651 (number)

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

Mathematical properties

Six hundred is a composite number, an abundant number, a pronic number and a Harshad number.

Credit and cars

* In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate.
* NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race.
* The Fiat 600 is a car, the SEAT 600 its Spanish version.

Integers from 601 to 699

600s

* 601 = prime number, centered pentagonal number
* 602 = 2 × 7 × 43, nontotient, oeis:A005897, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with area code 480, 480 and area code 623, 623
* 603 = 3² × 67, Harshad number, oeis:A005043, Riordan number, Area code 603, 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, oeis:A006002, sum of the nontriangular numbers between the two successive oeis:A000217, triangular numbers 55 and 66, oeis:A283877, number of non-isomorphic set-systems of weight 9.
* 606 = 2 × 3 × 101, sphenic number, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), oeis:A111592, admirable number
* 607 – prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, balanced prime, strictly non-palindromic number, Mersenne prime exponent
* 608 = 2⁵ × 19, Mertens function(608) = 0, nontotient, happy number
number of regions formed by drawing the line segments connecting any two of the perimeter points of a 3 times 4 grid of squares.
* 609 = 3 × 7 × 29, sphenic number, strobogrammatic number

610s

* 610 = 2 × 5 × 61, sphenic number, nontotient, Fibonacci number, Markov number. Also a kind of 610 (telephone), telephone wall socket used in Australia.
* 611 = 13 × 47, sum of the three standard board sizes in Go (9² + 13² + 19²), the oeis:A232543, 611th oeis:A100683, tribonacci number is prime
* 612 = 2² × 3² × 17, Harshad number, Zuckerman number , area code for Area code 612, 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, index of prime Lucas 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 613 mitzvot, Commandments in the Torah; 613 parts of the human body.
** The number 613 hangs from the rafters at Madison Square Garden in honor of New York Knicks coach Red Holzman's 613 victories.
* 614 = 2 × 307, nontotient, Knödel number, 2-Knödel number. 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 sequence, Padovan number, balanced number, an alternative value for the Number of the Beast (numerology), Number of the Beast (more commonly accepted to be 666 (number), 666).
* 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, number of compositions of 17 into distinct parts, oeis:A006450, prime index prime, index of prime Lucas number
** Area codes 617 and 857, Area code 617, a telephone area code covering the metropolitan Boston area.
* 618 = 2 × 3 × 103, sphenic number, oeis:A111592, admirable 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). The sum of the first 620 primes is itself prime.
* 621 = 3³ × 23, Harshad number, the discriminant of a totally real cubic field
* 622 = 2 × 311, nontotient, Fine number. OEIS:A000957, Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree It is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)
* 623 = 7 × 89, number of partitions of 23 into an even number of parts
* 624 = 2⁴ × 3 × 13 = Jordan's totient function, J₄(5), sum of a twin prime (311 + 313), Harshad number, Zuckerman number
* 625 = 25² = 5⁴, 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, Knödel number, 2-Knödel number. Stitch (Lilo & Stitch), Stitch's experiment number.
* 627 = 3 × 11 × 19, sphenic number, number of integer partition (number theory), partitions of 20, Smith number
* 628 = 2² × 157, nontotient, totient sum for first 45 integers
* 629 = 17 × 37, highly cototient number, Harshad number, number of diagonals in a 37-gon

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, balanced number
* 631 = Cuban prime number, centered triangular number, centered hexagonal number, Chen prime, lazy caterer number
* 632 = 2³ × 79, refactorable number, number of 13-bead necklaces with 2 colors
* 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223), Blum integer; 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, number of compositions of 13 into pairwise relatively prime parts
** "Project 635", the Irtysh River diversion project in China involving a Project 635 Dam, dam and a Irtysh–Karamay–Ürümqi Canal, 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 International Organization for Standardization, ISO's standard for codes for the representation of languages

