2000 (number)

Selected numbers in the range 2001–2999

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
• 2040 = \frac{15 \times 16 \times 17}{2}
• 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, super-prime
• 2064 = 1031 + 1033, which is a twin prime sum
• 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
• 2093 – Mertens function zero
• 2095 – Mertens function zero
• 2096 – Mertens function zero
• 2097 – Mertens function zero
• 2099 – Mertens function zero, super-prime, safe prime, highly cototient number

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
• 2166 – sum of the totient function for the first 84 integers
• 2169 – Leyland 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, number of prime knots with 12 crossings
• 2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4
• 2179 – Wedderburn–Etherington prime
• 2184 – equals both 37 − 3 and 133 − 13 and is believed to be the only such doubly strictly absurd number{{cite journal
• 2187 = 37, vampire number, perfect totient number
• 2188 – Motzkin number
• 2197 = 133, palindromic in base 12 (133112)
• 2199 – perfect totient number

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
• 2207 – safe prime, Lucas prime
• 2208 – Keith number
• 2209 = 472, palindromic in base 14 (B3B14), centered octagonal number
• 2211 – triangular number
• 2221 – super-prime, happy number
• 2222 – repdigit
• 2223 – Kaprekar number
• 2230 – sum of the totient function for the first 85 integers
• 2232 – decagonal number
• 2236 – Harshad number
• 2245 – centered square number
• 2248 – 211 + 200
• 2254 – member of the Mian–Chowla sequence
• 2255 – octahedral number
• 2256 – pronic number
• 2269 – super-prime, cuban prime
• 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
• 2278 – triangular number
• 2281 – star number, Mersenne prime exponent
• 2287 – balanced prime
• 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, member of a Ruth–Aaron pair with 2299 (first definition)
• 2301 – nonagonal number
• 2304 = 482
• 2306 – Mertens function zero
• 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number
• 2310 – fifth primorial
• 2311 – primorial prime, twin prime with 2309
• 2321 – Mertens function zero
• 2322 – Mertens function zero
• 2326 – centered pentagonal number
• 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128
• 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
• 2357 – Smarandache–Wellin prime
• 2368 – sum of the totient function for the first 88 integers
• 2372 – logarithmic number
• 2378 – Pell number
• 2379 – member of the Mian–Chowla sequence
• 2381 – super-prime, centered square number
• 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
• 2415 – triangular number
• 2417 – super-prime, balanced prime
• 2425 – decagonal number
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime, largest right-truncatable prime in base 5
• 2447 – safe prime
• 2450 – pronic number
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number
• 2459 – Sophie Germain prime, safe prime
• 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number
• 2470 – square pyramidal number
• 2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells
• 2477 – super-prime, cousin prime
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number
• 2484 – nonagonal number
• 2485 – triangular number, number of planar partitions of 13
• 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
• 2513 – member of the Padovan 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
• 2522 – Mertens function zero
• 2523 – Mertens function zero
• 2524 – Mertens function zero
• 2525 – Mertens function zero
• 2530 – Mertens function zero, Leyland number
• 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
• 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
• 2580 – Keith number, forms a column on a telephone or PIN pad
• 2584 – Fibonacci 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, 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
• 2626 – decagonal number
• 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
• 2647 – super-prime, centered heptagonal number
• 2652 – pronic number
• 2656 – sum of the totient function for the first 93 integers
• 2665 – centered square number
• 2674 – nonagonal number
• 2677 – balanced prime
• 2680 – number of 11-queens problem solutions
• 2683 – super-prime
• 2689 – Mertens function zero, Proth prime
• 2693 – Sophie Germain prime
• 2699 – Sophie Germain prime

2700 to 2799

• 2701 – triangular number, super-Poulet number
• 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
• **** – super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers. 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
• 2729 – highly cototient number
• 2731 – the only Wagstaff prime with four digits, Jacobsthal prime
• 2736 – octahedral number
• 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
• 2756 – pronic number
• 2774 – sum of the totient function for the first 95 integers
• 2775 – triangular number
• 2780 – member of the Mian–Chowla sequence
• 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

2800 to 2899

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

2900 to 2999

• 2902 – sum of the totient function for the first 97 integers
• 2903 – Sophie Germain prime, safe prime, balanced prime
• 2909 – super-prime
• 2914 – sum of the first 39 primes
• 2915 – Lucas–Carmichael number
• 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, member of the Mian-Chowla sequence
• 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
• 2964 – number of parallelogram polyominoes with 11 cells
• 2965 – greater of second pair of Smith brothers, centered square number
• 2969 – Sophie Germain prime
• 2970 – harmonic divisor number, pronic number
• 2976 – centered pentagonal number
• 2988 – number of reduced trees with 20 nodes
• 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

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