6000 (number)

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

← 5999 6000 6001 →
Cardinalsix thousand
Ordinal6000th
(six thousandth)
Factorization24 × 3 × 53
Greek numeral,Ϛ´
Roman numeralVM, or VI
Unicode symbol(s)VM, vm, VI, vi
Binary10111011100002
Ternary220200203
Senary434406
Octal135608
Duodecimal358012
Hexadecimal177016

Selected numbers in the range 6001–6999Edit

6001 to 6099Edit

6100 to 6199Edit

6200 to 6299Edit

6300 to 6399Edit

  • 6311super-prime
  • 6317 – balanced prime
  • 6322 – centered heptagonal number[1]
  • 6323 – Sophie Germain prime, balanced prime, super-prime
  • 6328 – triangular number
  • 6329 – Sophie Germain prime
  • 6346 – Number of verses in the Qur'an according to the sect founded by Rashad Khalifa.[11]
  • 6348pentagonal pyramidal number[12]
  • 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 6499Edit

  • 6400 = 802
  • 6408 – sum of the squares of the first thirteen primes
  • 6441 – triangular number
  • 6449 – Sophie Germain prime
  • 6466Markov number[13]
  • 6491 – Sophie Germain prime

6500 to 6599Edit

  • 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[3]
  • 6521Sophie Germain prime
  • 6542 – number of primes  .[14]
  • 6545tetrahedral 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] centered octagonal number[8]
  • 6563 – Sophie Germain prime
  • 6581 – Sophie Germain prime
  • 6599 – safe prime

6600 to 6699Edit

6700 to 6799Edit

  • 6719 – safe prime, highly cototient number[3]
  • 6724 = 822
  • 6728 – number of domino tilings of a 6×6 checkerboard
  • 6761 – Sophie Germain prime
  • 6765 – 20th Fibonacci number[18]
  • 6779 – safe prime
  • 6786 – triangular number

6800 to 6899Edit

  • 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[19]
  • 6859 = 193
  • 6863 – balanced prime
  • 6879 – number of planar partitions of 15[20]
  • 6880vampire number[21]
  • 6889 = 832, centered octagonal number[8]
  • 6899 – Sophie Germain prime, safe prime

6900 to 6999Edit

Prime numbersEdit

There are 117 prime numbers between 6000 and 7000:[22][23]

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 alsoEdit

ReferencesEdit

  1. ^ a b c d "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-09. Retrieved 2016-06-14.
  2. ^ a b "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-06-14.
  3. ^ a b c d "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-06-14.
  4. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-06-14.
  5. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-17. Retrieved 2016-06-14.
  6. ^ a b "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-06-14.
  7. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-06-14.
  8. ^ a b c "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-23. Retrieved 2016-06-14.
  9. ^ "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-06-14.
  10. ^ a b c "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-17. Retrieved 2016-06-14.
  11. ^ Gardner, Martin (September–October 1997), "The numerology of Dr. Rashad Khalifa", Skeptical Inquirer, archived from the original on 2004-09-27
  12. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-17. Retrieved 2016-06-14.
  13. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-29. Retrieved 2016-06-14.
  14. ^ Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  15. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-13. Retrieved 2016-06-14.
  16. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-14. Retrieved 2016-06-14.
  17. ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-08. Retrieved 2016-06-14.
  18. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-16. Retrieved 2016-06-14.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A006958 (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.
  20. ^ 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.
  21. ^ "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-16. Retrieved 2016-06-14.
  22. ^ 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.
  23. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.