# 600 (number)

Short description: Natural number
 ← 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
Quaternary211204
Quinary44005
Senary24406
Octal11308
Duodecimal42012
Vigesimal1A020
Base 36GO36

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

## 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

### 610s

Main page: 613 (number)
• 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.[9]
• In Judaism the number 613 is very significant, as its metaphysics, the Kabbalah, views every complete entity as divisible into 613 parts: 613 parts of every Sefirah; 613 mitzvot, or divine Commandments in the Torah; 613 parts of the human body.
• The number 613 hangs from the rafters at Madison Square Garden in honor of New York Knicks coach Red Holzman's 613 victories.
• 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
Main page: 616 (number)
• 616 = 23 × 7 × 11, Padovan number, balanced number,[10] an alternative value for the Number of the Beast (more commonly accepted to be 666).
• 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, number of compositions of 17 into distinct parts,[11] prime index prime, index of prime Lucas number[9]
• Area code 617, a telephone area code covering the metropolitan Boston area.
• 618 = 2 × 3 × 103, sphenic number, admirable number.
• 619 = prime number, strobogrammatic prime,[12] alternating factorial[13]

### 620s

• 620 = 22 × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97). The sum of the first 620 primes is itself prime.[14]
• 621 = 33 × 23, Harshad number, the discriminant of a totally real cubic field[15]
• 622 = 2 × 311, nontotient, Fine number. Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree It is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)
• 623 = 7 × 89, number of partitions of 23 into an even number of parts[16]
• 624 = 24 × 3 × 13 = J4(5),[17] sum of a twin prime (311 + 313), Harshad number, Zuckerman number
• 625 = 252 = 54, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number,[18] 1-automorphic number, Friedman number since 625 = 56−2[19]
• 626 = 2 × 313, nontotient, 2-Knödel number. Stitch's experiment number.
• 627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20,[20] Smith number[21]
• 628 = 22 × 157, nontotient, totient sum for first 45 integers
• 629 = 17 × 37, highly cototient number,[22] Harshad number, number of diagonals in a 37-gon[23]

### 630s

• 630 = 2 × 32 × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), triangular number, hexagonal number,[24] sparsely totient number,[25] Harshad number, balanced number[26]
• 631 = Cuban prime number, centered triangular number,[27] centered hexagonal number,[28] Chen prime, lazy caterer number (sequence A000124 in the OEIS)
• 632 = 23 × 79, refactorable number, number of 13-bead necklaces with 2 colors[29]
• 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223), Blum integer; also, in the title of the movie 633 Squadron
• 634 = 2 × 317, nontotient, Smith number[21]
• 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts[30]
• "Project 635", the Irtysh River diversion project in China involving a dam and a canal.
• 636 = 22 × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number,[21] Mertens function(636) = 0
• 637 = 72 × 13, Mertens function(637) = 0, decagonal number[31]
• 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), nontotient, centered heptagonal number[32]
• 639 = 32 × 71, sum of the first twenty primes, also ISO 639 is the ISO's standard for codes for the representation of languages

### 640s

• 640 = 27 × 5, Harshad number, refactorable number, hexadecagonal number,[33] number of 1's in all partitions of 24 into odd parts,[34] number of acres in a square mile
• 641 = prime number, Sophie Germain prime,[35] factor of 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime[36]
• 642 = 2 × 3 × 107 = 14 + 24 + 54,[37] sphenic number, admirable number
• 643 = prime number, largest prime factor of 123456
• 644 = 22 × 7 × 23, nontotient, Perrin number,[38] Harshad number, common umask, admirable number
• 645 = 3 × 5 × 43, sphenic number, octagonal number, Smith number,[21] Fermat pseudoprime to base 2,[39] Harshad number
• 646 = 2 × 17 × 19, sphenic number, also ISO 646 is the ISO's standard for international 7-bit variants of ASCII, number of permutations of length 7 without rising or falling successions[40]
• 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3647 - 2647 is prime[41]
• 648 = 23 × 34 = A331452(7, 1),[42] Harshad number, Achilles number, area of a square with diagonal 36[43]
• 649 = 11 × 59, Blum integer

### 650s

• 650 = 2 × 52 × 13, primitive abundant number,[44] square pyramidal number,[45] pronic number,[1] nontotient, totient sum for first 46 integers; (other fields) the number of seats in the House of Commons of the United Kingdom, admirable number
• 651 = 3 × 7 × 31, sphenic number, pentagonal number,[46] nonagonal number[47]
• 652 = 22 × 163, maximal number of regions by drawing 26 circles[48]
• 653 = prime number, Sophie Germain prime,[35] balanced prime,[3] Chen prime, Eisenstein prime with no imaginary part
• 654 = 2 × 3 × 109, sphenic number, nontotient, Smith number,[21] admirable number
• 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid[49]
• 656 = 24 × 41 = $\displaystyle{ \lfloor \frac{3^{16}}{2^{16}} \rfloor }$.[50] In Judaism, 656 is the number of times that Jerusalem is mentioned in the Hebrew Bible or Old Testament.
• 657 = 32 × 73, the largest known number not of the form a2+s with s a semiprime
• 658 = 2 × 7 × 47, sphenic number, untouchable number
• 659 = prime number, Sophie Germain prime,[35] sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Chen prime, Mertens function sets new low of −10 which stands until 661, highly cototient number,[22] Eisenstein prime with no imaginary part, strictly non-palindromic number[4]

