600 (number)

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

"611 (number)" and "688 (number)" redirect here. For the phone number, see 6-1-1. For other topics, see 611 (disambiguation) and 688 (disambiguation).

← 599 600 601 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	six hundred
Ordinal	600th (six hundredth)
Numeral system	sescentesimal
Factorization	23 × 3 × 52
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
Greek numeral	Χ´
Roman numeral	DC, dc
Binary	10010110002
Ternary	2110203
Senary	24406
Octal	11308
Duodecimal	42012
Hexadecimal	25816
Armenian	Ո
Hebrew	ת"ר / ם
Babylonian cuneiform	𒌋
Egyptian hieroglyph	𓍧

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, a Harshad number and a largely composite 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

601 is:

• a prime number

• a centered pentagonal number

602

602 = 2 × 7 × 43. It is:

• a nontotient
• the number of cubes of edge length 1 required to make a hollow cube of edge length 11

602 is an area code for Phoenix, AZ along with 480 and 623.

603

603 = 3² × 67. It is:

• a Harshad number
• a Riordan number

603 is an area code for New Hampshire.

604

604 = 2² × 151. It is:

• a nontotient
• the totient sum for first 44 integers,

604 is an area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky).

605

605 = 5 × 11². It is:

• a Harshad number
• the sum of the nontriangular numbers between the two successive triangular numbers 55 and 66
• the number of non-isomorphic set-systems of weight 9

606

606 = 2 × 3 × 101. It is:

• a sphenic number
• the sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109)
• an admirable number

606 is 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

607 is:

• a balanced prime number
• a Mersenne prime exponent
• the sum of three consecutive primes (197 + 199 + 211)
• a zero of the Mertens function
• a strictly non-palindromic number

608

608 = 2⁵ × 19. It is:

• a zero of the Mertens function
• a nontotient
• a happy number
• the 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

609 = 3 × 7 × 29. It is:

• a sphenic number
• a strobogrammatic number

610s

610

Main article: 610 (number)

611

611 = 13 × 47. It is:

• the sum of the three standard board sizes in Go (9² + 13² + 19²).

The 611th tribonacci number is prime.

612

612 = 2² × 3² × 17. It is:

• a Harshad number
• a Zuckerman number (sequence A007602 in the OEIS)
• an untouchable number

612 is an area code for Minneapolis, MN.

613

Main article: 613 (number)

614

614 = 2 × 307. It is:

• a nontotient
• a 2-Knödel number

According to Rabbi Emil Fackenheim, the number of Commandments in Judaism should be 614 rather than the traditional 613.

615

615 = 3 × 5 × 41. It is:

• a sphenic number

616

Main article: 616 (number)

616 = 2³ × 7 × 11. It is:

• a Padovan number
• a balanced number,

616 is an alternative value for the Number of the Beast (more commonly accepted to be 666)

617

617 is:

• a prime number
• the sum of five consecutive primes (109 + 113 + 127 + 131 + 137)
• a Chen prime
• an Eisenstein prime with no imaginary part
• the number of compositions of 17 into distinct parts,
• a super-prime
• an index of prime Lucas number

618

618 = 2 × 3 × 103. It is:

• a sphenic number
• an admirable number

619

619 is:

• a prime number
• a strobogrammatic prime,
• an alternating factorial

620s

620

620 = 2² × 5 × 31. It is:

• the sum of four consecutive primes (149 + 151 + 157 + 163)
• the sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97)

The sum of the first 620 primes is itself prime.

621

621 = 3³ × 23. It is:

• a Harshad number
• the discriminant of a totally real cubic field

622

622 = 2 × 311. It is:

• a nontotient
• a fine number (sequence A000957 in the OEIS)

623

623 = 7 × 89. It is:

• the number of partitions of 23 into an even number of parts

624

624 = 2⁴ × 3 × 13. It is:

• the sum of a twin prime pair (311 + 313)
• a Harshad number,
• a Zuckerman number

624=J₄(5).

625

625 = 25² = 5⁴ It is:

• the sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103)
• a centered octagonal number,
• a 1-automorphic number,
• a Friedman number because 625 = 5⁶⁻²,
• one of the two three-digit numbers that when squared or raised to a higher power that end in the same three digits, the other being 376.

