# 600 (number)

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

 ← 599 600 601 →
Cardinalsix hundred
Ordinal600th
(six hundredth)
Factorization23 × 3 × 52
Divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
Greek numeralΧ´
Roman numeralDC
Binary10010110002
Ternary2110203
Octal11308
Duodecimal42012

## Mathematical properties

Six hundred is a composite number, an abundant number, a pronic number 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

### 610s

• 613 = prime number, first number of prime triple (p, p + 4, p + 6), middle number of sexy prime triple (p − 6, p, p + 6). Geometrical numbers: Centered square number with 18 per side, circular number of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a lucky number, index of prime Lucas number.
• 614 = 2 × 307, nontotient, 2-Knödel number. According to Rabbi Emil Fackenheim, the number of Commandments in Judaism should be 614 rather than the traditional 613.
• 615 = 3 × 5 × 41, sphenic number

### 660s

• 660 = 22 × 3 × 5 × 11
• Sum of four consecutive primes (157 + 163 + 167 + 173).
• Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127).
• Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101).
• Sparsely totient number.
• Sum of 11th row when writing the natural numbers as a triangle.
• 661 = prime number
• Sum of three consecutive primes (211 + 223 + 227).
• Mertens function sets new low of −11 which stands until 665.
• Pentagram number of the form $5n^{2}-5n+1$ .
• Hexagram number of the form $6n^{2}-6n+1$  i.e. a star number.
• 662 = 2 × 331, nontotient, member of Mian–Chowla sequence
• 663 = 3 × 13 × 17, sphenic number, Smith number
• 664 = 23 × 83, number of knapsack partitions of 33
• 665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon
• 666 = 2 × 32 × 37, repdigit
• 667 = 23 × 29, lazy caterer number (sequence A000124 in the OEIS)
• 668 = 22 × 167, nontotient
• 669 = 3 × 223, blum integer

### 680s

• 680 = 23 × 5 × 17, tetrahedral number, nontotient
• 681 = 3 × 227, centered pentagonal number
• 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.
• 683 = prime number, Sophie Germain prime, sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime
• 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32
• 685 = 5 × 137, centered square number
• 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges
• 687 = 3 × 229, 687 days to orbit the sun (Mars) D-number
• 688 = 24 × 43, Friedman number since 688 = 8 × 86, 2-automorphic number
• 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

### 690s

• 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number, Smith number, 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
• 693 = 32 × 7 × 11, triangular matchstick number, the number of the "non-existing" Alabama State Constitution amendment, the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
• 694 = 2 × 347, centered triangular number, nontotient
• 695 = 5 × 139, 695!! + 2 is prime.
• 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 
• 697 = 17 × 41, cake number; the number of sides of Colorado
• 698 = 2 × 349, nontotient, sum of squares of two primes
• 699 = 3 × 233, D-number