6000 (number)#6800 to 6899

{{Redirect|6,000|the Jewish year|Year 6000|other uses|6000 (disambiguation)}}

{{Refimprove|date=December 2009}}

{{Infobox number

| number = 6000

|ordinal text=

| roman = {{Overline|V}}M, or {{Overline|VI}}

| unicode = {{Overline|V}}M, {{Overline|v}}m, {{Overline|VI}}, {{Overline|vi}}

|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=

  • 6101 – Sophie Germain prime
  • 6105triangular 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
  • 6143Thabit number
  • 61443-smooth number (211×3)
  • 6173 – Sophie Germain prime
  • 6174 – Kaprekar's constant
  • 6181octahedral number{{cite OEIS|A005900|2=Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.}}

=6200 to 6299=

  • 6200harmonic divisor number{{cite OEIS|A001599|Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.}}
  • 6201square pyramidal number{{cite OEIS|A000330|2=Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.}}
  • 6216 – triangular number
  • 6217super-prime, prime of the form 2p-1
  • 6229super-prime
  • 6232amicable number with 6368
  • {{vanchor|6236}} – Most widely accepted figure for the number of verses in the Qur'an{{citation needed|date=June 2014}}
  • 6241 = 792, centered octagonal number{{cite OEIS|A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers.}}
  • 6250Leyland number{{cite OEIS|A076980|2=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)).}}
  • 6263 – Sophie Germain prime, balanced prime
  • 6269 – Sophie Germain prime
  • 6280decagonal number{{cite OEIS|A001107|2=10-gonal (or decagonal) numbers: a(n) = n*(4*n-3).}}

=6300 to 6399=

  • 6311super-prime
  • 6317 – balanced prime
  • 6322 – centered heptagonal number
  • 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
  • {{vanchor|6346}} – Number of verses in the Qur'an according to the sect founded by Rashad Khalifa.{{Citation|last=Gardner|first=Martin|title=The numerology of Dr. Rashad Khalifa

| magazine = Skeptical Inquirer|date=September–October 1997|url=http://findarticles.com/p/articles/mi_m2843/is_n5_v21/ai_20121071 |url-status=dead |archiveurl=https://web.archive.org/web/20040927010219/http://findarticles.com/p/articles/mi_m2843/is_n5_v21/ai_20121071 |archivedate=2004-09-27 }}

  • 6348pentagonal pyramidal number{{cite OEIS|A002411|2=Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.}}
  • 6361 – prime of the form 2p-1, twin prime
  • 6364 – nonagonal number
  • 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
  • 6466Markov number{{cite OEIS|A002559|2=Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.}}
  • 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{{Cite OEIS|A100827|Highly cototient numbers}}
  • 6521Sophie Germain prime
  • 6542 – number of primes \leq 2^{16}.{{cite OEIS|A007053|2=Number of primes <= 2^n}}
  • 6545tetrahedral number{{cite OEIS|A000292|2=Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.}}
  • 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{{cite OEIS|A082897|Perfect totient numbers}}
  • 6563 – Sophie Germain prime
  • 6581 – Sophie Germain prime
  • 6599 – safe prime

=6600 to 6699=

  • 6601 - Carmichael number,{{cite OEIS|A002997|2=Carmichael numbers: composite numbers k such that a^(k-1) == 1 (mod k) for every a coprime to k.}} decagonal number, sum of the first 56 primes
  • 6623 – centered heptagonal number
  • 6659 – safe prime
  • 6666 – forty-fourth nonagonal number, and the 11th third-convolution of Fibonacci numbers.{{Cite OEIS|A001628 |Convolved Fibonacci numbers.}} In Christian demonology it represents the number of demons in a legion of demons.{{citation needed|date=August 2023}}
  • 6670triangular number,{{cite OEIS|A000217|2=Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n}} centered nonagonal number,{{cite OEIS|A060544|2=Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1}} centered 19-gonal number,{{cite OEIS|A069132|Centered 19-gonal numbers.}}

=6700 to 6799=

  • 6719 – safe prime, highly cototient number
  • 6724 = 822
  • 6733 - star prime
  • 6728 – number of domino tilings of a 6×6 checkerboard
  • 6761 – Sophie Germain prime
  • 6765 – 20th Fibonacci number{{cite OEIS|A000045|2=Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.}}
  • 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{{cite OEIS|A006958|Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused)}}
  • 6859 = 193
  • 6863 – balanced prime
  • 6870 - sum of the first 57 primes
  • 6879 – number of planar partitions of 15{{cite OEIS|A000219|Number of planar partitions (or plane partitions) of n}}
  • 6880vampire number{{cite OEIS|A014575|2=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.}}
  • 6889 = 832, centered octagonal number
  • 6899 – Sophie Germain prime, safe prime

=6900 to 6999=

  • 6903 – triangular number
  • 69123-smooth number (28×33)
  • 6924magic constant of n × n normal magic square and n-Queens Problem for n = 24.
  • 6929 – highly cototient number
  • 6930 – decagonal number, square pyramidal number
  • 6931 – centered heptagonal number
  • 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:{{Cite OEIS|A038823|Number of primes between n*1000 and (n+1)*1000}}{{cite web|last=Stein |first=William A. |author-link=William A. Stein |title=The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture |url=https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/ |website=wstein.org |date=10 February 2017 |access-date=6 February 2021}}

: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

References

{{reflist}}

{{Integers|10}}

Category:Integers