626

626 = 2 × 313. It is:

• a nontotient
• a 2-Knödel number,
• Stitch's experiment number

627

627 = 3 × 11 × 19. It is:

• a sphenic number
• the number of integer partitions of 20
• a Smith number

628

628 = 2² × 157. It is:

• a nontotient
• the totient sum for first 45 integers

629

629 = 17 × 37. It is:

• a highly cototient number
• a Harshad number
• the number of diagonals in a 37-gon

630s

630

630 = 2 × 3² × 5 × 7. It is:

• the sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113)
• the 35th triangular number
• a hexagonal number
• a sparsely totient number
• a Harshad number,
• a balanced number
• a largely composite number

631

631 is:

• a prime number

• a Cuban prime
• a Lucky prime
• a Chen prime
• a centered triangular number
• a centered hexagonal number
• a lazy caterer number (sequence A000124 in the OEIS)

632

632 = 2³ × 79. It is:

• a refactorable number
• the number of 13-bead necklaces with 2 colors

633

633 = 3 × 211. It is:

• the sum of three consecutive primes (199 + 211 + 223)
• a Blum integer

634

634 = 2 × 317. It is:

• a nontotient
• a Smith number

635

635 = 5 × 127. It is:

• the sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)
• a zero of the Mertens function
• the number of compositions of 13 into pairwise relatively prime parts

⁠635/504⁠ ≈ ∛2

636

636 = 2² × 3 × 53. It is:

• the sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83)
• a Smith number
• a zero of the Mertens function

637

637 = 7² × 13. It is:

• a zero of the Mertens function
• a decagonal number

638

638 = 2 × 11 × 29. It is:

• a sphenic number
• the sum of four consecutive primes (151 + 157 + 163 + 167)
• a nontotient
• a centered heptagonal number

639

639 = 3² × 71. It is:

• the sum of the first twenty primes

640s

640

640 = 2⁷ × 5. It is:

• a Harshad number
• a refactorable number
• a hexadecagonal number
• the number of 1's in all partitions of 24 into odd parts,

There are 640 acres in a square mile.

641

641 is:

• a prime number

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

642

• 642 = 2 × 3 × 107. It is:
• a sphenic number
• an admirable number

642= 1⁴ + 2⁴ + 5⁴, making 642 a counterexample of

643

643 is:

• a prime number
• the largest prime factor of 123456

644

• 644 = 2² × 7 × 23. It is:
• a nontotient
• a Perrin number
• a Harshad number
• a common umask
• an admirable number

645

645 = 3 × 5 × 43. It is:

• a sphenic number
• an octagonal number
• a Smith number
• a Fermat pseudoprime to base 2
• a Harshad number

646

646 = 2 × 17 × 19. It is:

• a sphenic number
• the number of permutations of length 7 without rising or falling successions

647

647 is:

• a Chen prime
• an Eisenstein prime with no imaginary part
• the sum of five consecutive primes (113 + 127 + 131 + 137 + 139)

3⁶⁴⁷ - 2⁶⁴⁷ is prime

648

648 = 2³ × 3⁴. It is:

• a Harshad number
• an Achilles number
• the area of a square with diagonal 36

649

649 = 11 × 59. It is:

• a Blum integer

650s

650

650 = 2 × 5² × 13. It is:

• a primitive abundant number
• a square pyramidal number
• a pronic number
• a nontotient
• the totient sum for first 46 integers
• an admirable number

651

651 = 3 × 7 × 31. It is:

• a sphenic number,
• a pentagonal number,
• a nonagonal number

652

652 = 2² × 163. It is:

• the maximal number of regions by drawing 26 circles

653

653 is:

• a prime number
• a Sophie Germain prime
• a balanced prime
• a Chen prime
• an Eisenstein prime with no imaginary part

654

654 = 2 × 3 × 109. It is:

• a sphenic number
• a nontotient,
• a Smith number
• an admirable number

655

655 = 5 × 131. It is:

• the number of toothpicks after 20 stages in a three-dimensional grid

656

656 = 2⁴ × 41 = $\lfloor {\frac {3^{16}}{2^{16}}}\rfloor$,

In Judaism, Jerusalem is mentioned in the Hebrew Bible and the Old Testament a total of 656 times.

657

• 657 = 3² × 73. It is:
• the largest known number not of the form a²+s with s a semiprime

658

• 658 = 2 × 7 × 47. It is:
• a sphenic number
• an untouchable number

659

659 is:

• a prime number
• a Sophie Germain prime
• the sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107),
• a Chen prime
• an Eisenstein prime with no imaginary part, strictly non-palindromic number
• highly cototient number

Mertens function sets new low of −10 at 659 which stands until 661.

660s

660

660 = 2² × 3 × 5 × 11. It is:

• the sum of four consecutive primes (157 + 163 + 167 + 173)
• the sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127)
• the sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)
• a sparsely totient number
• the sum of 11th row when writing the natural numbers as a triangle.
• a Harshad number.
• a largely composite number

661

661 is:

• a prime number

• the sum of three consecutive primes (211 + 223 + 227)
• a Pentagram number of the form $5n^{2}-5n+1$
• a Hexagram number of the form $6n^{2}-6n+1$ i.e. a star number

Mertens function sets new low of −11 at 661 which stands until 665.

