600 (number)

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For the years 600, see 600s BC (decade) and 600.
599 600 601
Cardinal Six hundred
Ordinal th
Factorization 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
Hexadecimal 25816
Vigesimal 1A020
Base 36 GO36

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 and a Harshad number.

In other fields[edit]

Integers from 601 to 699[edit]

600s[edit]

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, Happy number


609 = 3 × 7 × 29, sphenic number

610s[edit]


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.

Running Gag in the Disney Channel series Gravity Falls meaning June 18th, Alex Hirsch's birthdate.


619 prime number, strobogrammatic prime, alternating factorial

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, 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[edit]


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[edit]


640 = 27 × 5, Harshad number, number of acres in a square mile


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[edit]


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[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, 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 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[edit]


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[edit]


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. i686 is another name for Intel P6 microarchitecture.


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[edit]


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

References[edit]

  1. ^ Lewis and Short, A Latin Dictionary, s.v. sescenti