640s

* 640 = 2⁷ × 5, Harshad number, refactorable number, hexadecagonal number, number of 1's in all partitions of 24 into odd parts, number of acres in a square mile
* 641 = prime number, Sophie Germain prime, factor of 4294967297 (number), 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime
* 642 = 2 × 3 × 107 = 1⁴ + 2⁴ + 5⁴, sphenic number, oeis:A111592, admirable number
* 643 = prime number, largest prime factor of 123456
* 644 = 2² × 7 × 23, nontotient, Perrin number, Harshad number, common umask, oeis:A111592, admirable number
* 645 = 3 × 5 × 43, sphenic number, octagonal 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, number of permutations of length 7 without rising or falling successions
* 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3⁶⁴⁷ - 2⁶⁴⁷ is prime
* 648 = 2³ × 3⁴
A331452(7, 1)
Harshad number, Achilles number, area of a square with diagonal 36
* 649 = 11 × 59, Blum integer

650s

* 650 = 2 × 5² × 13, primitive abundant number, square pyramidal number, pronic number, nontotient, totient sum for first 46 integers; (other fields) the number of seats in the House of Commons of the United Kingdom, oeis:A111592, admirable number
* 651 = 3 × 7 × 31, sphenic number, pentagonal number, nonagonal number
* 652 = 2² × 163, maximal number of regions by drawing 26 circles
* 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, oeis:A111592, admirable number
* 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid
* 656 = 2⁴ × 41 = $\lfloor \frac \rfloor$. 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 ''a''²+''s'' with ''s'' a semiprime
* 658 = 2 × 7 × 47, sphenic number, untouchable 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.
**Sum of 11th row when writing the natural numbers as a triangle.
**Harshad number.
* 661 = prime number
**Sum of three consecutive primes (211 + 223 + 227).
**Mertens function sets new low of −11 which stands until 665.
**Pentagram number of the form $5n^-5n+1$.
**Hexagram number of the form $6n^-6n+1$ i.e. a star number.
* 662 = 2 × 331, nontotient, member of Mian–Chowla sequence
* 663 = 3 × 13 × 17, sphenic number, Smith number
* 664 = 2³ × 83, refactorable number, number of knapsack partitions of 33
**Telephone area code 664, area code for Montserrat.
**Area code 664 (Mexico), Area code for Tijuana within Mexico.
**Model number for the Amstrad CPC664 home computer.
* 665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon
* 666 (number), 666 = 2 × 3² × 37, repdigit
* 667 = 23 × 29, lazy caterer number
* 668 = 2² × 167, nontotient
* 669 = 3 × 223, blum integer

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 Eight queens puzzle, ''n''-queens problem for ''n'' = 11.
* 672 = 2⁵ × 3 × 7, harmonic divisor number, Zuckerman number, oeis:A111592, admirable number
* 673 = prime number, Proth prime
* 674 = 2 × 337, nontotient, Knödel number, 2-Knödel number
* 675 = 3³ × 5², Achilles number
* 676 = 2² × 13² = 26², palindromic square
* 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10
* 678 = 2 × 3 × 113, sphenic number, nontotient, number of surface points of an octahedron with side length 13, oeis:A111592, admirable number
* 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), smallest number of multiplicative persistence 5

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), number of moves to solve the Norwegian puzzl
strikketoy

* 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, number of graphical forest partitions of 32
* 685 = 5 × 137, centered square number
* 686 = 2 × 7³, nontotient, number of multigraphs on infinite set of nodes with 7 edges
* 687 = 3 × 229, 687 days to orbit the sun (Mars) Knödel number, D-number
* 688 = 2⁴ × 43, Friedman number since 688 = 8 × 86, 2-automorphic number
* 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

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 ''B''₁₂ = -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, number of partitions of 48 into powers of 2
* 693 (number), 693 = 3² × 7 × 11, triangular matchstick number, the number of sections in Ludwig Wittgenstein's ''Philosophical Investigations''.
* 694 = 2 × 347, centered triangular number, nontotient
* 695 = 5 × 139, 695!! + 2 is prime.
* 696 = 2³ × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice
* 697 = 17 × 41, cake number; the number of sides of Colorado
* 698 = 2 × 349, nontotient, sum of squares of two primes
* 699 = 3 × 233, Knödel number, D-number

References

{{Integers, 6

Integers