662

662 = 2 × 331. It is:

• a nontotient
• a member of Mian–Chowla sequence

663

663 = 3 × 13 × 17. It is:

• a sphenic number,
• a Smith number

664

664 = 2³ × 83. It is:

• a refactorable number
• the number of knapsack partitions of 33

665

665 = 5 × 7 × 19. It is:

• a sphenic number,
• the number of diagonals in a 38-gon

Mertens function sets new low of −12 at 665 which stands until 1105.

666

Main article: 666 (number)

667

667 = 23 × 29. It is:

• a lazy caterer number (sequence A000124 in the OEIS)

668

668 = 2² × 167. It is:

• a nontotient

669

• 669 = 3 × 223. It is:
• a Blum integer

670s

670

670 = 2 × 5 × 67. It is:

• a sphenic number
• an octahedral number
• a nontotient

671

671 = 11 × 61.

The magic constant of n×n normal magic square and n-queens problem for n = 11 is 671.

672

672 = 2⁵ × 3 × 7. It is:

• a harmonic divisor number
• a Zuckerman number
• an admirable number
• a largely composite number
• a triperfect number

673

673 is:

• a prime number
• a lucky prime
• a Proth prime

674

674 = 2 × 337. It is:

• a nontotient
• a 2-Knödel number

675

675 = 3³ × 5². It is:

• an Achilles number

676

676 = 2² × 13² = 26². It is:

• a palindromic square

677

677 is:

• a prime number
• a Chen prime
• an Eisenstein prime with no imaginary part
• the number of non-isomorphic self-dual multiset partitions of weight 10

678

678 = 2 × 3 × 113. It is:

• a sphenic number
• a nontotient
• an admirable number
• the number of surface points of an octahedron with side length 13,

679

679 = 7 × 97. It is:

• the sum of three consecutive primes (223 + 227 + 229)
• the sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97)
• the smallest number of multiplicative persistence 5

680s

680

680 = 2³ × 5 × 17. It is:

• a tetrahedral number
• a nontotient

681

681 = 3 × 227. It is:

• a centered pentagonal number

682

• 682 = 2 × 11 × 31. It is:
• a sphenic number
• the sum of four consecutive primes (163 + 167 + 173 + 179)
• the sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)

Solving the Norwegian puzzle strikketoy requires 682 moves.

683

683 is:

• a prime number
• a Sophie Germain prime,
• a Chen prime
• an Eisenstein prime with no imaginary part
• a Wagstaff prime
• the sum of five consecutive primes (127 + 131 + 137 + 139 + 149)

684

684 = 2² × 3² × 19. It is:

• a Harshad number
• the number of graphical forest partitions of 32

685

685 = 5 × 137 It is:

• centered square number

686

• 686 = 2 × 7³.It is:
• a nontotient,
• the number of multigraphs on infinite set of nodes with 7 edges

687

• 687 = 3 × 229. It is:
• a D-number

Mars takes 687 days to orbit around the sun.

688

• 688 = 2⁴ × 43. It is:
• a Friedman number since 688 = 8 × 86,
• a 2-automorphic number

689

• 689 = 13 × 53. It is:
• the sum of three consecutive primes (227 + 229 + 233),
• the sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109)
• a Strobogrammatic number

690s

690

690 = 2 × 3 × 5 × 23. It is:

• the sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131)
• a sparsely totient number
• a Smith number
• a Harshad number

691

691 is a prime number. Ramanujan's tau function τ and the divisor function σ₁₁ are related by the congruence τ(n) ≡ σ₁₁(n) (mod 691). Negative 691 is the numerator of the Bernoulli number B₁₂ = -691/2730. 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

692 = 2² × 173. It is:

• the number of partitions of 48 into powers of 2

693

693 = 3² × 7 × 11. It is:

• a triangular matchstick number

694

• 694 = 2 × 347. It is:
• a centered triangular number,
• a nontotient,
• the smallest pandigital number in base 5.

695

695 = 5 × 139.

695!! + 2 is prime.

696

• 696 = 2³ × 3 × 29. It is:
• the sum of a twin prime pair (347 + 349), sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103)
• the totient sum for first 47 integers
• the number of trails of length 9 on honeycomb lattice

697

• 697 = 17 × 41. It is:
• a cake number

The US state of Colorado has 697 sides.

698

• 698 = 2 × 349.
• a nontotient
• the sum of squares of two primes

699

699 = 3 × 233. It is;

• a D-number