700 (seven hundred) is the natural number following 699 and preceding 701.
It is a composite number and the sum of four consecutive primes (167 + 173 + 179 + 181).
Integers from 701 to 799 700s
701 701 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of three consecutive primes (229 + 233 + 239). 702 702 = 2 × 33 × 13. It is a pronic number, a nontotient, and a Harshad number. 703 703 = 19 × 37. It is a hexagonal number, a Kaprekar number and the 37th triangular number. It is the smallest number requiring 73 fifth powers for Waring representation.
703 is commonly found in the formula for body mass index.
704 704 = 26 × 11. It is a Harshad number and a lazy caterer number.
705 705 = 3 × 5 × 47. It is a sphenic number the smallest Bruckman-Lucas pseudoprime. 706 706 = 2 × 353. It is a nontotient a Smith number. 707 707 = 7 × 101. It is a palindromic number and the sum of five consecutive primes (131 + 137 + 139 + 149 + 151). There are 707 lattice paths from (0,0) to (5,5) with steps (0,1), (1,0) and, when on the diagonal, (1,1).
708 708 = 22 × 3 × 59. There are 708 partitions of 28 that do not contain 1 as a part.
709 709 is a prime number and a happy number.
It is the seventh in the series 2, 3, 5, 11, 31, 127, 709 where each number is the nth prime with n being the number preceding it in the series, therefore, it is a prime index number.
710s
710 710 = 2 × 5 × 71. It is a sphenic number and a nontotient. There are 710 forests with 11 vertices. 711
711 = 32 × 79. It is a Harshad number. There are 711 planar Berge perfect graphs on 7 nodes.
712 712 = 23 × 89. It is a refactorable number, the totient sum for first 48 integers, and the sum of the first twenty-one primes.
It is the largest known number such that it and its 8th power (66,045,000,696,445,844,586,496) have no common digits.
713 713 = 23 × 31. It is a Blum integer.
In Judaism there are 713 letters on a Mezuzah scroll.
714 714 = 2 × 3 × 7 × 17. It is a nontotient and a balanced number, and the sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83). It forms a Ruth–Aaron pair with 715 (either definition). It is the sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17).
715 715 = 5 × 11 × 13. It is a sphenic number, a pentagonal number, and a Harshad number. It forms a Ruth-Aaron pair with 714 (either definition).
It is a pentatope number because 713=.
The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17).
716 716 = 22 × 179.
717 717 = 3 × 239. It is a palindromic number.
718 718 = 2 × 359.
719 719 is a prime number, a Sophie Germain prime, a safe prime, a Chen prime, and an Eisenstein prime with no imaginary part.
Because 719 = 6! − 1, 719 is a factorial prime.
It is the sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113).
720s
720
721 721 = 7 × 103. It is a centered hexagonal number and the sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101). It is the smallest number that is the difference of two positive cubes in two ways.
722 722 = 2 × 192. It is a nontotient. There are 722 odd parts in all partitions of 15.
723 723 = 3 × 241. It is the side length of an almost-equilateral Heronian triangle.
724 724 = 22 × 181. It is a nontotient and the side length of an almost-equilateral Heronian triangle. It is the sum of four consecutive primes (173 + 179 + 181 + 191) and the sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137). There are 724 n-queens problem solutions for n = 10.
725 725 = 52 × 29. It is the side length of an almost-equilateral Heronian triangle.
726 726 = 2 × 3 × 112. It is a pentagonal pyramidal number.
727 727 is a prime number, a palindromic prime, and a lucky prime. 728 728 = 23 × 7 × 13. It is a nontotient, a Smith number, and a cabtaxi number. There are 728 cubes of edge length 1 required to make a hollow cube of edge length 12.There are 728 connected graphs on 5 labelled vertices.
728!! - 1 is prime.
72864 + 1 is prime.
729 729 = 272 = 93 = 36. It is a perfect totient number, a Smith number, and a centered octagonal number. It is the largest three-digit cube (93) and the only three-digit sixth power (36).
A philosopher king's pleasure is 729 times a tyrant's pleasure according to Plato in the Republic.
730s
730 730 = 2 × 5 × 73. It is a sphenic number, a nontotient, and a Harshad number. There are 730 generalized weak orders on 5 points. 731 731 = 17 × 43. It is the sum of three consecutive primes (239 + 241 + 251). There are 731 Euler trees with total weight 7. 732 732 = 22 × 3 × 61. It is a Harshad number.
It is the sum of eight consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107) and the sum of ten consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97).
There are 732 collections of subsets of {1, 2, 3, 4} that are closed under union and intersection.
733 733 is a prime number, a balanced prime, a permutable prime, and an emirp. It is the sum of five consecutive primes (137 + 139 + 149 + 151 + 157) 734 734 = 2 × 367. It is a nontotient. There are 734 traceable graphs on 7 nodes. 735 735 = 3 × 5 × 72. It is a Harshad number and a Zuckerman number. the smallest number such that uses the same digits as its distinct prime factors
736 736 = 25 × 23. It is a centered heptagonal number, a happy number, a Harshad number, and a nice Friedman number since 736 = 7 + 36. 737 737 = 11 × 67. It is a palindromic number and a blum integer. 738 738 = 2 × 32 × 41. It is a Harshad number.
739 739 is a prime number, a lucky prime, a prime index prime, a happy number, and a strictly non-palindromic number.
