2000 (number)

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 number
smallest four digit eban number
Selected numbers in the range 2001–2999
2001 to 2099
2001 – sphenic number
2002 – palindromic number
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 X 4 matrices with nonnegative integer entries and row and column sums equal to 3
2009 = 74 − 73 − 72
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 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, 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
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 * 17 * 17 – multiple of 7 with digit sum equal to 7, sum of squares of digits equals 17
2024 – tetrahedral number
2025 = 452, sum of the cubes of the first nine integers, centered octagonal number
2027 – super-prime, safe prime
2029 – member of the Mian–Chowla sequence
2030 = 212 + 222 + 232 + 242 = 252 + 262 + 272
2031 – centered pentagonal number
2039 – Sophie Germain prime, safe prime
2045 – number of partially ordered set with 7 unlabeled elements
2047 – super-Poulet number, Woodall number, decagonal number, a centered octahedral number. Also, 2047 = 211 - 1 = 23 × 89 and is the first Mersenne number that is composite for a prime exponent.
2048 = 211
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. 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
2069 – Sophie Germain prime
2070 – pronic 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
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
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.
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
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
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 = 74, 492, 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
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. Also 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 – 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
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
Integers