2000 (number)

2000 is a natural number following 1999 and preceding 2001.
It is:

Selected numbers in the range 2001–2999

2001 to 2099

2001 – sphenic number2002 = 7⁴ – 7³ – 7² – 7. Palindromic number in decimal, base 76, 90, 142, and 11 other non-trivial bases. A binomial coefficient, equal to.2003 – Sophie Germain prime and the smallest prime number in the 2000s2004 – Area of the 24th 2005 – A vertically symmetric number2006 – number of subsets of with relatively prime elements2007 – 2²⁰⁰⁷ + 2007² is prime2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 32009 = 28² + 35², sum of two squares2010 – number of compositions of 12 into relatively prime parts2011 – sexy prime with 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 2112012 – The number 8 × 10²⁰¹² − 1 is a prime number2013 – number of widely totally strongly normal compositions of 172014 – 5 × 2²⁰¹⁴ - 1 is prime2015 – Lucas–Carmichael number2016 – second-smallest Erdős–Nicolas number, triangular number, number of 5-cubes in a 9-cube, 2¹¹-2⁵2017 – Mertens function zero, sexy prime with 20112018 – Number of partitions of 60 into prime parts2019 – 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 + 31²2020 – sum of the totient function for the first 81 integers; Self-descriptive number2021 = 43 × 47, consecutive prime numbers, next is 24912022 – non-isomorphic colorings of a toroidal 3 × 3 grid using exactly three colors under translational symmetry, beginning of a run of 4 consecutive Niven numbers2023 = 7 × 17² – multiple of 7 with digit sum equal to 7, sum of squares of digits equals 172024 – tetrahedral number2025 = 45², square of the sum of the first nine positive integers, 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 vertices2027 – super-prime, safe prime2028 = 13³ – 13²2029 – member of the Mian–Chowla sequence2030 = 21² + 22² + 23² + 24² = 25² + 26² + 27²2031 – centered pentagonal number2032 – number of binary Lyndon words of length 16 with an even number of 1's2033 – number of rooted trees with 9 nodes and a single labeled node2034 – number of unlabeled graphs on 11 nodes whose components are unicyclic graphs2035 – Wolstenholme number2036 – Eulerian number2037 = 2¹¹ - 112038 – Number of unlabeled Euler graphs with 9 nodes2039 – Sophie Germain prime, safe prime2040 = 2041 – Number of 11-node connected graphs with at most one cycle2042 = 2 × 1021. All the digits of all the prime factors are smaller than 32043 – Number of partitions of 35 in which the number of parts divides 352044 = 2045 – Number of partially ordered set with 7 unlabeled elements2046 = 2¹¹ - 2 = the expected number of tosses of a fair coin to get 10 consecutive heads2047 – 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 exponent2048 = 2¹¹2049 = 2¹¹ + 2⁰. A sum of two positive powers of two2050 = 31² + 33². Sum of 2 consecutive odd squares2051 = 1⁵ + 1⁵ + 1⁵ + 4⁵ + 4⁵. Sum of 5 positive 5th powers2052 = 2¹¹ + 2². A sum of two positive powers of two2053 – star number2054 = 1⁹ + 1⁹ + 1⁹ + 1⁹ + 1⁹ + 1⁹ + 2⁹ + 2⁹ + 2⁹ + 2⁹. Sum of 10 positive 9th powers2055 = 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 2¹⁰ + 2¹⁰. Sum of 9 positive 10th powers2056 – magic constant of n × n normal magic square and n-queens problem for n = 162057 = 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 2¹⁰ + 2¹⁰. Sum of 11 positive 10th powers2058 = 2059 = 3⁷-2⁷2060 – sum of the totient function for the first 82 integers2061 – Number of sets of positive integers with arithmetic mean 72062 = 2063 – Sophie Germain prime, safe prime, super-prime2064 = 1031 + 1033, which is a twin prime sum2065 = Number of distinct lines through the origin in the fourdimensional lattice of side length 62066 – Bell number2067 = Number of Golomb partitions of 302068 – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed2069 – Sophie Germain prime2070 – pronic number2071 = Number of sensed planar maps with 6 edges2072 = 45² + 45 + 22073 – Genocchi number2074 = Number of Baxter permutations of length 72075 = 411 + 413 + 415 + 417 + 419 = 25 + 50×412076 = Number of disconnected regular graphs with 17 nodes2077 = Number of canonical polygons with 16 edges having 2-fold rotational symmetry2078 = Number of reversible strings with 12 beads using exactly two different colors2079 =, 5-dimensional pyramidal number2080 – triangular number2081 – super-prime2093 – Mertens function zero2095 – Mertens function zero2096 – Mertens function zero2097 – Mertens function zero2099 – Mertens function zero, super-prime, safe prime, highly cototient number

