + \sigma(2062)) •
2063 –
Sophie Germain prime,
safe prime, •
2065 = Number of distinct lines through the origin in the fourdimensional lattice of side length 6 •
2066 – Bell number •
2067 = Number of Golomb partitions of 30 •
2068 – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed •
2069 –
Sophie Germain prime •
2070 –
pronic number •
2071 = Number of sensed planar maps with 6 edges •
2072 = 452 + 45 + 2 •
2073 – Genocchi number •
2074 = Number of Baxter permutations of length 7 •
2075 = 411 + 413 + 415 + 417 + 419 = 25 + 50×41 •
2076 = Number of disconnected regular graphs with 17 nodes •
2077 = Number of canonical polygons with 16 edges having 2-fold rotational symmetry •
2078 = Number of reversible strings with 12 beads using exactly two different colors •
2079 = \frac{9 \cdot 10 \cdot 11 \cdot 12 \cdot (2\cdot 9 + 3)}{5!}, 5-dimensional pyramidal number •
2080 – triangular number •
2081 –
super-prime, first member of a
prime quadruplet •
2082 = 211+25+21 •
2083 – second member of a prime quadruplet •
2084 = \lfloor 4 \times \phi^{13}\rfloor, where \phi is the
golden ratio •
2085 – average of a prime quadruplet •
2086 = \sum_{k=1}^{19} p(k), where p(k) = number of
partions of k •
2087 – third member of a prime quadruplet •
2088 – The number 20886 + 5 is a prime number •
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,
2100 to 2199 •
2100 – Mertens function zero •
2101 –
centered heptagonal number •
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, 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,
centered square number •
2116 = 462 •
2117 – Mertens function zero •
2119 – Mertens function zero •
2120 – Mertens function zero, Fine number •
2122 – Mertens function zero •
2125 –
nonagonal number •
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 224 •
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 •
2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices •
2162 – pronic number •
2171 – Mertens function zero •
2172 – Mertens function zero •
2175 – smallest number requiring 143 seventh powers for Waring representation •
2176 –
pentagonal pyramidal number, centered pentagonal number, •
2179 –
Wedderburn–Etherington prime •
2184 – equals both 37 − 3 and 133 − 13 and is believed to be the only such
doubly strictly absurd number •
2187 =
37,
vampire number,
perfect totient number •
2188 –
Motzkin number •
2197 = 133, palindromic in base 12 (133112) •
2199 – perfect totient number •
2207 –
safe prime, •
2208 –
Keith number •
2209 = 472, palindromic in base 14 (B3B14), centered octagonal number •
2230 – sum of the totient function for the first 85 integers •
2232 – decagonal number •
2256 – pronic number •
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 •
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, •
2311 – primorial prime, twin prime with 2309 •
2321 – Mertens function zero •
2322 – Mertens function zero •
2326 – centered pentagonal number •
2331 –
centered cube number •
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 •
2368 – sum of the totient function for the first 88 integers •
2372 – logarithmic number •
2378 –
Pell number •
2379 – member of the Mian–Chowla sequence •
2470 – square pyramidal number •
2477 –
super-prime,
cousin prime •
2480 – sum of the totient function for the first 90 integers •
2481 – centered pentagonal number •
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 •
2504 –
Friedman number •
2505 –
Friedman number •
2506 –
Friedman number •
2507 –
Friedman number •
2508 –
Friedman number •
2509 –
Friedman number •
2510 – member of the Mian–Chowla sequence •
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 . 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 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 . •
2521 –
star prime, centered square number 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, In 1997 it was conjectured that this is also the largest such odd number. It is now known this is true if the
generalized Riemann hypothesis is true. •
2728 –
Kaprekar number Jacobsthal prime •
2736 – octahedral number •
2819 –
Sophie Germain prime,
safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421) •
2850 – triangular number •
2862 – pronic number •
2875 – number of lines on a
quintic threefold •
2879 –
safe prime 2900 to 2999 •
2902 – sum of the
totient function for the first 97 integers •
2903 –
Sophie Germain prime,
safe prime, •
2965 – greater of second pair of
Smith brothers, centered square number pronic number •
2989 – in
hexadecimal, reads as "
BAD" •
2997 – 1000-gonal number •
2999 –
safe prime Prime numbers There are 127
prime numbers between 2000 and 3000: :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 ==