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| {{Unreferenced|date=December 2009}}
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| {{hatnote|This article is about the numbers 700 through 799; for each individual number, see its section below.}}
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| {{Infobox number
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| | number = 700
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| }}
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| '''700''' ('''seven hundred''') is the [[natural number]] following 699 and preceding 701.
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| It is the sum of four consecutive [[Prime number|prime]]s (167 + 173 + 179 + 181). It is a [[Harshad number]].
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| 700 is also:
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| * The year AD, see '''[[700]]'''.
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| * The decade beginning in the year 700 BC, see '''[[709–700 BC|700s BC]]'''.
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| * A television show that aired on the [[Christian Broadcasting Network]], see ''[[The 700 Club]]''.
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| ==700s==
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| 700 — see above
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| ----
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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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| ----
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| 702 = 2 × 3<sup>3</sup> × 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]], [[703 area code|area code]] for [[Northern Virginia]] along with [[571 area code|571]], a number commonly found in the formula for [[body mass index]]
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| 704 = 2<sup>6</sup> × 11, [[Harshad number]], area code for the [[Charlotte, NC]] area.
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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 = 2<sup>2</sup> × 3 × 59
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| 709 is a prime number. It is also a [[happy number]].
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| 710 = 2 × 5 × 71, sphenic number, nontotient
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| 711 = 3<sup>2</sup> × 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 = 2<sup>3</sup> × 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 8<sup>th</sup> power (66,045,000,696,445,844,586,496) have no common digits.
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| 713 = 23 × 31, [[Area codes 281, 713, and 832|main area code]] for [[Houston, TX]].
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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 smallest number that uses the same digits in bases 2 and 5, area code for [[Orange County, California]].
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| 715 = 5 × 11 × 13, sphenic number, pentagonal number, [[pentatope number]] ( [[binomial coefficient]] <math>\tbinom {13}4</math> ),
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| Harshad number, member of Ruth-Aaron pair (either definition)
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| 716 = 2<sup>2</sup> × 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 (number)|720]]（''seven hundred [and] twenty''）= 2<sup>4</sup> × 3<sup>2</sup> × 5.
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| *[[6 (number)|6]] [[factorial]], [[highly composite number]], [[Harshad number]] in every base from binary to decimal, [[highly totient number]].
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| *two [[turn (geometry)|round angle]]s (= 2 × [[360 (number)|360]]).
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| *five [[Gross (unit)|gross]] (= 500 duodecimal, 5 × [[144 (number)|144]]).
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| *241-[[polygonal number|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, [[happy number]]
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| 722 = 2 × 19<sup>2</sup>, nontotient
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| * [[G.722]] is a freely available file format for audio file compression. The files are often named with the extension "722".
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| 723 = 3 × 241
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| 724 = 2<sup>2</sup> × 181, sum of four consecutive primes (173 + 179 + 181 + 191), sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137), nontotient
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| the number of [[Eight queens puzzle|''n''-queens problem]] solutions for ''n'' = 10,
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| 725 = 5<sup>2</sup> × 29
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| 726 = 2 × 3 × 11<sup>2</sup>, [[pentagonal pyramidal number]]
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| 727 prime number, [[palindromic prime]], [[Lucky prime]]
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| 728 = 2<sup>3</sup> × 7 × 13, nontotient, [[Smith number]], [[cabtaxi number]]
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| '''729'''（''seven hundred [and] twenty-nine''） = 3<sup>6</sup> = 27<sup>2</sup>.
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| *the [[square number|square]] of [[27 (number)|27]], and the [[cube (arithmetics)|cube]] of [[9 (number)|9]], and as a consequence of these properties, a [[perfect totient number]].
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| *[[centered octagonal number]], Smith number
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| *the number of times a philosopher's pleasure is greater than a tyrant's pleasure according to Plato in [[The Republic (Plato)|the Republic]]
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| *the largest three digit cube. (9 x 9 x 9)
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| *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, [[happy number]]
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| 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251)
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| 732 = 2<sup>2</sup> × 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 × 7<sup>2</sup>, [[Harshad number]], Zuckerman number, smallest number such that uses same digits as its distinct prime factors
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| 736 = 2<sup>5</sup> × 23, [[centered heptagonal number]], nice [[Friedman number]] since 736 = 7 + 3<sup>6</sup>, [[Harshad number]]
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| 737 = 11 × 67, [[Boeing 737]] jet airliner.