2100 to 2199

2100 – Mertens function zero2101 – centered heptagonal number2107 – member of a Ruth–Aaron pair with 2108 2108 – member of a Ruth–Aaron pair with 2107 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 Rush2113 – Mertens function zero, Proth prime, centered square number2116 = 46²2117 – Mertens function zero2119 – Mertens function zero2120 – Mertens function zero, Fine number2122 – Mertens function zero2125 – nonagonal number2127 – sum of the first 34 primes2129 – Sophie Germain prime2135 – Mertens function zero2136 – Mertens function zero2137 – prime of the form 2p-12138 – Mertens function zero2141 – Sophie Germain prime2142 – sum of the totient function for the first 83 integers2143 – almost exactly 22⁴2145 – triangular number2153 – with 2161, smallest consecutive primes that have the same sum of digits as each other's prime indices2160 – largely composite number2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices2162 – pronic number2166 – sum of the totient function for the first 84 integers2169 – Leyland number2171 – Mertens function zero2172 – Mertens function zero2175 – smallest number requiring 143 seventh powers for Waring representation2176 – pentagonal pyramidal number, centered pentagonal number, number of prime knots with 12 crossings2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 42179 – Wedderburn–Etherington prime2184 – equals both 3⁷ − 3 and 13³ − 13 and is believed to be the only such doubly strictly absurd number2187 = 3⁷, vampire number, perfect totient number2188 – Motzkin number2197 = 13³, palindromic in base 12 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 numbers2203 – Mersenne prime exponent2205 – odd abundant number2207 – safe prime, Lucas prime2208 – Keith number2209 = 47², palindromic in base 14, centered octagonal number2211 – triangular number2221 – super-prime, happy number2222 – repdigit2223 – Kaprekar number2230 – sum of the totient function for the first 85 integers2232 – decagonal number2236 – Harshad number 2245 – centered square number2248 – 2¹¹ + 2002254 – member of the Mian–Chowla sequence2255 – octahedral number2256 – pronic number2269 – super-prime, cuban prime2272 – sum of the totient function for the first 86 integers2273 – Sophie Germain prime2276 – sum of the first 35 primes, centered heptagonal number2278 – triangular number2281 – star number, Mersenne prime exponent2287 – balanced prime2294 – Mertens function zero2295 – Mertens function zero2296 – Mertens function zero2299 – member of a Ruth–Aaron pair with 2300

2300 to 2399

2300 – tetrahedral number, member of a Ruth–Aaron pair with 2299 2301 – nonagonal number2304 = 48²2306 – Mertens function zero2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number2310 – fifth primorial2311 – primorial prime, twin prime with 23092321 – Mertens function zero2322 – Mertens function zero2326 – centered pentagonal number2328 – sum of the totient function for the first 87 integers, the number of groups of order 1282331 – centered cube number2338 – Mertens function zero2339 – Sophie Germain prime, twin prime with 23412341 – super-prime, twin prime with 23392346 – triangular number2347 – sum of seven consecutive primes 2351 – Sophie Germain prime, super-prime2352 – pronic number2357 – Smarandache–Wellin prime2368 – sum of the totient function for the first 88 integers2372 – logarithmic number2378 – Pell number2379 – member of the Mian–Chowla sequence2381 – super-prime, centered square number2393 – Sophie Germain prime2397 – sum of the squares of the first ten primes2399 – Sophie Germain prime

2400 to 2499

2400 – perfect score on SAT tests administered after 20052401 = 49² = 7⁴, centered octagonal number2415 – triangular number2417 – super-prime, balanced prime2425 – decagonal number2427 – sum of the first 36 primes2431 – product of three consecutive primes2437 – cuban prime, largest right-truncatable prime in base 52447 – safe prime2450 – pronic number2456 – sum of the totient function for the first 89 integers2458 – centered heptagonal number2459 – Sophie Germain prime, safe prime2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number2470 – square pyramidal number2471 – number of ways to partition and then partition each cell into subcells2477 – super-prime, cousin prime2480 – sum of the totient function for the first 90 integers2481 – centered pentagonal number2484 – nonagonal number2485 – triangular number, number of planar partitions of 132491 = 47 * 53, consecutive prime numbers, member of Ruth–Aaron pair with 2492 under second definition2492 – member of Ruth–Aaron pair with 2491 under second definition

