6000 (number)

"6,000" redirects here. For the Jewish year, see Year 6000. For other uses, see 6000 (disambiguation).

← 5999 6000 6001 →
List of numbers Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	six thousand
Ordinal	6000th (six thousandth)
Factorization	24 × 3 × 53
Greek numeral	,Ϛ´
Roman numeral	VM, or VI
Unicode symbol(s)	VM, vm, VI, vi
Binary	10111011100002
Ternary	220200203
Senary	434406
Octal	135608
Duodecimal	358012
Hexadecimal	177016
Armenian	Ց

6000 (six thousand) is the natural number following 5999 and preceding 6001.

Selected numbers in the range 6001–6999

6001 to 6099

• 6025 – Stage name of rhythm guitarist of the Dead Kennedys from June 1978 to March 1979. Full name is Carlos Cadona.
• 6028 – centered heptagonal number ^[1]
• 6037 – super-prime, prime of the form 2p-1
• 6042 – 6042 Cheshirecat is a Mars-crossing asteroid.
• 6047 – safe prime
• 6053 – Sophie Germain prime
• 6069 – nonagonal number ^[2]
• 6073 – balanced prime
• 6079 – The serial number Winston Smith is referred to as in the George Orwell novel Nineteen Eighty-Four
• 6084 = 78², sum of the cubes of the first twelve integers
• 6081 - sum of the first 54 primes
• 6089 – highly cototient number ^[3]
• 6095 – magic constant of n × n normal magic square and n-Queens Problem for n = 23.

6100 to 6199

• 6101 – Sophie Germain prime
• 6105 – triangular number
• 6113 – Sophie Germain prime, super-prime
• 6121 – prime of the form 2p-1
• 6131 – Sophie Germain prime, twin prime with 6133
• 6133 – 800th prime number, twin prime with 6131
• 6143 – Thabit number
• 6144 – 3-smooth number (2¹¹×3)
• 6173 – Sophie Germain prime
• 6174 – Kaprekar's constant
• 6181 – octahedral number ^[4]

6200 to 6299

• 6200 – harmonic divisor number ^[5]
• 6201 – square pyramidal number ^[6]
• 6216 – triangular number
• 6217 – super-prime, prime of the form 2p-1
• 6229 – super-prime
• 6232 – amicable number with 6368
• 6236 – Most widely accepted figure for the number of verses in the Qur'an ^{[ citation needed ]}
• 6241 = 79², centered octagonal number ^[7]
• 6250 – Leyland number ^[8]
• 6263 – Sophie Germain prime, balanced prime
• 6269 – Sophie Germain prime
• 6280 – decagonal number ^[9]

6300 to 6399

• 6311 – super-prime
• 6317 – balanced prime
• 6322 – centered heptagonal number ^[1]
• 6323 – Sophie Germain prime, balanced prime, super-prime
• 6328 – triangular number
• 6329 – Sophie Germain prime
• 6337 - star prime
• 6338 - sum of the first 55 primes
• 6346 – Number of verses in the Qur'an according to the sect founded by Rashad Khalifa. ^[10]
• 6348 – pentagonal pyramidal number ^[11]
• 6361 – prime of the form 2p-1, twin prime
• 6364 – nonagonal number ^[2]
• 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 ^[12]
• 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 ^[13]
• 6521 – Sophie Germain prime
• 6542 – number of primes ${\displaystyle \leq 2^{16}}$. ^[14]
• 6545 – tetrahedral number ^[15]
• 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 ^[16]
• 6563 – Sophie Germain prime
• 6581 – Sophie Germain prime
• 6599 – safe prime

6600 to 6699

• 6601 - Carmichael number, ^[17] decagonal number, ^[9] sum of the first 56 primes
• 6623 – centered heptagonal number ^[1]
• 6659 – safe prime
• 6666 – forty-fourth nonagonal number, ^[2] and the 11th third-convolution of Fibonacci numbers. ^[18] In Christian demonology it represents the number of demons in a legion of demons.^{[ citation needed ]}
• 6670 – triangular number, ^[19] centered nonagonal number, ^[20] centered 19-gonal number, ^[21]

6700 to 6799

• 6719 – safe prime, highly cototient number ^[13]
• 6724 = 82²
• 6733 - star prime
• 6728 – number of domino tilings of a 6×6 checkerboard
• 6761 – Sophie Germain prime
• 6765 – 20th Fibonacci number ^[22]
• 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 ^[23]
• 6859 = 19³
• 6863 – balanced prime
• 6870 - sum of the first 57 primes
• 6879 – number of planar partitions of 15 ^[24]
• 6880 – vampire number ^[25]
• 6889 = 83², centered octagonal number ^[7]
• 6899 – Sophie Germain prime, safe prime

6900 to 6999

• 6903 – triangular number
• 6912 – 3-smooth number (2⁸×3³)
• 6924 – magic constant of n × n normal magic square and n-Queens Problem for n = 24.
• 6929 – highly cototient number ^[13]
• 6930 – decagonal number, ^[9] square pyramidal number ^[6]
• 6931 – centered heptagonal number ^[1]
• 6969 – 2015 comedic progressive rock song by the band Ninja Sex Party
• 6975 – nonagonal number
• 6977 – balanced prime
• 6983 – Sophie Germain prime, safe prime
• 6997 – 900th prime number

Prime numbers

There are 117 prime numbers between 6000 and 7000: ^{[26] [27]}

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

• Year 6000

References

1. Sloane, N. J. A. (ed.). "SequenceA069099(Centered heptagonal numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA001106(9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA100827(Highly cototient numbers: records for a(n) in A063741.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA005900(Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Sloane, N. J. A. (ed.). "SequenceA001599(Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. Sloane, N. J. A. (ed.). "SequenceA000330(Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
7. Sloane, N. J. A. (ed.). "SequenceA016754(Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
8. Sloane, N. J. A. (ed.). "SequenceA076980(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)).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
9. Sloane, N. J. A. (ed.). "SequenceA001107(10-gonal (or decagonal) numbers: a(n) = n*(4*n-3).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
10. Gardner, Martin (September–October 1997), "The numerology of Dr. Rashad Khalifa", Skeptical Inquirer, archived from the original on 2004-09-27
11. Sloane, N. J. A. (ed.). "SequenceA002411(Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
12. Sloane, N. J. A. (ed.). "SequenceA002559(Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
13. Sloane, N. J. A. (ed.). "SequenceA100827(Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
14. Sloane, N. J. A. (ed.). "SequenceA007053(Number of primes <= 2^n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
15. Sloane, N. J. A. (ed.). "SequenceA000292(Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
16. Sloane, N. J. A. (ed.). "SequenceA082897(Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
17. Sloane, N. J. A. (ed.). "SequenceA002997(Carmichael numbers: composite numbers k such that a^(k-1) == 1 (mod k) for every a coprime to k.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
18. Sloane, N. J. A. (ed.). "SequenceA001628(Convolved Fibonacci numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
19. Sloane, N. J. A. (ed.). "SequenceA000217(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.
20. Sloane, N. J. A. (ed.). "SequenceA060544(Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
21. Sloane, N. J. A. (ed.). "SequenceA069132(Centered 19-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
22. Sloane, N. J. A. (ed.). "SequenceA000045(Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
23. Sloane, N. J. A. (ed.). "SequenceA006958(Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
24. Sloane, N. J. A. (ed.). "SequenceA000219(Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
25. Sloane, N. J. A. (ed.). "SequenceA014575(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.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
26. Sloane, N. J. A. (ed.). "SequenceA038823(Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
27. Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.