# 600 (number)

(Redirected from 633 (number))
 ← 599 600 601 →
Cardinal six hundred
Ordinal 600th
(six hundredth)
Factorization 23× 3 × 52
Divisors 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
Greek numeral Χ´
Roman numeral DC
Binary 10010110002
Ternary 2110203
Quaternary 211204
Quinary 44005
Senary 24406
Octal 11308
Duodecimal 42012
Vigesimal 1A020
Base 36 GO36

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.

## 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.
• 614 = 2 × 307, nontotient. 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

### 640s

• 640 = 27 × 5, Harshad number, number of acres in a square mile
• 641= prime number, Sophie Germain prime,[21] factor of 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime[22]
• 642 = 2 × 3 × 107, sphenic number
• 643 = prime number, largest prime factor of 123456
• 644 = 22 × 7 × 23, nontotient, Perrin number,[23] Harshad number, common umask.
• 645 = 3 × 5 × 43, sphenic number, Smith number,[13] Fermat pseudoprime to base 2,[24] Harshad number
• 646 = 2 × 17 × 19, sphenic number, also ISO 646 is the ISO's standard for international 7-bit variants of ASCII
• 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part
• 648 = 23 × 34, Harshad number
• 649 = 11 × 59

### 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,[16] Harshad number
• 661 = prime number, sum of three consecutive primes (211 + 223 + 227), Mertens function sets new low of −11 which stands until 665, star number
• 662 = 2 × 331, nontotient, member of Mian–Chowla sequence[29]
• 663 = 3 × 13 × 17, sphenic number, Smith number[13]
• 664 = 23 × 83

Country calling code for Montserrat (+1) 664

• 665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105
• 666 = 2 × 332 × 7,
• 667 = 23 × 29
• 668 = 22 × 167, nontotient
• 669 = 3 × 223

### 680s

• 680 = 23 × 5 × 17, tetrahedral number,[32] nontotient
• 681 = 3 × 227, centered pentagonal number[3]
• 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)
• 683 = prime number, Sophie Germain prime,[21] sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime[33]
• 684 = 22 × 32 × 19, Harshad number
• 685 = 5 × 137, centered square number[34]
• 686 = 2 × 73, nontotient,

The code for international direct dial phone calls to Kiribati. 686 is name of a company for snowboarding apparel. i686 is another name for Intel P6 microarchitecture.

• 687 = 3 × 229
• 688 = 24 × 43, Friedman number since 688 = 8 × 86[11]
• 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[35]

### 690s

• 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,[16] Smith number,[13] 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
• 693 = 32 × 7 × 11, 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,[17] nontotient
• 695 = 5 × 139. The number of people dead in the single deadliest tornado in United States history
• 696 = 23 × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers
• 697 = 17 × 41
• 698 = 2 × 349, nontotient
• 699 = 3 × 233

## References

1. ^ a b "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
2. ^ Lewis and Short, A Latin Dictionary, s.v. sescenti
3. ^ a b "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
4. ^ a b "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
5. ^ a b "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
6. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
7. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
8. ^ "Sloane's A007597 : Strobogrammatic primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
9. ^ "Sloane's A005165 : Alternating factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
10. ^ "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
11. ^ a b "Sloane's A036057 : Friedman numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
12. ^ "Sloane's A000041 : a(n) = number of partitions of n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
13. "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
14. ^ a b "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
15. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
16. ^ a b c "Sloane's A036913 : Sparsely totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundatioin. Retrieved 2016-06-11.
17. ^ a b "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
18. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
19. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
20. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
21. ^ a b c d "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
22. ^ a b "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
23. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
24. ^ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
25. ^ "Sloane's A071395 : Primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
26. ^ "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
27. ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
28. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
29. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
30. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
31. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
32. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
33. ^ "Sloane's A000979 : Wagstaff primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
34. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
35. ^ "Sloane's A000787 : Strobogrammatic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.