### 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.[25]
• Sum of 11th row when writing the natural numbers as a triangle.[51]
• 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 $\displaystyle{ 5n^{2}-5n+1 }$.
• Hexagram number of the form $\displaystyle{ 6n^{2}-6n+1 }$ i.e. a star number.
• 662 = 2 × 331, nontotient, member of Mian–Chowla sequence[52]
• 663 = 3 × 13 × 17, sphenic number, Smith number[21]
• 664 = 23 × 83, refactorable number, number of knapsack partitions of 33[53]
• Telephone area code for Montserrat.
• Area code for Tijuana within Mexico.
• Model number for the Amstrad CPC664 home computer.
• 665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon[23]
• 666 = 2 × 32 × 37, Harshad number, repdigit
• 667 = 23 × 29, lazy caterer number (sequence A000124 in the OEIS)
• 668 = 22 × 167, nontotient
• 669 = 3 × 223, blum integer

### 670s

• 670 = 2 × 5 × 67, sphenic number, octahedral number,[54] nontotient
• 671 = 11 × 61. This number is the magic constant of n×n normal magic square and n-queens problem for n = 11.
• 672 = 25 × 3 × 7, harmonic divisor number,[55] Zuckerman number, admirable number
• 673 = prime number, Proth prime[36]
• 674 = 2 × 337, nontotient, 2-Knödel number
• 675 = 33 × 52, Achilles number
• 676 = 22 × 132 = 262, palindromic square
• 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10[56]
• 678 = 2 × 3 × 113, sphenic number, nontotient, number of surface points of an octahedron with side length 13,[57] admirable number
• 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5[58]

### 680s

• 680 = 23 × 5 × 17, tetrahedral number,[59] 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.[60]
• 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[61]
• 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32[62]
• 685 = 5 × 137, centered square number[63]
• 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges[64]
• 687 = 3 × 229, 687 days to orbit the sun (Mars) D-number[65]
• 688 = 24 × 43, Friedman number since 688 = 8 × 86,[19] 2-automorphic number[66]
• 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[67]

### 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[68]
• 693 = 32 × 7 × 11, triangular matchstick number,[69] the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
• 694 = 2 × 347, centered triangular number,[27] nontotient
• 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[65]

