2000 (number)

From Wikipedia, the free encyclopedia
See also: millennium, 2000, Y2K, and 2000 (disambiguation)
← 1999 2000 2001 →
List of numbers — Integers
← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinaltwo thousand
Ordinal2000th
(two thousandth)
Factorization24 × 53
Greek numeral,Β´
Roman numeralMM
Unicode symbol(s)MM, mm
Binary111110100002
Ternary22020023
Octal37208
Duodecimal11A812
Hexadecimal7D016

2000 (two thousand) is a natural number following 1999 and preceding 2001.

Two thousand is the highest number expressible using only two unmodified characters in Roman numerals (MM).

Selected numbers in the range 2001–2999[]

2001 to 2099[]

2100 to 2199[]

  • 2100 – Mertens function zero
  • 2101 – centered heptagonal number[14]
  • 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[15]
  • 2112 – The break-through album of the band Rush
  • 2113 – Mertens function zero, Proth prime,[16] centered square number[17]
  • 2116 = 462
  • 2117 – Mertens function zero
  • 2119 – Mertens function zero
  • 2120 – Mertens function zero
  • 2122 – Mertens function zero
  • 2125 – nonagonal number[18]
  • 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 22π4
  • 2145 – triangular number
  • 2162 – pronic number[12]
  • 2166 – sum of the totient function for the first 84 integers
  • 2169 – Leyland number[19]
  • 2171 – Mertens function zero
  • 2172 – Mertens function zero
  • 2175 – smallest number requiring 143 seventh powers for Waring representation
  • 2176 – pentagonal pyramidal number,[20] centered pentagonal number[8]
  • 2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4.[21]
  • 2179 – Wedderburn–Etherington prime[22]
  • 2184 – equals both 37 − 3 and 133 − 13 and is believed to be the only such doubly strictly absurd number.[23][unreliable source?]
  • 2187 = 37, vampire number,[24] perfect totient number[25]
  • 2188 – Motzkin number[26]
  • 2197 = 133, palindromic in base 12 (133112)
  • 2199 – perfect totient number[25]

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[27]
  • 2207 – safe prime,[6] Lucas prime[28]
  • 2208 – Keith number[29]
  • 2209 = 472, palindromic in base 14 (B3B14), centered octagonal number[5]
  • 2211 – triangular number
  • 2221 – super-prime, happy number
  • 2222 – repdigit
  • 2223 – Kaprekar number[30]
  • 2230 – sum of the totient function for the first 85 integers
  • 2232 – decagonal number[11]
  • 2236 – Harshad number
  • 2245 – centered square number[17]
  • 2254 – member of the Mian–Chowla sequence[7]
  • 2255 – octahedral number[31]
  • 2256 – pronic number[12]
  • 2269 – super-prime, cuban prime[32]
  • 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[14]
  • 2278 – triangular number
  • 2281 – star number, Mersenne prime exponent
  • 2287 – balanced prime[33]
  • 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,[4] member of a Ruth–Aaron pair with 2299 (first definition)
  • 2301 – nonagonal number[18]
  • 2304 = 482
  • 2306 – Mertens function zero
  • 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number[13]
  • 2310 – fifth primorial[34]
  • 2311 – primorial prime, twin prime with 2309
  • 2321 – Mertens function zero
  • 2322 – Mertens function zero
  • 2326 – centered pentagonal number[8]
  • 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128[35]
  • 2331 – centered cube number[36]
  • 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[12]
  • 2357 – Smarandache–Wellin prime[37]
  • 2368 – sum of the totient function for the first 88 integers
  • 2378 – Pell number[38]
  • 2379 – member of the Mian–Chowla sequence[7]
  • 2381 – super-prime, centered square number[17]
  • 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[5]
  • 2415 – triangular number
  • 2417 – super-prime, balanced prime[33]
  • 2425 – decagonal number[11]
  • 2427 – sum of the first 36 primes
  • 2431 – product of three consecutive primes
  • 2437 – cuban prime,[32] largest right-truncatable prime in base 5
  • 2447 – safe prime[6]
  • 2450 – pronic number[12]
  • 2456 – sum of the totient function for the first 89 integers
  • 2458 – centered heptagonal number[14]
  • 2459 – Sophie Germain prime, safe prime[6]
  • 2465 – magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number[39]
  • 2470 – square pyramidal number[15]
  • 2477 – super-prime, cousin prime
  • 2480 – sum of the totient function for the first 90 integers
  • 2481 – centered pentagonal number[8]
  • 2484 – nonagonal number[18]
  • 2485 – triangular number
  • 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[7]
  • 2513 – member of the Padovan sequence[40]
  • 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 (sequence A072938 in the OEIS). Not only is it the 7th (and last) number with more divisors than any number double itself but it also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 (sequence A095921 in the OEIS) 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.(sequence A106037 in the OEIS)
  • 2521 – star prime, centered square number[17]
  • 2522 – Mertens function zero
  • 2523 – Mertens function zero
  • 2524 – Mertens function zero
  • 2525 – Mertens function zero
  • 2530 – Mertens function zero, Leyland number[19]
  • 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[12]
  • 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[6]
  • 2580 – Keith number,[29] forms a column on a telephone or PIN pad
  • 2584 – Fibonacci number,[41] 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,[4] 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 – amicable number with 2924
  • 2626 – decagonal number[11]
  • 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[8]
  • 2647 – super-prime, centered heptagonal number[14]
  • 2652 – pronic number
  • 2656 – sum of the totient function for the first 93 integers
  • 2665 – centered square number[17]
  • 2674 – nonagonal number[18]
  • 2677 – balanced prime[33]
  • 2680 – number of 11-queens problem solutions
  • 2683 – super-prime
  • 2689 – Mertens function zero, Proth prime[16]
  • 2693 – Sophie Germain prime
  • 2699 – Sophie Germain prime

2700 to 2799[]

  • 2701 – triangular number, super-Poulet number[9]
  • 2702 – sum of the totient function for the first 94 integers
  • 2704 = 522
  • 2707 – model number for the concept supersonic airliner Boeing 2707
  • 2719 – super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.[42] In 1997 it was conjectured that this is also the largest such odd number.[43] It is now known this is true if the generalized Riemann hypothesis is true.[44]
  • 2728 – Kaprekar number[30]
  • 2729 – highly cototient number[13]
  • 2731 – the only Wagstaff prime with four digits,[45] Jacobsthal prime
  • 2736 – octahedral number[31]
  • 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[16]
  • 2756 – pronic number
  • 2774 – sum of the totient function for the first 95 integers
  • 2775 – triangular number
  • 2780 – member of the Mian–Chowla sequence[7]
  • 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[32]

2800 to 2899[]

  • 2801 – first base 7 repunit prime
  • 2803 – super-prime
  • 2806 – centered pentagonal number,[8] sum of the totient function for the first 96 integers
  • 2809 = 532, centered octagonal number[5]
  • 2813 – centered square number[17]
  • 2819 – Sophie Germain prime, safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)[6]
  • 2821 – Carmichael number[39]
  • 2835 – odd abundant number,[27] decagonal number[11]
  • 2843 – centered heptagonal prime[46]
  • 2850 – triangular number
  • 2862 – pronic number
  • 2870 – square pyramidal number[15]
  • 2871 – nonagonal number[18]
  • 2872 – tetranacci number[47]
  • 2879 – safe prime[6]
  • 2897 – super-prime, Markov prime[48]

2900 to 2999[]

Prime numbers[]

There are 127 prime numbers between 2000 and 3000:[51][52]

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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  45. ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A144974 (Centered heptagonal prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  49. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.
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