# 600 (number)

(Redirected from 667 (number))
For the years 600, see 600s BC (decade), 600s, and 600.
 ← 599 600 601 →
Cardinal Six hundred
Ordinal th
Factorization ${\displaystyle 2^{3}\cdot 3\cdot 5^{2}}$
Prime 1, 2, 3, 5
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
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

### 600s

601 prime number, centered pentagonal number[3]

602 = 2 × 7 × 43, nontotient, area code for Phoenix, AZ along with 480 and 623

603 = 32 × 67, Harshad number, area code for New Hampshire

604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky)

605 = 5 × 112, Harshad number

606 = 2 × 3 × 101, sphenic number, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109)

607 prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, balanced prime,[4] strictly non-palindromic number[5]

608 = 25 × 19, Mertens function(608) = 0, nontotient, happy number

609 = 3 × 7 × 29, sphenic number

### 610s

610 = 2 × 5 × 61, sphenic number, nontotient, Fibonacci number,[6] Markov number.[7] Also a kind of telephone wall socket used in Australia. China's 6-10 office (also called 610 office) is an extra-constitutional Gestapo-like organisation established to persecute practitioners of Falun Gong.

611 = 13 × 47

612 = 22 × 32 × 17, Harshad number, area code for Minneapolis, MN

613 = Primes: 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.

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 legendary New York Knicks coach Red Holzman's 613 victories.

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

616 = 23 × 7 × 11, Padovan number, 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

Area code 617, a telephone area code covering the metropolitan Boston area.

618 = 2 × 3 × 103, sphenic number.

619 prime number, strobogrammatic prime,[8] alternating factorial[9]

### 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)

621 = 33 × 23, Harshad number

622 = 2 × 311, nontotient

It is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)

623 = 7 × 89

624 = 24 × 3 × 13, sum of a twin prime (311 + 313), Harshad number, Zuckerman number

625 = 54 = 252, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number,[10] 1-automorphic number, Friedman number since 625 = 56−2[11]

626 = 2 × 313, nontotient

627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20,[12] Smith number[13]

628 = 22 × 157, nontotient, totient sum for first 45 integers

629 = 17 × 37, highly cototient number,[14] Harshad number

### 630s

630 = 2 × 32 × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), triangular number, hexagonal number,[15] sparsely totient number,[16] Harshad number

631 prime number, centered triangular number,[17] centered hexagonal number,[18] Chen prime; (other fields) the number of seats in Bundestag

632 = 23 × 79

633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223); also, in the title of the movie 633 Squadron

634 = 2 × 317, nontotient, Smith number[13]

635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0.

"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,[13] Mertens function(636) = 0,

637 = 72 × 13, Mertens function(637) = 0, decagonal number[19]

638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), nontotient, centered heptagonal number[20]

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, 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, number of total Pokémon species as of Pokémon Black and White

### 650s

650 = 2 × 52 × 13, primitive abundant number,[25] square pyramidal number,[26] 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

651 = 3 × 7 × 31, sphenic number, pentagonal number,[27] nonagonal number[28]

652 = 22 × 163

653 prime number, Sophie Germain prime,[21] balanced prime,[4] Chen prime, Eisenstein prime with no imaginary part

654 = 2 × 3 × 109, sphenic number, nontotient, Smith number[13]

655 = 5 × 131

656 = 24 × 41. In Judaism, 656 is the number of times that Jerusalem is mentioned in the Hebrew Bible or Old Testament.

657 = 32 × 73, probably the largest number not of the form a2+s with s a semiprime

658 = 2 × 7 × 47, sphenic number

659 prime number, Sophie Germain prime,[21] 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,[14] Eisenstein prime with no imaginary part, strictly non-palindromic number[5]

### 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: See 666 (number)

667 = 23 × 29

668 = 22 × 167, nontotient

669 = 3 × 223

### 670s

670 = 2 × 5 × 67, sphenic number, octahedral number,[30] 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,[31] Zuckerman number,

673 prime number, Proth prime[22]

674 = 2 × 337, nontotient

675 = 33 × 52

676 = 22 × 132 = 262

677 prime number, Chen prime, Eisenstein prime with no imaginary part

678 = 2 × 3 × 113, sphenic number, nontotient

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)

### 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 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]

"689" is the nickname of Hong Kong Chief Executive Leung Chun-ying who won the election with 689 electoral votes.

### 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

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.
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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.
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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.