4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number.[1]
| ||||
---|---|---|---|---|
Cardinal | four thousand | |||
Ordinal | 4000th (four thousandth) | |||
Factorization | 25 × 53 | |||
Greek numeral | ,Δ´ | |||
Roman numeral | MV, or IV | |||
Unicode symbol(s) | MV, mv, IV, iv | |||
Binary | 1111101000002 | |||
Ternary | 121110113 | |||
Senary | 303046 | |||
Octal | 76408 | |||
Duodecimal | 239412 | |||
Hexadecimal | FA016 | |||
Armenian | Տ | |||
Egyptian hieroglyph | 𓆿 |
Selected numbers in the range 4001–4999
edit4001 to 4099
edit- 4005 – triangular number[2]
- 4007 – safe prime
- 4010 – magic constant of n × n normal magic square and n-queens problem for n = 20
- 4013 – balanced prime[3]
- 4019 – Sophie Germain prime
- 4021 – prime of the form 2p-1
- 4027 – super-prime
- 4028 – sum of the first 45 primes
- 4030 – third weird number[4]
- 4031 – sum of the cubes of the first six primes
- 4032 – pronic number[5]
- 4033 – sixth super-Poulet number;[6] strong pseudoprime in base 2[7]
- 4057 – prime of the form 2p-1
- 4060 – tetrahedral number[8]
- 4073 – Sophie Germain prime
- 4079 – safe prime
- 4091 – super-prime
- 4092 – an occasional glitch in the game The Legend of Zelda: Ocarina of Time causes the Gossip Stones to say this number
- 4095 – triangular number[2] and odd abundant number;[9] number of divisors in the sum of the fifth and largest known unitary perfect number, largest Ramanujan–Nagell number of the form
[10]
- 4096 = 642 = 163 = 84 = 46 = 212, smallest number with exactly 13 factors, a superperfect number[11]
4100 to 4199
edit- 4104 = 23 + 163 = 93 + 153
- 4127 – safe prime
- 4133 – super-prime
- 4139 – safe prime
- 4140 – Bell number[12]
- 4141 – centered square number[13]
- 4147 – smallest cyclic number in duodecimal represented in base-12 notation as 249712
2×4147dez = 497212
3×4147dez = 724912
4×4147dez = 972412 - 4153 – super-prime
- 4160 – pronic number[5]
- 4166 – centered heptagonal number[14]
- 4167 = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14[15]
- 4169 – a number of points of norm <= 10 in cubic lattice[16]
- 4177 – prime of the form 2p-1
- 4181 – Fibonacci number,[17] Markov number[18]
- 4186 – triangular number[2]
- 4187 – factor of R13, the record number of wickets taken in first-class cricket by Wilfred Rhodes
- 4199 – highly cototient number,[19] product of three consecutive primes
4200 to 4299
edit- 4200 – nonagonal number,[20] pentagonal pyramidal number[21]
- 4210 – 11th semi-meandric number[22]
- 4211 – Sophie Germain prime
- 4213 – Riordan number
- 4217 – super-prime, happy number
- 4219 – cuban prime of the form x = y + 1,[23] centered hexagonal number
- 4225 = 652, centered octagonal number[24]
- 4227 – sum of the first 46 primes
- 4240 – Leyland number[25]
- 4257 – decagonal number[1]
- 4259 – safe prime
- 4261 – prime of the form 2p-1
- 4271 – Sophie Germain prime
- 4273 – super-prime, number of non-isomorphic set-systems of weight 11
- 4278 – triangular number[2]
- 4279 – little Schroeder number
- 4283 – safe prime
- 4289 – highly cototient number[19]
- 4290 – pronic number[5]
4300 to 4399
edit- 4324 – 23rd square pyramidal number[26]
- 4325 – centered square number[13]
- 4339 – super-prime, twin prime
- 4349 – Sophie Germain prime
- 4356 = 662, sum of the cubes of the first eleven integers
- 4357 – prime of the form 2p-1
- 4359 – perfect totient number[27]
- 4369 – seventh super-Poulet number[6]
- 4371 – triangular number[2]
- 4373 – Sophie Germain prime
- 4374 – The largest number such that both it and the next number (4375) are 7-smooth
- 4375 – perfect totient number (the smallest not divisible by 3)[27]
- 4391 – Sophie Germain prime
- 4397 – Year of Comet Hale–Bopp's return, super-prime
4400 to 4499
edit- 4400 – the number of missing persons in the sci-fi show The 4400
- 4409 – Sophie Germain prime, highly cototient number,[19] balanced prime,[3] 600th prime number
- 4410 – member of the Padovan sequence[28]
- 4411 – centered heptagonal number[14]
- 4421 – super-prime, alternating factorial[29]
- 4422 – pronic number[5]
- 4425 = 15 + 25 + 35 + 45 + 55[30]
- 4438 – sum of the first 47 primes
- 4444 - repdigit
- 4446 – nonagonal number[20]
- 4447 – cuban prime of the form x = y + 1[23]
- 4457 – balanced prime[3]
- 4463 – super-prime
- 4465 – triangular number[2]
- 4481 – Sophie Germain prime
- 4489 = 672, centered octagonal number[24]
