600 (number)

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

Mathematical properties[edit]

Six hundred is a composite number, an abundant number, a pronic number^[1] and a Harshad number.

In other fields[edit]

• In the United States, a credit score of 600 or below is considered a poor score, thus limiting available credit (or requiring the borrower to pay higher interest rates).
• 600 is the advertised number of miles that NASCAR runs in the Coca-Cola 600, the longest race on any of the NASCAR circuits.
• Fiat 600
• In Latin, sescenti often denoted a very large but indefinite number, perhaps from the size of a Roman cohort.^[2]

Integers from 601 to 699[edit]

600s[edit]

• 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[edit]

• 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, sum of the three standard board sizes in Go (9² + 13² + 19²)
• 612 = 2² × 3² × 17, Harshad number, area code for Minneapolis, MN

• 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.
  • 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[edit]

• 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 = 5^6−2[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[edit]

• 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[edit]

• 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

650s[edit]

• 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, the largest known 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[edit]

• 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 × 3² × 37,
• 667 = 23 × 29
• 668 = 2² × 167, nontotient
• 669 = 3 × 223

670s[edit]

• 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[edit]

• 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[edit]

• 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[edit]