6000 (number)
Appearance
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Cardinal | six thousand | |||
Ordinal | 6000th (six thousandth) | |||
Factorization | 24× 3 × 53 | |||
Greek numeral | ,Ϛ´ | |||
Roman numeral | VM, orVI | |||
Unicodesymbol(s) | VM,vm,VI,vi | |||
Binary | 10111011100002 | |||
Ternary | 220200203 | |||
Senary | 434406 | |||
Octal | 135608 | |||
Duodecimal | 358012 | |||
Hexadecimal | 177016 | |||
Armenian | Ց |
6000(six thousand) is thenatural numberfollowing 5999 and preceding 6001.
Selected numbers in the range 6001–6999
[edit]6001 to 6099
[edit]- 6025– Stage name of rhythm guitarist of theDead Kennedysfrom June 1978 to March 1979. Full name isCarlos Cadona.
- 6028–centered heptagonal number[1]
- 6037–super-prime,prime of the form 2p-1
- 6042–6042 Cheshirecatis aMars-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 theGeorge OrwellnovelNineteen Eighty-Four
- 6084= 782,sum of the cubes of the first twelve integers
- 6089–highly cototient number[3]
- 6095–magic constantofn×nnormalmagic squareandn-Queens Problemforn= 23.
6100 to 6199
[edit]- 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 primewith 6133
- 6133– 800th prime number, twin prime with 6131
- 6143–Thabit number
- 6144–3-smoothnumber (211×3)
- 6173– Sophie Germain prime
- 6174– Kaprekar's constant
- 6181–octahedral number[4]
6200 to 6299
[edit]- 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 numberwith 6368
- 6236– Most widely accepted figure for the number of verses in theQur'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
[edit]- 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
- 6346– Number of verses in theQur'anaccording to the sect founded byRashad 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
[edit]- 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
[edit]- 6502– model number of theMOS Technology 6502which 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.[14]
- 6545–tetrahedral number[15]
- 6551– Sophie Germain prime
- 6555– triangular number
- 6556– member of aRuth-Aaron pairwith 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
[edit]- 6601-Carmichael number,[17]decagonal number[9]
- 6623– centered heptagonal number[1]
- 6659– safe prime
- 6666– forty-fourth nonagonal number,[2]and the 11ththird-convolutionofFibonacci numbers.[18]InChristian demonologyit represents thenumber of demonsin a legion of demons.[citation needed]
- 6670–triangular number,[19]centered nonagonal number,[20]centered 19-gonal number,[21]
6700 to 6799
[edit]- 6719– safe prime, highly cototient number[13]
- 6724= 822
- 6728– number of domino tilings of a 6×6checkerboard
- 6761– Sophie Germain prime
- 6765– 20thFibonacci number[22]
- 6779– safe prime
- 6786– triangular number
6800 to 6899
[edit]- 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- largestright-truncatable primein base 7
- 6842– number of parallelogram polyominoes with 12 cells[23]
- 6859= 193
- 6863– balanced prime
- 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
[edit]- 6903– triangular number
- 6912–3-smoothnumber (28×33)
- 6924–magic constantofn×nnormalmagic squareandn-Queens Problemforn= 24.
- 6929– highly cototient number[13]
- 6930– decagonal number,[9]square pyramidal number[6]
- 6931– centered heptagonal number[1]
- 6969– 2015 comedicprogressive rocksong by the bandNinja Sex Party
- 6975– nonagonal number
- 6977– balanced prime
- 6983– Sophie Germain prime, safe prime
- 6997– 900th prime number
Prime numbers
[edit]There are 117prime numbersbetween 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
[edit]References
[edit]- ^abcdSloane, N. J. A.(ed.)."Sequence A069099 (Centered heptagonal numbers.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^abcSloane, N. J. A.(ed.)."Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A100827 (Highly cototient numbers: records for a(n) in A063741.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A005900 (Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A001599 (Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^abSloane, N. J. A.(ed.)."Sequence A000330 (Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 +... + n^2 = n*(n+1)*(2*n+1)/6.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^abSloane, N. J. A.(ed.)."Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A076980 (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)).)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^abcSloane, N. J. A.(ed.)."Sequence A001107 (10-gonal (or decagonal) numbers: a(n) = n*(4*n-3).)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Gardner, Martin (September–October 1997),"The numerology of Dr. Rashad Khalifa",Skeptical Inquirer,archived fromthe originalon 2004-09-27
- ^Sloane, N. J. A.(ed.)."Sequence A002411 (Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A002559 (Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^abcSloane, N. J. A.(ed.)."Sequence A100827 (Highly cototient numbers)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A007053 (Number of primes <= 2^n)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A082897 (Perfect totient numbers)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A002997 (Carmichael numbers: composite numbers k such that a^(k-1) == 1 (mod k) for every a coprime to k.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A001628 (Convolved Fibonacci numbers.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A000217 (Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 +... + n)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A060544 (Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A069132 (Centered 19-gonal numbers.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A000045 (Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A000219 (Number of planar partitions (or plane partitions) of n)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A014575 (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.)".TheOn-Line Encyclopedia of Integer Sequences.OEIS Foundation.
- ^Sloane, N. J. A.(ed.)."Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)".TheOn-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.Retrieved6 February2021.