740s
740 740 = 22 × 5 × 37. It is a nontotient. There are 740 connected square free graphs on 9 nodes. 741 741 = 3 × 13 × 19. It is a sphenic number and the 38th triangular number. 742 742 = 2 × 7 × 53. It is a sphenic number, a decagonal number, an icosahedral number, and a lazy caterer number. There are 742 partitions of 30 into divisors of 30. the smallest number that is one more than triple its reverse.
743 It is a prime number and an eisenstein prime with no imaginary part. 743 is a Sophie Germain prime because 2 × 743 + 1 = 1487 and 1487 is also prime. 743 is an emirp, because 347 (the reversal of its digits) is prime.
There are exactly 743 independent sets in a four-dimensional (16 vertex) hypercube graph, and exactly 743 connected cubic graphs with 16 vertices and girth four.
744 744 is 2*2*2*3*3, semiperfect number and an abundant number.
The -invariant, an important function in the study of modular forms and Monstrous moonshine, can be written as a Fourier series in which the constant term is 744: where . One consequence of this is that 744 appears in expressions for Ramanujan's constant and other almost integers.
745 745 = 5 × 149. There are 745 non-connected simple labeled graphs covering 6 vertices.
746 746 = 2 × 373.
It is a nontotient. There are 746 non-normal semi-magic squares with sum of entries equal to 6.
746=15 + 24 + 36 = 17 + 24 + 36.
747 747 = 32 × 83. It is a palindromic number.
747=
748 748 = 22 × 11 × 17. It is a nontotient, a happy number, and a primitive abundant number.
749 749 = 7 × 107. It is a blum integer and the sum of three consecutive primes (241 + 251 + 257). 750s
750 750 = 2 × 3 × 53. It is an enneagonal number.
751 751 is a prime number, a Chen prime, and an emirp.
752 752 = 24 × 47. It is a nontotient. There are 752 partitions of 11 into parts of 2 kinds
753 753 = 3 × 251. It is a blum integer.
754 754 = 2 × 13 × 29. It is a sphenic number, a nontotient, and the totient sum for first 49 integers.
There are 754 different ways to divide a 10 × 10 square into sub-squares.
755 755 = 5 × 151. There are 755 vertices in a regular drawing of the complete bipartite graph K9,9.
756 756 = 22 × 33 × 7. It is a pronic number, a Harshad number, and the sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139). 757 757 is a prime number, a palindromic prime, a happy number, and the sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127).
758 758 = 2 × 379.
It is a nontotient and a prime number of measurement.
759 759 = 3 × 11 × 23.
It is a sphenic number, a q-Fibonacci number for q=3, and the sum of five consecutive primes (139 + 149 + 151 + 157 + 163).
760s
760 760 = 23 × 5 × 19.
It is a centered triangular number. There are 760 fixed heptominoes.
761 761 is a prime number, an emirp, a Sophie Germain prime, a Chen prime, an Eisenstein prime with no imaginary part, and a centered square number. 762 762 = 2 × 3 × 127. It is a sphenic number, a nontotient, a Smith number, an admirable number, and the sum of four consecutive primes (181 + 191 + 193 + 197).
There are 762 1's in all partitions of 25 into odd parts There are Six nines in the decimal representation of pi after the 762nd digit.
763 763 = 7 × 109.
It is the sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103). There are 763 degree-8 permutations of order exactly 2.
764 764 = 22 × 191. It is a telephone number.
765 765=32 × 5 × 17.
It is an octagonal pyramidal number.
It is a Japanese word-play for Namco.
766 766 = 2 × 383. It is a centered pentagonal number, a nontotient, and the sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).
767 767 = 13 × 59. It is a palindromic number and a Thabit number because 767 = 28 × 3 − 1
768 768 = 28 × 3. It is the sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109).
769 769 is a prime number, a Chen prime, a lucky prime, and a Proth prime.
770s
770 770 = 2 × 5 × 7 × 11. It is a nontotient and a Harshad number.
is prime
It holds special importance in the Chabad-Lubavitch Hasidic movement.
771 771 = 3 × 257.
It is sum of three consecutive primes in arithmetic progression (251 + 257 + 263). Since 771 is the product of the distinct Fermat primes 3 and 257, a regular polygon with 771 sides can be constructed using compass and straightedge, and can be written in terms of square roots.
772 772 = 22 × 193.
772!!!!!!+1 is prime.
773 773 is a prime number, an Eisenstein prime with no imaginary part, a prime index prime, and a tetranacci number. the sum of the number of cells that make up the convex, regular 4-polytopes
774 774 = 2 × 32 × 43. It is a nontotient, a Harshad number, and the totient sum for first 50 integers
775 775 = 52 × 31. It is a member of the Mian–Chowla sequence
776 776 = 23 × 97.
It is a refactorable number. There are 776 compositions of 6 whose parts equal to q can be of q2 kinds.
777
778 778 = 2 × 389. It is a nontotient and a Smith number.
779 779 = 19 × 41. It is a highly cototient number.
780s
780 780 = 22 × 3 × 5 × 13. It is a hexagonal number, a Harshad number, and the 39th triangular number. It is the sum of four consecutive primes in a quadruplet (191, 193, 197, and 199) and the sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101).
780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.
781 781 = 11 × 71. It is a zero of the Mertens function and a lazy caterer number It is the sum of powers of 5, or equivalently, repdigit in base 5 (11111) 782 782 = 2 × 17 × 23. It is a sphenic number, a nontotient, a pentagonal number, and a Harshad number. 783 783 = 33 × 29. It is a heptagonal number.
784 784 = 24 × 72. It is a happy number.
Since 784=282, 784 is a perfect square. It is the sum of the cubes of the first seven positive integers; .
785