600 (number)

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For the years 600, see 600s BC (decade), 600s, and 600.
← 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
Senary24406
Octal11308
Duodecimal42012
Hexadecimal25816

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.

In other fields

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.

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 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]

"689" is the nickname of Hong Kong Chief Executive Leung Chun-ying who won the election with 689 electoral votes in 2012 Hong Kong chief executive election.

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. ^ a b c d e f g "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.
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