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651 (number)

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651 (number)

For the years 600, see 600s BC (decade) and 600.

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 and a Harshad number.

In other fields

  • 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 also the advertised number of miles that NASCAR runs in the Coca-Cola 600, the longest race on any of the NASCAR circuits.
  • Fiat 600

Integers from 601 to 699

600s

601 prime number, centered pentagonal number


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, strictly non-palindromic number


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


609 = 3 × 7 × 29, sphenic number

610s


610 = 2 × 5 × 61, sphenic number, nontotient, Fibonacci number, Markov number. 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


618 = 2 × 3 × 103, sphenic number


619 prime number, strobogrammatic prime, alternating factorial

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, 1-automorphic number, Friedman number since 625 = 56−2


626 = 2 × 313, nontotient


627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20, Smith number


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


629 = 17 × 37, highly cototient number, Harshad number

630s


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


631 prime number, centered triangular number, centered hexagonal number, Chen prime


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


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, Mertens function(636) = 0,


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


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


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


641 prime number, Sophie Germain prime, factor of 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime


642 = 2 × 3 × 107, sphenic number


643 prime number, largest prime factor of 123456


644 = 22 × 7 × 23, nontotient, Perrin number. Harshad number, common umask.


645 = 3 × 5 × 43, sphenic number, Smith number, Fermat pseudoprime to base 2, 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, square pyramidal number, pronic number, nontotient, totient sum for first 46 integers


651 = 3 × 7 × 31, sphenic number, pentagonal number, nonagonal number


652 = 22 × 163


653 prime number, Sophie Germain prime, balanced prime, Chen prime, Eisenstein prime with no imaginary part


654 = 2 × 3 × 109, sphenic number, nontotient, Smith number


655 = 5 × 131


656 = 24 × 41


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, 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, Eisenstein prime with no imaginary part, strictly non-palindromic number

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, 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


663 = 3 × 13 × 17, sphenic number, Smith number


664 = 23 × 83


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, 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, Zuckerman number,

track 5 of The Dresden Dolls.


673 prime number, Proth prime


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, nontotient


681 = 3 × 227, centered pentagonal number


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, sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime


684 = 22 × 32 × 19, Harshad number


685 = 5 × 137, centered square number


686 = 2 × 73, nontotient, The code for international direct dial phone calls to Kiribati. 686 is name of company for snowboarding apparel.


687 = 3 × 229


688 = 24 × 43, Friedman number since 688 = 8 × 86


689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109)

690s


690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number, Smith number, 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, 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

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