This article is about the numbers 700 through 799; for each individual number, see its section below.
Natural number
700 (seven hundred) is the natural number following 699 and preceding 701.
It is the sum of four consecutive primes (167 + 173 + 179 + 181). It is a Harshad number.
Integers from 701 to 799
700s
- 701 = prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part
- 702 = 2 × 33 × 13, pronic number,[1] nontotient, Harshad number
- 703 = 19 × 37, triangular number,[2] hexagonal number,[3] smallest number requiring 73 fifth powers for Waring representation, Kaprekar number,[4] area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index
- 704 = 26 × 11, Harshad number, area code for the Charlotte, NC area.
- 705 = 3 × 5 × 47, sphenic number, smallest Lucas pseudoprime
- 706 = 2 × 353, nontotient, Smith number[5]
- 707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151), palindromic number
- 708 = 22 × 3 × 59
- 709 = prime number; happy number.
710s
- 710 = 2 × 5 × 71, sphenic number, nontotient
- 711 = 32 × 79, Harshad number. Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.
- 712 = 23 × 89, sum of the first twenty-one primes, totient sum for first 48 integers. 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 = 23 × 31, main area code for Houston, TX. In Judaism there is 713 letters on a Mezuzah scroll.
- 714 = 2 × 3 × 7 × 17, sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), nontotient, member of Ruth–Aaron pair (either definition); the smallest number that uses the same digits in bases 2 and 5, area code for Orange County, California.
- 714 is the number of career home runs hit by Babe Ruth, a record that stood from his last home run on May 25, 1935 until being broken by Hank Aaron on April 8, 1974.
- Flight 714 to Sidney is a Tintin graphic novel.
- 714 is the badge number of Sergeant Joe Friday.
- 715 = 5 × 11 × 13, sphenic number, pentagonal number,[6] pentatope number ( binomial coefficient
),[7]
Harshad number, member of Ruth-Aaron pair (either definition)
- 716 = 22 × 179, area code for Buffalo, NY
- 717 = 3 × 239, palindromic number
- 718 = 2 × 359, area code for Brooklyn, NY and Bronx, NY
- 719 = prime number, factorial prime (6! − 1),[8] Sophie Germain prime,[9] safe prime,[10] sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part
720s
- 720 (seven hundred [and] twenty)= 24 × 32 × 5.
- 721 = 7 × 103, sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), centered hexagonal number,[11] smallest number that is the difference of two positive cubes in two ways,
- 722 = 2 × 192, nontotient
- G.722 is a freely available file format for audio file compression. The files are often named with the extension "722".
- 723 = 3 × 241
- 724 = 22 × 181, sum of four consecutive primes (173 + 179 + 181 + 191), sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137), nontotient
- 725 = 52 × 29
- 726 = 2 × 3 × 112, pentagonal pyramidal number[12]
- 727 = prime number, palindromic prime, lucky prime[13]
- 728 = 23 × 7 × 13, nontotient, Smith number,[5] cabtaxi number[14]
- 729 = 36 = 272.
730s
- 730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, happy number
- 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251)
- 732 = 22 × 3 × 61, sum of eight consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), sum of ten consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), Harshad number
- 733 = prime number, balanced prime,[17] permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
- 734 = 2 × 367, nontotient
- 735 = 3 × 5 × 72, Harshad number, Zuckerman number, smallest number such that uses same digits as its distinct prime factors
- 736 = 25 × 23, centered heptagonal number,[18] nice Friedman number since 736 = 7 + 36, Harshad number
- 737 = 11 × 67, palindromic number, model number of the Boeing 737 jet airliner.
- 738 = 2 × 32 × 41, Harshad number, designation for a Boeing 737-800 jet airliner.
- 739 = prime number, strictly non-palindromic number,[19] lucky prime,[13] happy number
740s
- 740 = 22 × 5 × 37, nontotient
- 741 = 3 × 13 × 19, sphenic number, triangular number[2]
- 742 = 2 × 7 × 53, sphenic number, decagonal number.[20] It is the smallest number that is one more than triple its reverse.
- 743 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part
- 744 = 23 × 3 × 31, sum of four consecutive primes (179 + 181 + 191 + 193). It is the coefficient of the first degree term of the expansion of Klein's j-invariant. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra E8.
- 745 = 5 × 149
- 746 = 2 × 373, nontotient
- 747 = 32 × 83, palindromic number, model number of the Boeing 747 jet airliner
- 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number[21]
- 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257)
750s
- 750 = 2 × 3 × 53, enneagonal number.[22]
- 751 = prime number, Chen prime
- 752 = 24 × 47, nontotient
- 753 = 3 × 251
- 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers
- 755 = 5 × 151. In 1976, Major League Baseball player Hank Aaron ended his career with a Major League record 755 home runs (record now held by Barry Bonds).
- 756 = 22 × 33 × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,[1] Harshad number
- 757 = prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127), happy number
- 758 = 2 × 379, nontotient
- 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163)
760s
- 760 = 23 × 5 × 19, centered triangular number[23]
- 761 = prime number, Sophie Germain prime,[9] Chen prime, Eisenstein prime with no imaginary part, centered square number[24]
- 762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number,[5] see also Six nines in pi
- 763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103)
- 764 = 22 × 191, telephone number[25]
- 765 = 32 × 5 × 17
- 766 = 2 × 383, centered pentagonal number,[26] nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), happy number
- 767 = 13 × 59, Thabit number (28 × 3 − 1), palindromic number
- 768 = 28 × 3, sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109)
- 769 = prime number, Chen prime, lucky prime,[13] Proth prime[27]
770s
- 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
- 771 = 3 × 257, 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 = 22 × 193
- 773 = prime number, Eisenstein prime with no imaginary part, tetranacci number[28]
- 774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number
- 775 = 52 × 31, member of the Mian–Chowla sequence,[29] happy number
- 776 = 23 × 97
780s
- 780 = 22 × 3 × 5 × 13, sum of four consecutive primes in a quadruplet (191, 193, 197, and 199); sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number,[2] hexagonal number,[3] Harshad number
- 780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.
- 781 = 11 × 71, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0
- 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,[6] Harshad number, also, 782 gear used by U.S. Marines
- 783 = 33 × 29
- 784 = 24 × 72 = 282 =
, the sum of the cubes of the first seven integers, happy number
- 785 = 5 × 157, Mertens function(785) = 0
- 786 = 2 × 3 × 131, sphenic number. See also its use in Muslim numerological symbolism.
- 787 = prime number, sum of five consecutive primes (149 + 151 + 157 + 163 + 167), Chen prime, lucky prime,[13] palindromic prime.
- 788 = 22 × 197, nontotient
- 789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269)
790s
- 790 = 2 × 5 × 79, sphenic number, nontotient
- 791 = 7 × 113, sum of the first twenty-two primes, sum of seven consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131)
- 792 = 23 × 32 × 11, number of partitions of 21,[33] binomial coefficient
, Harshad number
- 793 = 13 × 61, Mertens function(793) = 0, star number,[34] happy number
- 794 = 2 × 397, nontotient
- 795 = 3 × 5 × 53, Mertens function(795) = 0
- 796 = 22 × 199, sum of six consecutive primes (113 + 127 + 131 + 137 + 139 + 149), Mertens function(796) = 0
- 797 = prime number, Chen prime, Eisenstein prime with no imaginary part, palindromic prime
- 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient
- 799 = 17 × 47
References