600_(number)

600 (number)

600 (number)

Natural number


600 (six hundred) is the natural number following 599 and preceding 601.

Quick Facts ← 599 600 601 →, Cardinal ...

Mathematical properties

Six hundred is a composite number, an abundant number, a pronic number[1] and a Harshad number.

Credit and cars

  • In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate.
  • NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race.
  • The Fiat 600 is a car, the SEAT 600 its Spanish version.

Integers from 601 to 699

600s

610s

620s

630s

640s

650s

660s

670s

680s

  • 680 = 23 × 5 × 17, tetrahedral number,[58] nontotient
  • 681 = 3 × 227, centered pentagonal number[2]
  • 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzle strikketoy.[59]
  • 683 = prime number, Sophie Germain prime,[35] sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime[60]
  • 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32[61]
  • 685 = 5 × 137, centered square number[62]
  • 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges[63]
  • 687 = 3 × 229, 687 days to orbit the Sun (Mars) D-number[64]
  • 688 = 24 × 43, Friedman number since 688 = 8 × 86,[19] 2-automorphic number[65]
  • 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). Strobogrammatic number[66]

690s

  • 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,[25] Smith number,[21] Harshad number
    • ISO 690 is the ISO's standard for bibliographic references
  • 691 = prime number, (negative) numerator of the Bernoulli number B12 = -691/2730. Ramanujan's tau function τ and the divisor function σ11 are related by the remarkable congruence τ(n) ≡ σ11(n) (mod 691).
    • In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved.
  • 692 = 22 × 173, number of partitions of 48 into powers of 2[67]
  • 693 = 32 × 7 × 11, triangular matchstick number,[68] the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
  • 694 = 2 × 347, centered triangular number,[27] nontotient, smallest pandigital number in base 5.[69]
  • 695 = 5 × 139, 695!! + 2 is prime.[70]
  • 696 = 23 × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice [71]
  • 697 = 17 × 41, cake number; the number of sides of Colorado[72]
  • 698 = 2 × 349, nontotient, sum of squares of two primes[73]
  • 699 = 3 × 233, D-number[64]

References

  1. Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.

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