619

Mathematical properties

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

Credit

In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate

Integers from 601 to 699

600s

601 is a prime number and a centered pentagonal number.

602 = 2 × 7 × 43. It is a nontotient. There are 602 cubes of edge length 1 required to make a hollow cube of edge length 11

603 = 32 × 67. It is a Harshad number and a Riordan number.

604 = 22 × 151. It is a nontotient and the totient sum for first 44 integers.

605 = 5 × 112. It is a Harshad number and the sum of the nontriangular numbers between the two successive triangular numbers 55 and 66. There are 605 non-isomorphic set-systems of weight 9.

606 = 2 × 3 × 101. It is a sphenic number, an admirable number and the sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109).

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

608 = 25 × 19. It is a nontotient, a happy number, and a zero of the Mertens function. There are 608 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. It is a sphenic number and a strobogrammatic number.

610s

610 =2 × 5 × 61. It is a deficient number, a Markov number, a sphenic number, and a member of the Fibonacci sequence.

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 = 22 × 32 × 17. It is a Harshad number, an untouchable number, and a Zuckerman number (sequence A007602 in the OEIS).

614 = 2 × 307. It is a nontotient and a 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. It is a sphenic number.

616 = 23 × 7 × 11. It is a Padovan number and a balanced number.

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

617 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, a super-prime, an index of prime Lucas number, and the sum of five consecutive primes (109 + 113 + 127 + 131 + 137).

There are 617 compositions of 17 into distinct parts.

618 = 2 × 3 × 103. It is a sphenic number and an admirable number.

619 is a prime number, a strobogrammatic prime, and an alternating factorial.

620s

620 = 22 × 5 × 31. It is the sum of four consecutive primes (149 + 151 + 157 + 163) and 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 = 33 × 23. It is a Harshad number, and it is the discriminant of a totally real cubic field.

622 = 2 × 311. It isa nontotient and a fine number (sequence A000957 in the OEIS).

623 = 7 × 89. There are 623 partitions of 23 into an even number of parts.

624 = 24 × 3 × 13. It is a Harshad number, a Zuckerman number and the sum of a twin prime pair (311 + 313).

624=J4(5).

625 = 252 = 54 It is a centered octagonal number, a 1-automorphic number, a Friedman number because 625 = 56−2, the sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103).

It is 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 = 2 × 313. It is a nontotient and a 2-Knödel number,

Stitch's experiment number

627 = 3 × 11 × 19. It is a sphenic number and a Smith number There are 627 integer partitions of 20.

628 = 22 × 157. It is a nontotient and the totient sum for first 45 integers.

629 = 17 × 37. It is a highly cototient number and a Harshad number. There are 629 diagonals in a 37-gon.

630s

630 = 2 × 32 × 5 × 7. It is a hexagonal number, a sparsely totient number, a Harshad number, a balanced number, a largely composite number, the 35th triangular number, and the sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113).

631 is a prime number, a Cuban prime, a Lucky prime a Chen prime, a centered triangular number, a centered hexagonal number, and a lazy caterer number (sequence A000124 in the OEIS).

632 = 23 × 79. It is a refactorable number. There are 632 13-bead necklaces with 2 colors

633 = 3 × 211. It is a Blum integer and the sum of three consecutive primes (199 + 211 + 223).

634 = 2 × 317. It is a nontotient and a Smith number.

635 = 5 × 127. It is a zero of the Mertens function and the sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).

There are 635 compositions of 13 into pairwise relatively prime parts.

⁠635/504⁠ ≈ ∛2

636 = 22 × 3 × 53. It is a Smith number, a zero of the Mertens function, and the sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).

637 = 72 × 13. It is a decagonal number and a zero of the Mertens function.

638 = 2 × 11 × 29. It is a sphenic number, a nontotient, a centered heptagonal number, and the sum of four consecutive primes (151 + 157 + 163 + 167).

639 = 32 × 71. It is the sum of the first twenty primes.

640

640 = 27 × 5. It is a Harshad number, a refactorable number, and a hexadecagonal number

There are 640 1's in all partitions of 24 into odd parts,

There are 640 acres in a square mile.

641 is a prime number, a Sophie Germain prime, a Chen prime, an Eisenstein prime with no imaginary part and a Proth prime. It is a factor of 4294967297, the smallest nonprime Fermat number.

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

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

643 is a prime number.

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

645 = 3 × 5 × 43. It is a sphenic number, an octagonal number, a Smith number, a Harshad number and a Fermat pseudoprime to base 2.

646 = 2 × 17 × 19. It is a sphenic number

There are 646 permutations of length 7 without rising or falling successions.

