600 (number)

Mathematical properties

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, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with 480 and 623
• 603 = 3² × 67, Harshad number, Riordan number, area code for New Hampshire
• 604 = 2² × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia
• 605 = 5 × 11², Harshad number, sum of the nontriangular numbers between the two successive triangular numbers 55 and 66, number of non-isomorphic set-systems of weight 9
• 606 = 2 × 3 × 101, sphenic number, sum of six consecutive primes, admirable number, One of the numbers associated with Christ - ΧϚʹ - see the Greek numerals Isopsephy and the reason why other numbers siblings with this one are Beast's numbers.
• 607 – prime number, sum of three consecutive primes, Mertens function = 0, balanced prime, strictly non-palindromic number, Mersenne prime exponent
• 608 = 2⁵ × 19, Mertens function = 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, Fibonacci number, Markov number, also a kind of telephone wall socket used in Australia
• 611 = 13 × 47, sum of the three standard board sizes in Go, the 611th tribonacci number is prime
• 612 = 2² × 3² × 17, Harshad number, Zuckerman number, untouchable number, area code for Minneapolis, MN
• 613 = prime number, first number of prime triple, middle number of sexy prime triple. 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 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, 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 number, balanced number, an alternative value for the Number of the Beast
• 617 = prime number, sum of five consecutive primes, Chen prime, Eisenstein prime with no imaginary part, number of compositions of 17 into distinct parts, prime index prime, index of prime Lucas number
• * Area code 617, a telephone area code covering the metropolitan Boston area
• 618 = 2 × 3 × 103, sphenic number, admirable number
• 619 = prime number, strobogrammatic prime, alternating factorial

620s

• 620 = 2² × 5 × 31, sum of four consecutive primes, sum of eight consecutive primes, 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,, it is also the standard diameter of modern road bicycle wheels
• 623 = 7 × 89, number of partitions of 23 into an even number of parts
• 624 = 2⁴ × 3 × 13 = J₄(5), sum of a twin prime pair, Harshad number, Zuckerman number
• 625 = 25² = 5⁴, sum of seven consecutive primes, centered octagonal number, 1-automorphic number, Friedman number since 625 = 5⁶⁻², one of the two three-digit numbers when squared or raised to a higher power that end in the same three digits, the other being 376
• 626 = 2 × 313, nontotient, 2-Knödel number, Stitch's experiment number
• 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, number of diagonals in a 37-gon

630s

• 630 = 2 × 3² × 5 × 7, sum of six consecutive primes, the 35th triangular number, a hexagonal number, sparsely totient number, Harshad number, balanced number, largely composite number
• 631 = Cuban prime number, Lucky prime, 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, 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, Mertens function = 0, number of compositions of 13 into pairwise relatively prime parts
• * "Project 635", the Irtysh River diversion project in China involving a dam and a canal
• 636 = 2² × 3 × 53, sum of ten consecutive primes, Smith number, Mertens function = 0
• 637 = 7² × 13, Mertens function = 0, decagonal number
• 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes, 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, 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, Chen prime, Eisenstein prime with no imaginary part, Proth prime
• 642 = 2 × 3 × 107 = 1⁴ + 2⁴ + 5⁴, sphenic number, admirable number
• 643 = prime number, largest prime factor of 123456
• 644 = 2² × 7 × 23, nontotient, Perrin number, Harshad number, common umask, 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, Chen prime, Eisenstein prime with no imaginary part, 3⁶⁴⁷ - 2⁶⁴⁷ is prime
• 648 = 2³ × 3⁴ =, 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; the number of seats in the House of Commons of [the United Kingdom], 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, admirable number
• 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid
• 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, untouchable number
• 659 = prime number, Sophie Germain prime, sum of seven consecutive primes, 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
• *Sum of six consecutive primes
• *Sum of eight consecutive primes
• *Sparsely totient number
• *Sum of 11th row when writing the natural numbers as a triangle.
• *Harshad number.
• *largely composite number
• 661 = prime number
• *Sum of three consecutive primes
• *Mertens function sets new low of −11 which stands until 665
• *Pentagram number of the form
• *Hexagram number of the form 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 for Montserrat
• *Area code for Tijuana within Mexico
• *Model number for the Amstrad CPC 664 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 = 2 × 3² × 37, 36th triangular number, Harshad number, 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 n''-queens problem for n = 11.
• 672 = 2⁵ × 3 × 7, harmonic divisor number, Zuckerman number, admirable number, largely composite number, triperfect number
• 673 = prime number, lucky prime, Proth prime
• 674 = 2 × 337, nontotient, 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, admirable number
• 679 = 7 × 97, sum of three consecutive primes, sum of nine consecutive primes, 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, sum of ten consecutive primes, number of moves to solve the Norwegian puzzle
• 683 = prime number, Sophie Germain prime, sum of five consecutive primes, 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 D-number
• 688 = 2⁴ × 43, Friedman number since 688 = 8 × 86, 2-automorphic number
• 689 = 13 × 53, sum of three consecutive primes, sum of seven consecutive primes. Strobogrammatic number

690s

• 690 = 2 × 3 × 5 × 23, sum of six consecutive primes, sparsely totient number, Smith number, Harshad number
• * ISO 690 is the ISO's standard for bibliographic references
• 691 = prime number, 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 ≡ σ₁₁.
• * In number theory, 691 is a "marker" : 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 = 3² × 7 × 11, triangular matchstick number, the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
• 694 = 2 × 347, centered triangular number, nontotient, smallest pandigital number in base 5.
• 695 = 5 × 139, 695!! + 2 is prime.
• 696 = 2³ × 3 × 29, sum of a twin prime pair, sum of eight consecutive primes, 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, D-number