## References

1. "Sloane's A005891 : Centered pentagonal numbers". OEIS Foundation.
2. "Sloane's A006562 : Balanced primes". OEIS Foundation.
3. "Sloane's A016038 : Strictly non-palindromic numbers". OEIS Foundation.
4. Sloane, N. J. A., ed. "Sequence A331452". OEIS Foundation. Retrieved 2022-05-09.
5. Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. Retrieved 2022-05-07.
6. "Sloane's A000045 : Fibonacci numbers". OEIS Foundation.
7. "Sloane's A002559 : Markoff (or Markov) numbers". OEIS Foundation.
8. Sloane, N. J. A., ed. "Sequence A001606 (Indices of prime Lucas numbers)". OEIS Foundation.
9. Sloane, N. J. A., ed. "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". OEIS Foundation. Retrieved 2022-05-24.
10. "Sloane's A007597 : Strobogrammatic primes". OEIS Foundation.
11. "Sloane's A005165 : Alternating factorials". OEIS Foundation.
12. Sloane, N. J. A., ed. "Sequence A006832 (Discriminants of totally real cubic fields)". OEIS Foundation. Retrieved 2022-05-31.
13. Sloane, N. J. A., ed. "Sequence A027187 (Number of partitions of n into an even number of parts)". OEIS Foundation. Retrieved 2022-05-31.
14. Sloane, N. J. A., ed. "Sequence A059377 (Jordan function J_4(n))". OEIS Foundation. Retrieved 2022-05-24.
15. "Sloane's A036057 : Friedman numbers". OEIS Foundation.
16. "Sloane's A000041 : a(n) = number of partitions of n". OEIS Foundation.
17. "Sloane's A006753 : Smith numbers". OEIS Foundation.
18. "Sloane's A100827 : Highly cototient numbers". OEIS Foundation.
19. Sloane, N. J. A., ed. "Sequence A000096 (a(n) = n*(n+3)/2)". OEIS Foundation. Retrieved 2022-05-31.
20. "Sloane's A000384 : Hexagonal numbers". OEIS Foundation.
21. "Sloane's A036913 : Sparsely totient numbers". OEIS Foundation.
22. "Sloane's A005448 : Centered triangular numbers". OEIS Foundation.
23. "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation.
24. Sloane, N. J. A., ed. "Sequence A101268 (Number of compositions of n into pairwise relatively prime parts)". OEIS Foundation. Retrieved 2022-05-31.
25. "Sloane's A001107 : 10-gonal (or decagonal) numbers". OEIS Foundation.
26. "Sloane's A069099 : Centered heptagonal numbers". OEIS Foundation.
27. Sloane, N. J. A., ed. "Sequence A051868 (16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6))". OEIS Foundation. Retrieved 2022-05-31.
28. "Sloane's A005384 : Sophie Germain primes". OEIS Foundation.
29. "Sloane's A080076 : Proth primes". OEIS Foundation.
30. Sloane, N. J. A., ed. "Sequence A074501 (a(n) = 1^n + 2^n + 5^n)". OEIS Foundation. Retrieved 2022-05-31.
31. "Sloane's A001608 : Perrin sequence". OEIS Foundation.
32. "Sloane's A001567 : Fermat pseudoprimes to base 2". OEIS Foundation.
33. Sloane, N. J. A., ed. "Sequence A057468 (Numbers k such that 3^k - 2^k is prime)". OEIS Foundation. Retrieved 2022-05-31.
34. "Sloane's A331452". OEIS Foundation.
35. Sloane, N. J. A., ed. "Sequence A001105 (a(n) = 2*n^2)". OEIS Foundation.
36. "Sloane's A071395 : Primitive abundant numbers". OEIS Foundation.
37. "Sloane's A000330 : Square pyramidal numbers". OEIS Foundation.
38. "Sloane's A000326 : Pentagonal numbers". OEIS Foundation.
39. Sloane, N. J. A., ed. "Sequence A014206 (a(n) = n^2 + n + 2)". OEIS Foundation. Retrieved 2022-05-31.
40. Sloane, N. J. A., ed. "Sequence A160160 (Toothpick sequence in the three-dimensional grid)". OEIS Foundation. Retrieved 2022-05-31.
41. Sloane, N. J. A., ed. "Sequence A002379 (a(n) = floor(3^n / 2^n))". OEIS Foundation. Retrieved 2022-05-31.
42. Sloane, N. J. A., ed. "Sequence A027480 (a(n) = n*(n+1)*(n+2)/2)". OEIS Foundation. Retrieved 2022-05-31.
43. "Sloane's A005282 : Mian-Chowla sequence". OEIS Foundation.
44. Sloane, N. J. A., ed. "Sequence A108917 (Number of knapsack partitions of n)". OEIS Foundation. Retrieved 2022-05-31.
45. "Sloane's A005900 : Octahedral numbers". OEIS Foundation.
46. "Sloane's A001599 : Harmonic or Ore numbers". OEIS Foundation.
47. Sloane, N. J. A., ed. "Sequence A316983 (Number of non-isomorphic self-dual multiset partitions of weight n)". OEIS Foundation. Retrieved 2022-05-31.
48. Sloane, N. J. A., ed. "Sequence A005899 (Number of points on surface of octahedron with side n)". OEIS Foundation. Retrieved 2022-05-31.
49. Sloane, N. J. A., ed. "Sequence A003001 (Smallest number of multiplicative persistence n)". OEIS Foundation. Retrieved 2022-05-31.
50. "Sloane's A000292 : Tetrahedral numbers". OEIS Foundation.
51. Sloane, N. J. A., ed. "Sequence A000975 (Lichtenberg sequence)". OEIS Foundation. Retrieved 2022-05-31.
52. "Sloane's A000979 : Wagstaff primes". OEIS Foundation.
53. Sloane, N. J. A., ed. "Sequence A000070 (a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041))". OEIS Foundation. Retrieved 2022-05-31.
54. "Sloane's A001844 : Centered square numbers". OEIS Foundation.
55. Sloane, N. J. A., ed. "Sequence A050535 (Number of multigraphs on infinite set of nodes with n edges)". OEIS Foundation. Retrieved 2022-05-31.
56. Sloane, N. J. A., ed. "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n divides k^(n-2)-k for all k with gcd(k, n) = 1)". OEIS Foundation. Retrieved 2022-05-31.
57. Sloane, N. J. A., ed. "Sequence A030984 (2-automorphic numbers)". OEIS Foundation. Retrieved 2021-09-01.
58. "Sloane's A000787 : Strobogrammatic numbers". OEIS Foundation.
59. Sloane, N. J. A., ed. "Sequence A000123 (Number of binary partitions: number of partitions of 2n into powers of 2)". OEIS Foundation. Retrieved 2022-05-31.
60. Sloane, N. J. A., ed. "Sequence A045943 (Triangular matchstick numbers: a(n) = 3*n*(n+1)/2)". OEIS Foundation. Retrieved 2022-05-31.
61. Sloane, N. J. A., ed. "Sequence A076185 (Numbers n such that n!! + 2 is prime)". OEIS Foundation. Retrieved 2022-05-31.
62. Sloane, N. J. A., ed. "Sequence A006851 (Trails of length n on honeycomb lattice)". OEIS Foundation. Retrieved 2022-05-18.
63. Sloane, N. J. A., ed. "Sequence A045636 (Numbers of the form p^2 + q^2, with p and q primes)". OEIS Foundation. Retrieved 2022-05-31.