647 is a Chen prime, an Eisenstein prime with no imaginary part, and the sum of five consecutive primes (113 + 127 + 131 + 137 + 139).

3647 - 2647 is prime

648 = 23 × 34. It is a Harshad number and an Achilles number.

649 = 11 × 59. It is a Blum integer.

650s

650 = 2 × 52 × 13. It is a primitive abundant number, a square pyramidal number, a pronic number, a nontotient an admirable number, and the totient sum for first 46 integers.

651 = 3 × 7 × 31. It is a sphenic number, a pentagonal number, and a nonagonal number.

652 = 22 × 163. It is the maximal number of regions by drawing 26 circles

653 is a prime number, a Sophie Germain prime, a balanced prime, a Chen prime, and an Eisenstein prime with no imaginary part.

654 = 2 × 3 × 109. It is a sphenic number, a nontotient, a Smith number, and an admirable number

655 = 5 × 131. There are 655 toothpicks after 20 stages in a three-dimensional grid.

656 = 24 × 41 =

⌊

3

16

2

16

⌋

{\displaystyle \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 = 32 × 73. It is the largest known number not of the form a2+s with s a semiprime

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

660s

660 = 22 × 3 × 5 × 11. It is a sparsely totient number, a Harshad number, and a largely composite number. It is the sum of four consecutive primes (157 + 163 + 167 + 173), the sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127), and the sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101). It is the sum of 11th row when writing the natural numbers as a triangle.

661 is:

a prime number

the sum of three consecutive primes (211 + 223 + 227)

a Pentagram number of the form

5

n

2

−

5

n

+

1

{\displaystyle 5n^{2}-5n+1}

a Hexagram number of the form

6

n

2

−

6

n

+

1

{\displaystyle 6n^{2}-6n+1}

i.e. a star number

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

662 = 2 × 331. It is a nontotient and a member of Mian–Chowla sequence.

670s

670 = 2 × 5 × 67. It is a sphenic number, an octahedral number, and a nontotient.

671 = 11 × 61.

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

672 = 25 × 3 × 7. It is a harmonic divisor number, a Zuckerman number, an admirable number, a largely composite number, and a triperfect number.

673 is a prime number, a lucky prime, and a Proth prime.

674 = 2 × 337. It is a nontotient and a 2-Knödel number.

675 = 33 × 52. It is an Achilles number.

676 = 22 × 132 = 262. It is a palindromic square.

677 is a prime number, a Chen prime, and an Eisenstein prime with no imaginary part.

There are 677 non-isomorphic self-dual multiset partitions of weight 10.

678 = 2 × 3 × 113. It is a sphenic number, a nontotient, and an admirable number.

There are 678 surface points of an octahedron with side length 13.

679 = 7 × 97. It is the sum of three consecutive primes (223 + 227 + 229) and the sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97). It is the smallest number of multiplicative persistence 5.

680s

680 = 23 × 5 × 17. It is a tetrahedral number and a nontotient.

681 = 3 × 227. It is a centered pentagonal number.

682 = 2 × 11 × 31. It is a sphenic number, the sum of four consecutive primes (163 + 167 + 173 + 179), and 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 is a prime number, a Sophie Germain prime, a Chen prime, an Eisenstein prime with no imaginary part, a Wagstaff prime, and the sum of five consecutive primes (127 + 131 + 137 + 139 + 149).

684 = 22 × 32 × 19. It is a Harshad number.

There are 684 graphical forest partitions of 32.

685 = 5 × 137 It is a centered square number.

686 = 2 × 73.It is a nontotient. There are 686 multigraphs on infinite set of nodes with 7 edges.

687 = 3 × 229. It is a D-number.

Mars takes 687 days to orbit around the sun.

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

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

690s

690 = 2 × 3 × 5 × 23. It is a sparsely totient number, a Smith number, a Harshad number, and the sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131).

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, it is a sign that Bernoulli numbers are involved.

692 = 22 × 173. There are 692 partitions of 48 into powers of 2.

693 = 32 × 7 × 11.

693 appears as the first three digits after the decimal point in the decimal form for the natural logarithm of 2. To 10 digits, this number is 0.6931471805. As a result, if an event has a constant probability of 0.1% of occurring, 693 is the smallest number of trials that must be performed for there to be at least a 50% chance that the event occurs at least once. More generally, for any probability p, the probability that the event occurs at least once in a sample of n items, assuming the items are independent, is given by the following formula:

1 − (1 − p)n

For p = 10−3 = 0.001, plugging in n = 692 gives, to four decimal places, 0.4996, while n = 693 yields 0.5001.

693 is a palindrome in binary in bases 32, 62, 76, 98, 230, and 692.

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

695 = 5 × 139.

695!! + 2 is prime.