6000 (number) explained
Number: | 6000 |
Roman: | M, or |
Unicode: | M, m,, |
Lang1: | Armenian |
Lang1 Symbol: | Ց |
6000 (six thousand) is the natural number following 5999 and preceding 6001.
Selected numbers in the range 6001–6999
6001 to 6099
6100 to 6199
6200 to 6299
6300 to 6399
- 6311 – super-prime
- 6317 – balanced prime
- 6322 – centered heptagonal number
- 6323 – Sophie Germain prime, balanced prime, super-prime
- 6328 – triangular number
- 6329 – Sophie Germain prime
- – Number of verses in the Qur'an according to the sect founded by Rashad Khalifa.
- 6348 – pentagonal pyramidal number[7]
- 6361 – prime of the form 2p-1, twin prime
- 6364 – nonagonal number[1]
- 6367 – balanced prime
- 6368 – amicable number with 6232
- 6373 – balanced prime, sum of three and seven consecutive primes (2113 + 2129 + 2131 and 883 + 887 + 907 + 911 + 919 + 929 + 937)
- 6397 – sum of three consecutive primes (2129 + 2131 + 2137)
- 6399 – smallest integer that cannot be expressed as a sum of fewer than 279 eighth powers
6400 to 6499
- 6400 = 802
- 6408 – sum of the squares of the first thirteen primes
- 6441 – triangular number
- 6449 – Sophie Germain prime
- 6466 – Markov number[8]
- 6480 – smallest number with exactly 50 factors
- 6491 – Sophie Germain prime
6500 to 6599
- 6502 – model number of the MOS Technology 6502 which equipped early computers such as the Apple I and II, Commodore PET, Atari and others.
- 6509 – highly cototient number
- 6521 – Sophie Germain prime
- 6542 – number of primes
.
[9] - 6545 – tetrahedral number[10]
- 6551 – Sophie Germain prime
- 6555 – triangular number
- 6556 – member of a Ruth-Aaron pair with 6557 (first definition)
- 6557 – member of a Ruth-Aaron pair with 6556 (first definition)
- 6561 = 812 = 94 = 38, perfect totient number,
- 6563 – Sophie Germain prime
- 6581 – Sophie Germain prime
- 6599 – safe prime
6600 to 6699
6700 to 6799
- 6719 – safe prime, highly cototient number
- 6724 = 822
- 6728 – number of domino tilings of a 6×6 checkerboard
- 6761 – Sophie Germain prime
- 6765 – 20th Fibonacci number[14]
- 6779 – safe prime
- 6786 – triangular number
6800 to 6899
- 6811 – member of a Ruth-Aaron pair with 6812 (first definition)
- 6812 – member of a Ruth-Aaron pair with 6811 (first definition)
- 6827 – safe prime
- 6841 - largest right-truncatable prime in base 7
- 6842 – number of parallelogram polyominoes with 12 cells
- 6859 = 193
- 6863 – balanced prime
- 6879 – number of planar partitions of 15
- 6880 – vampire number[15]
- 6889 = 832, centered octagonal number[4]
- 6899 – Sophie Germain prime, safe prime
6900 to 6999
Prime numbers
There are 117 prime numbers between 6000 and 7000:[16]
6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997
See also
Notes and References
- 9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2..
- Octahedral numbers: a(n) = n*(2*n^2 + 1)/3..
- Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6..
- Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers..
- Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e., n,k > 1 (to avoid n = (n-1)^1 + 1^(n-1))..
- 10-gonal (or decagonal) numbers: a(n) = n*(4*n-3)..
- Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2..
- Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z..
- Number of primes <= 2^n.
- Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6..
- Carmichael numbers: composite numbers k such that a^(k-1)
1 (mod k) for every a coprime to k.
.
- Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.
- Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1.
- Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1..
- Vampire numbers (definition 2): numbers n with an even number of digits which have a factorization n = i*j where i and j have the same number of digits and the multiset of the digits of n coincides with the multiset of the digits of i and j..
- Web site: Stein . William A. . William A. Stein . The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture . wstein.org . 10 February 2017 . 6 February 2021.