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| 738 = 2 × 3<sup>2</sup> × 41, Harshad number, designation for a [[Boeing 737-800]] jet airliner.
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| 739 prime number, [[strictly non-palindromic number]], Lucky prime, [[happy number]]
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| 740 = 2<sup>2</sup> × 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 = 2<sup>3</sup> × 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 (mathematics)|''E''<sub>8</sub>]].
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| 745 = 5 × 149
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| 746 = 2 × 373, nontotient
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| 746 = 1<sup>7</sup> + 2<sup>4</sup> + 3</sup>6
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| 747 = 3<sup>2</sup> × 83, model number of the [[Boeing 747]], perhaps the most famous Boeing aircraft
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| 748 = 2<sup>2</sup> × 11 × 17, nontotient, [[happy number]], primitive abundant number
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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 × 5<sup>3</sup>, [[nonagonal number|enneagonal number]]. | |
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| 751 prime number, Chen prime
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| 752 = 2<sup>4</sup> × 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 = 2<sup>2</sup> × 3<sup>3</sup> × 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), [[happy number]]
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| * "The 757" is a local nickname for the [[Hampton Roads]] area in the U.S. state of [[Virginia]], derived from [[Area code 757|the telephone area code]] that covers almost all of the metropolitan area.
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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 = 2<sup>3</sup> × 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 = 2<sup>2</sup> × 191, [[Telephone number (mathematics)|telephone number]]
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| 765 = 3<sup>2</sup> × 5 × 17
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| *a [[Japanese language|Japanese]] word-play for [[Namco]];
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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), [[happy number]]
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| 767 = 13 × 59, [[Thabit number]] (2<sup>8</sup> × 3 − 1)
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| 768 = 2<sup>8</sup> × 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
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| * 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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| *[[770 Eastern Parkway#Importance of 770|Holds special importance]] in the [[Chabad]]-Lubavitch [[Hasidic Judaism|Hasidic movement]].
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| 771 = 3 × 257, sum of three consecutive primes (251 + 257 + 263)
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| 772 = 2<sup>2</sup> × 193
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| 773 prime number, Eisenstein prime with no imaginary part, [[tetranacci number]]
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| 774 = 2 × 3<sup>2</sup> × 43, nontotient, totient sum for first 50 integers, Harshad number
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| 775 = 5<sup>2</sup> × 31, member of the [[Mian–Chowla sequence]], [[happy number]]
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| 776 = 2<sup>3</sup> × 97
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| 777 = 3 × 7 × 37, sphenic number, Harshad number, 3333 in [[senary]] (base 6) counting.
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| *The numbers 3 and 7 are considered both "perfect numbers" under Hebrew tradition.{{Citation needed|date=October 2007}} 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 = 2<sup>2</sup> × 3 × 5 × 13, sum of four consecutive [[prime number|primes]] in a [[Prime quadruplet|quadruplet]]; sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), [[triangular number]], [[hexagonal number]], [[Harshad number]]
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| 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, sum of powers of 5/repdigit in base 5 (11111), [[Mertens function]](781) = 0
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| 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number, Harshad number, also, 782 gear used by U.S. Marines
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| 783 = 3<sup>3</sup> × 29
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| 784 = 2<sup>4</sup> × 7<sup>2</sup> = 28<sup>2</sup> = <math>1^3+2^3+3^3+4^3+5^3+6^3+7^3</math>, the sum of the cubes of the first seven integers, [[happy number]]
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| 785 = 5 × 157, Mertens function(785) = 0
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| 786 = 2 × 3 × 131, sphenic number. See also [[Basmala#Numerology|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 = 2<sup>2</sup> × 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 = 2<sup>3</sup> × 3<sup>2</sup> × 11, no of [[partition (number theory)|Partitions]] of 21, [[binomial coefficient]] <math>\tbinom {12}5</math>, Harshad number
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| 793 = 13 × 61, Mertens function(793) = 0, [[star number]], [[happy 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 = 2<sup>2</sup> × 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
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| {{Integers|7}}
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| [[Category:Integers|79e02 700]]
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