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 (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) • 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 (89 + 97 + 101 + 103 + 107 + 109),
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 (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,
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 (92 + 132 + 192), 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 (
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
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 (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, number of compositions of 17 into distinct parts,
prime index prime, index of prime Lucas number
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, , 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 =
J4(5), sum of a twin prime pair (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, 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 (97 + 101 + 103 + 107 + 109 + 113), 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 (199 + 211 + 223),
Blum integer; also, in the title of the movie
633 Squadron • 634 = 2 × 317,
nontotient, Smith number • "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, • 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,
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 (the smallest nonprime
Fermat number), 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, 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), • 649 = 11 × 59,
Blum integer 650s • 650 = 2 × 52 × 13,
primitive abundant number,
square pyramidal number, pronic number,
nonagonal number • 652 = 22 × 163, maximal number of regions by drawing 26 circles • 653 = prime number, Sophie Germain prime, • 656 = 24 × 41 = \lfloor \frac{3^{16}}{2^{16}} \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
a2+
s with
s a
semiprime • 658 = 2 × 7 × 47,
sphenic number,
untouchable number • 659 = prime number, Sophie Germain prime, •
Harshad number. •
largely composite 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^{2}-5n+1 •
Hexagram number of the form 6n^{2}-6n+1 i.e. a
star number • 662 = 2 × 331,
nontotient, member of
Mian–Chowla sequence • 663 = 3 × 13 × 17,
sphenic number, Smith number • 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
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 • 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 (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 • 683 = prime number, Sophie Germain 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)
D-number • 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).
Strobogrammatic number 690s • 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number, •
693 = 32 × 7 × 11, triangular matchstick number, the number of sections in
Ludwig Wittgenstein's
Philosophical Investigations. • 694 = 2 × 347, centered triangular number, • 695 = 5 × 139, 695!! + 2 is prime. • 696 = 23 × 3 × 29, sum of a twin prime pair (347 + 349), 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,
D-number == References ==