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.

List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
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:

• The year AD, see 700.
• The decade beginning in the year 700 BC, see 700s BC.
• A television show aired on the Christian Broadcasting Network, see The 700 Club.

700s

700 — see above

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701 prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part

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702 = 2 × 3³ × 13, pronic number, nontotient, Harshad number

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

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704 = 2⁶ × 11, Harshad number.

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

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706 = 2 × 353, nontotient, Smith number

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

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708 = 2² × 3 × 59

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709 prime number

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710 = 2 × 5 × 71, sphenic number, nontotient

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711 = 3² × 79, Harshad number. Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.

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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 8^th power have no common digits.

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

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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.

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

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716 = 2² × 179

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717 = 3 × 239

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718 = 2 × 359

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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

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720（seven hundred [and] twenty）= 2⁴ × 3² × 5.

• 6 factorial, highly composite number, Harshad number in every base from binary to decimal, highly totient number.
• two round angles (= 2 × 360).
• five gross (= 500 duodecimal, 5 × 144).
• 241-gonal number.

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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

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722 = 2 × 19², nontotient

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723 = 3 × 241

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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,

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725 = 5² × 29

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726 = 2 × 3 × 11², pentagonal pyramidal number

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727 prime number, palindromic prime, Lucky prime

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

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729（seven 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)

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730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number

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731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251)

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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

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733 prime number, balanced prime, permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)

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734 = 2 × 367, nontotient

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735 = 3 × 5 × 7², Harshad number, Zuckerman number, smallest number such that uses same digits as its distinct prime factors

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736 = 2⁵ × 23, centered heptagonal number, nice Friedman number since 736 = 7 + 3⁶, Harshad number

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737 = 11 × 67, name of a Boeing plane

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738 = 2 × 3² × 41, Harshad number

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

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740 = 2² × 5 × 37, nontotient

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

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742 = 2 × 7 × 53, sphenic number, decagonal number. It is the smallest number that is one more than triple its reverse.

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743 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part

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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.

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745 = 5 × 149

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746 = 2 × 373, nontotient 746 = 1⁷ + 2⁴ + 36

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

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748 = 2² × 11 × 17, nontotient

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

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

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751 prime number, Chen prime

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752 = 2⁴ × 47, nontotient

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753 = 3 × 251

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754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers

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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).

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756 = 2² × 3³ × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number, Harshad number

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

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758 = 2 × 379, nontotient

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

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760 = 2³ × 5 × 19, centered triangular number

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

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

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

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764 = 2² × 191

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

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

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

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

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

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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

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

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772 = 2² × 193

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

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

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

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776 = 2³ × 97

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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.

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778 = 2 × 389, nontotient, Smith number

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779 = 19 × 41, highly cototient number

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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.

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781 = 11 × 71, Mertens function(781) = 0

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

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783 = 3³ × 29

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

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785 = 5 × 157, Mertens function(785) = 0

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786 = 2 × 3 × 131, sphenic number. See also its use in Muslim numerological symbolism.

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787 prime number, sum of five consecutive primes (149 + 151 + 157 + 163 + 167), Chen prime, Lucky prime, palindromic prime.

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788 = 2² × 197, nontotient

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

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790 = 2 × 5 × 79, sphenic number, nontotient

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791 = 7 × 113, sum of the first twenty-two primes, sum of seven consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131)

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792 = 2³ × 3² × 11, Harshad number

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

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794 = 2 × 397, nontotient

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795 = 3 × 5 × 53, Mertens function(795) = 0

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796 = 2² × 199, sum of six consecutive primes (113 + 127 + 131 + 137 + 139 + 149), Mertens function(796) = 0

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797 prime number, Chen prime, Eisenstein prime with no imaginary part, palindromic prime

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798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient

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799 = 17 × 47