700 (number)

700 (number)
This article is about the numbers 700 through 799; for each individual number, see its section below.

700 (seven hundred) is the natural number following 699 and preceding 701.

Cardinal 700
seven hundred
Ordinal 700th
seven hundredth
Factorization 2^2 \cdot 5^2 \cdot 7
Roman numeral DCC
Roman numeral (Unicode) DCC, dcc
Binary 1010111100
Octal 1274
Duodecimal 4A4
Hexadecimal 2BC
Vigesimal 1F0

It is the sum of four consecutive primes (167 + 173 + 179 + 181). It is a Harshad number.

700 is also:

700s

700 — see above


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, nontotient, Harshad number


703 = 19 × 37, triangular number, hexagonal number, smallest number requiring 73 fifth powers for Waring representation, Kaprekar number


704 = 26 × 11, Harshad number.


705 = 3 × 5 × 47, sphenic number, smallest Lucas pseudoprime


706 = 2 × 353, nontotient, Smith number


707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151)


708 = 22 × 3 × 59


709 prime number


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, the number of the ambulance on the TV show Saved. It is the largest known number such that it and its 8th power have no common digits.


713 = 23 × 31, main area code for Houston, TX, vault containing the philosopher's stone in Harry Potter and the Philosopher's Stone.


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 number of home runs Babe Ruth scored in his career; see also 714 (disambiguation). 714 is the smallest number that uses the same digits in bases 2 and 5.


715 = 5 × 11 × 13, sphenic number, pentatope number, Harshad number, member of Ruth-Aaron pair (either definition)


716 = 22 × 179


717 = 3 × 239


718 = 2 × 359


719 prime number, factorial prime (6! − 1), Sophie Germain prime, safe prime, sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part


720seven 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, smallest number that is the difference of two positive cubes in two ways


722 = 2 × 192, nontotient


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

the number of n-queens problem solutions for n = 10,


725 = 52 × 29


726 = 2 × 3 × 112, pentagonal pyramidal number


727 prime number, palindromic prime, Lucky prime


728 = 23 × 7 × 13, nontotient, Smith number, cabtaxi number


729seven hundred [and] twenty-nine) = 36 = 272.

  • the square of 27, and the cube of 9, and as a consequence of these properties, a perfect totient number.
  • centered octagonal number, Smith number
  • the number of times a philosopher's pleasure is greater than a tyrant's pleasure according to Plato in the Republic
  • the largest three digit cube. (9 x 9 x 9)
  • the largest three digit sixth power. (3 x 3 x 3 x 3 x 3 x 3)

730 = 2 × 5 × 73, sphenic number, nontotient, Harshad 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, 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, nice Friedman number since 736 = 7 + 36, Harshad number


737 = 11 × 67, name of a Boeing plane


738 = 2 × 32 × 41, Harshad number


739 prime number, strictly non-palindromic number, Lucky prime


740 = 22 × 5 × 37, nontotient


741 = 3 × 13 × 19, sphenic number, triangular number


742 = 2 × 7 × 53, sphenic number, decagonal number. 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 746 = 17 + 24 + 36


747 = 32 × 83, model number of the Boeing 747, perhaps the most famous Boeing aircraft


748 = 22 × 11 × 17, nontotient


749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257)


750seven hundred [and] fifty)= 2 × 3 × 53, enneagonal number.


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, Harshad number


757 prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127)


758 = 2 × 379, nontotient


759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163)


760 = 23 × 5 × 19, centered triangular number


761 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, centered square number


762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number, see also Feynman point


763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103)


764 = 22 × 191


765 = a Japanese word-play for Namco; 32 × 5 × 17


766 = 2 × 383, centered pentagonal number, nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)


767 = 13 × 59, Thabit number (28 × 3 − 1)


768 = 28 × 3, sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109)


769 prime number, Chen prime, lucky prime, Proth prime


770 = 2 × 5 × 7 × 11, nontotient, Harshad number

  • Famous room party in New Orleans hotel room 770, giving the name to a well known science fiction fanzine called File 770

771 = 3 × 257, sum of three consecutive primes (251 + 257 + 263)


772 = 22 × 193


773 prime number, Eisenstein prime with no imaginary part, tetranacci number


774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number


775 = 52 × 31, member of the Mian–Chowla sequence


776 = 23 × 97


777 = 3 × 7 × 37, sphenic number, Harshad number, 3333 in senary (base 6) counting. The numbers 3 and 7 are considered both "perfect numbers" under Hebrew tradition.[citation needed] 777 is also found in the title of the book 777 and other Qabalistic writings of Aleister Crowley.


778 = 2 × 389, nontotient, Smith number


779 = 19 × 41, highly cototient number


780 = 22 × 3 × 5 × 13, sum of four consecutive primes in a quadruplet; sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number, hexagonal number, 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, Mertens function(781) = 0


782 = 2 × 17 × 23, sphenic number, nontotient, Harshad number, also, 782 gear used by U.S. Marines


783 = 33 × 29


784 = 24 × 72 = 282 = 13 + 23 + 33 + 43 + 53 + 63 + 73, the sum of the cubes of the first seven integers.


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, palindromic prime.


788 = 22 × 197, nontotient


789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269)


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, Harshad number


793 = 13 × 61, Mertens function(793) = 0, star 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


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