2000 (two thousand) is a natural number following 1999 and preceding 2001.
In mathematics 2000 is: the highest number expressible using only two unmodified characters in Roman numerals (MM) an Achilles number smallest four digit eban number the sum of all the nban numbers
Selected numbers in the range 2001–2999
2001 to 2099 2002 2002 = 2 × 7 × 11 × 13. It is a palindromic number in decimal, base 76, 90, 142, and 11 other non-trivial bases.
2003 2003 is a Sophie Germain prime.
2005 2005 = 5 × 401. It is a vertically symmetric number.
2011 2011 is a sexy prime with 2017. It is also the sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211
2015 2015 = 5 × 13 × 31. It is a Lucas–Carmichael number.
2016 2016 = 25 × 32 × 7. It is the second-smallest Erdős–Nicolas numberand a triangular number.
2017 2017 is a sexy prime with 2011.
2024 2024 = 23 × 11 × 23. It is a tetrahedral number.
2025 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.
2027 2027 is a super-prime and a safe prime.
2029 2029 is a prime number and a member of the Mian–Chowla sequence.
2031 2031 = 3 × 677. It is a centered pentagonal number.
2035 2035 = 5 × 11 × 37. It is a Wolstenholme number.
2036 2036 = 22 × 509. It is an Eulerian number.
2039 2039 is a Sophie Germain prime and a safe prime.
2047 2047 = 23 × 89 = 211 − 1 and it is the first Mersenne number that is composite for a prime exponent. It is a super-Poulet number, a Woodall number, a decagonal number, and a centered octahedral number.
2053 2053 is a prime number and a star number.
2056 2056 = 23 × 257. It is the magic constant of an n × n normal magic square and the n-queens problem for n = 16.
2063 2063 is a Sophie Germain prime, a safe prime, and a super-prime.
2066 2066 = 2 × 1033. It is a Bell number.
2069 2069 is a Sophie Germain prime.
2080 2080 = 25 × 5 × 13. It is a triangular number.
2081, 2083, 2087, and 2089 2081, 2083, 2087, and 2089 form a prime quadruplet.
2081 is also a super-prime.
2099 2099 is a super-prime, a safe prime, and a highly cototient number.
2100 to 2199
2101 2101 = 11 × 191. It is a centered heptagonal number.
2107 and 2108 2107 and 2108 form a Ruth–Aaron pair under the first definition.
2109 2109 = 3 × 19 × 37. It is a square pyramidal number.
2113 2113 is a Proth prime and a centered square number.
2116 2116 = 462 = 22 × 232.
2125 2125 = 53 × 17. It is a nonagonal number.
2129 2129 is a Sophie Germain prime.
2141 2141 is a Sophie Germain prime.
2145 2145 = 3 × 5 × 11 × 13. It is a triangular number.
2160 2160 = 24 × 33 × 5. It is a largely composite number.
2176 2176 = 27 × 17. It is a pentagonal pyramidal number and a centered pentagonal number.
2179 2179 is a prime number and a Wedderburn–Etherington number.
2187 2187 = 37. It is a vampire number and a perfect totient number.
2188 2188 = 22 × 547. It is a Motzkin number.
2199 2199 = 3 × 733. It is a perfect totient number.
2200 to 2299
2201 2201 – only known non-palindromic number whose cube is palindromic; also no known fourth or higher powers are palindromic for non-palindromic numbers
2207 2207 – safe prime, Lucas prime
2208 2208 – Keith number
2209 2209 = 472, palindromic in base 14 (B3B14), centered octagonal number
2211 2211 – triangular number
2221 2221 – super-prime, happy number
2223 2223 – Kaprekar number
2232 2232 – decagonal number
2245 2245 – centered square number
2254 2254 – member of the Mian–Chowla sequence
2255 2255 – octahedral number
2269 2269 – super-prime, cuban prime
2273 2273 – Sophie Germain prime
2276 2276 _ centered heptagonal number
2278 2278 – triangular number
2281 2281 – star number,
2287 2287 – balanced prime
2299 2299 – member of a Ruth–Aaron pair with 2300 (first definition)
2300 to 2399
2300 2300 – tetrahedral number, member of a Ruth–Aaron pair with 2299 (first definition)
2301 2301 – nonagonal number 2309 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number
2310 2310 – fifth primorial
2311 2311 – primorial prime, twin prime with 2309
2326 2326 – centered pentagonal number
2328 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128.
2331 2331 – centered cube number
2339 2339 – Sophie Germain prime, twin prime with 2341
2341 2341 – super-prime, twin prime with 2339
2346 2346 – triangular number
2351 2351 – Sophie Germain prime, super-prime
2352 2352 – pronic number
2357 2357 – Smarandache–Wellin prime
2378 2378 – Pell number
2379 2379 – member of the Mian–Chowla sequence
2381 2381 – super-prime, centered square number
2393 2393 – Sophie Germain prime
2399 2399 – Sophie Germain prime
2400 to 2499
2401 2401 = 492 = 74, centered octagonal number
2415 2415 – triangular number
2417 2417 – super-prime, balanced prime
2425 2425 – decagonal number
2437 2437 – cuban prime, largest right-truncatable prime in base 5
2447 2447 – safe prime
2450 2450 – pronic number
2458 2458 – centered heptagonal number
2459 2459 – Sophie Germain prime, safe prime
2465 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number
2470 2470 – square pyramidal number
2477 2477 – super-prime, cousin prime
2481 2481 – centered pentagonal number
2484 2484 – nonagonal number
2485 2485 – triangular number, number of planar partitions of 13
2491 2491 = member of Ruth–Aaron pair with 2492 under second definition
2492 2492 – member of Ruth–Aaron pair with 2491 under second definition
2500 to 2599 2510 – member of the Mian–Chowla sequence 2513 – member of the Padovan sequence 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 2530 – Leyland number 2543 – Sophie Germain prime, sexy prime with 2549 2549 – Sophie Germain prime, super-prime, sexy prime with 2543 2550 – pronic number 2556 – triangular number 2579 – safe prime, palindromic prime in bases 5, 25, and 28: 2579 = 403045 = 43425 = 38328 2580 – Keith number, 2584 – Fibonacci number,
2600 to 2699 2600 – tetrahedral number, member of a Ruth–Aaron pair with 2601 (first definition) 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 2641 – centered pentagonal number 2647 – super-prime, centered heptagonal number 2652 – pronic number 2665 – centered square number 2674 – nonagonal number 2677 – balanced prime 2680 – number of 11-queens problem solutions 2683 – super-prime 2689 – 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 2707 – strong prime – 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 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421) 2821 – Carmichael number 2835 – 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 2903 – Sophie Germain prime, safe prime, balanced prime 2909 – super-prime 2915 – Lucas–Carmichael number 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 2963 – Sophie Germain prime, safe prime, balanced prime 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 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