- 4495 – tetrahedral number[8]
4500 to 4599
edit- 4503 – largest number not the sum of four or fewer squares of composites
- 4505 – fifth Zeisel number[31]
- 4513 – centered square number
- 4516 – centered pentagonal number
- 4517 – super-prime, happy number
- 4522 – decagonal number[1]
- 4547 – safe prime
- 4549 – super-prime
- 4556 – pronic number[5]
- 4560 – triangular number[2]
- 4567 – super-prime
- 4579 – octahedral number[32]
- 4597 – balanced prime[3]
4600 to 4699
edit- 4604 – sum of the only two known Wieferich primes, 1093 and 3511
- 4607 – Woodall number[33]
- 4608 – 3-smooth number (29×32)
- 4619 – highly cototient number[19]
- 4621 – prime of the form 2p-1
- 4624 = 682
- 4641 – magic constant of n × n normal magic square and n-queens problem for n = 21
- 4655 – number of free decominoes
- 4656 – triangular number[2]
- 4657 – balanced prime[3]
- 4661 – sum of the first 48 primes
- 4663 – super-prime, centered heptagonal number[14]
- 4679 – safe prime
- 4681 – eighth super-Poulet number[6]
- 4688 – 2-automorphic number[34]
- 4689 – sum of divisors and number of divisors are both triangular numbers[35]
- 4691 – balanced prime[3]
- 4692 – pronic number[5]
- 4699 – nonagonal number[20]
4700 to 4799
edit- 4703 – safe prime
- 4705 = 482 + 492 = 172 + 182 + … + 262, centered square number
- 4727 – sum of the squares of the first twelve primes
- 4731 – centered pentagonal number
- 4733 – Sophie Germain prime
- 4753 – triangular number[2]
- 4759 – super-prime
- 4761 = 692, centered octagonal number[24]
- 4769 = number of square (0,1)-matrices without zero rows and with exactly 5 entries equal to 1[36]
- 4787 – safe prime, super-prime
- 4788 – 14th Keith number[37]
- 4793 – Sophie Germain prime
- 4795 – decagonal number[1]
- 4799 – safe prime
4800 to 4899
edit- 4801 – super-prime, cuban prime of the form x = y + 2,[38] smallest prime with a composite sum of digits in base 7
- 4830 – pronic number[5]
- 4840 - square yards in an acre
- 4851 – triangular number,[2] pentagonal pyramidal number[21]
- 4862 – Catalan number[39]
- 4871 – Sophie Germain prime
- 4877 – super-prime
- 4879 – 11th Kaprekar number[40]
- 4888 – sum of the first 49 primes
4900 to 4999
edit- 4900 = 702, the only square-pyramidal square other than 1 ([1])
- 4901 – centered square number
- 4913 = 173
- 4919 – Sophie Germain prime, safe prime
- 4922 – centered heptagonal number[14]
- 4933 – super-prime
- 4941 – centered cube number[41]
- 4943 – Sophie Germain prime, super-prime
- 4950 – triangular number,[2] 12th Kaprekar number[40]
- 4951 – centered pentagonal number
- 4957 – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009)
- 4959 – nonagonal number[20]
- 4960 – tetrahedral number;[8] greater of fourth pair of Smith brothers
- 4970 – pronic number[5]
- 4973 – the 666th prime
- 4991 – Lucas–Carmichael number
- 4993 – balanced prime[3]
- 4999 – prime of the form
[42]
Prime numbers
editThere are the 119 prime numbers between 4000 and 5000:[43][44]
- 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999
References
edit- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006037 (Weird numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001262 (Strong pseudoprimes to base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005231 (Odd abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A076046 (Ramanujan-Nagell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A019279 (Superperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000605 (Number of points of norm <= n in cubic lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000682 (Semimeanders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A031971 (a(n) = Sum_{k=1..n} k^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051015 (Zeisel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A030984 (2-automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-09-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A070996 (Numbers n whose sum of divisors and number of divisors are both triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A122400 (Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002648 (A variant of the cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A066436 (Primes of the form 2*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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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