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.
• 2003 – Sophie Germain prime and the smallest prime number in the 2000s
• 2004 – Area of the 24th
• 2005 – A vertically symmetric number
• 2006 – number of subsets of 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, 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 =
• 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 =
• 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 =
• 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 =
• 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 =, 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
• 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 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
• 2187 = 3⁷, vampire number, perfect totient number
• 2188 – Motzkin number
• 2197 = 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 numbers
• 2203 – Mersenne prime exponent
• 2205 – odd abundant number
• 2207 – safe prime, Lucas prime
• 2208 – Keith number
• 2209 = 47², palindromic in base 14, 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