2500 to 2599

2500 = 50², palindromic in base 7 2501 – Mertens function zero2502 – Mertens function zero2503 – Friedman prime2510 – member of the Mian–Chowla sequence2513 – member of the Padovan sequence2517 – Mertens function zero2519 – the smallest number congruent to 1, 2, 3,..., 9 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 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. 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 and is not divisible by 1 to 7. 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 number2522 – Mertens function zero2523 – Mertens function zero2524 – Mertens function zero2525 – Mertens function zero2530 – Mertens function zero, Leyland number2533 – Mertens function zero2537 – Mertens function zero2538 – Mertens function zero2543 – Sophie Germain prime, sexy prime with 25492548 = 14³ - 14²2549 – Sophie Germain prime, super-prime, sexy prime with 25432550 – pronic number2552 – sum of the totient function for the first 91 integers2556 – triangular number2567 – Mertens function zero2568 – Mertens function zero, number of digits in the decimal expansion of 1000!, or the product of all natural numbers from 1 to 10002570 – Mertens function zero2579 – safe prime2580 – Keith number, forms a column on a telephone or PIN pad2584 – Fibonacci number, sum of the first 37 primes2592 – 3-smooth number 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

* 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 console2601 = 51², member of a Ruth–Aaron pair with 2600 2609 – super-prime2620 – telephone number, amicable number with 29242625 = a centered octahedral number2626 – decagonal number2628 – triangular number2632 – number of consecutive baseball games played by Cal Ripken Jr.2633 – sum of twenty-five consecutive primes 2641 – centered pentagonal number2647 – super-prime, centered heptagonal number2652 – pronic number2656 – sum of the totient function for the first 93 integers2665 – centered square number2674 – nonagonal number2677 – balanced prime2680 – number of 11-queens problem solutions2683 – super-prime2689 – Mertens function zero, Proth prime2693 – Sophie Germain prime2699 – Sophie Germain prime

2700 to 2799

2701 – triangular number, super-Poulet number2702 – sum of the totient function for the first 94 integers2704 = 52²2707 – 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 number2729 – highly cototient number2731 – the only Wagstaff prime with four digits, Jacobsthal prime2736 – octahedral number2741 – Sophie Germain prime, 400th prime number2744 = 14³, palindromic in base 13 2747 – sum of the first 38 primes2749 – super-prime, cousin prime with 27532753 – Sophie Germain prime, Proth prime2756 – pronic number2774 – sum of the totient function for the first 95 integers2775 – triangular number2780 – member of the Mian–Chowla sequence2783 – member of a Ruth–Aaron pair with 2784 2784 – member of a Ruth–Aaron pair with 2783 2791 – cuban prime

2800 to 2899

2801 – first base 7 repunit prime2803 – super-prime2806 – centered pentagonal number, sum of the totient function for the first 96 integers2809 = 53², centered octagonal number2813 – centered square number2816 – number of parts in all compositions of 102819 – Sophie Germain prime, safe prime, sum of seven consecutive primes 2821 – Carmichael number2835 – odd abundant number, decagonal number2843 – centered heptagonal prime2850 – triangular number2862 – pronic number2870 – square pyramidal number2871 – nonagonal number2872 – tetranacci number2875 – number of lines on a quintic threefold2879 – safe prime2897 – super-prime, Markov prime

2900 to 2999

2902 – sum of the totient function for the first 97 integers2903 – Sophie Germain prime, safe prime, balanced prime2909 – super-prime2914 – sum of the first 39 primes2915 – Lucas–Carmichael number2916 = 54²2924 – amicable number with 26202925 – magic constant of n × n normal magic square and n-queens problem for n = 18, tetrahedral number, member of the Mian-Chowla sequence2926 – triangular number2939 – Sophie Germain prime2944 – sum of the totient function for the first 98 integers2963 – Sophie Germain prime, safe prime, balanced prime2964 – number of parallelogram polyominoes with 11 cells2965 – greater of second pair of Smith brothers, centered square number2969 – Sophie Germain prime2970 – harmonic divisor number, pronic number2976 – centered pentagonal number2988 – number of reduced trees with 20 nodes2989 – in hexadecimal, reads as "BAD"2997 – 1000-gonal number2999 – safe prime

Prime numbers

There are 127 prime numbers between 2000 and 3000: