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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. 700 is also: * The year AD, see 700. * The decade beginning in the year 700 BC, see 700s BC. * A television show that aired on the Christian Broadcasting Network, see ''The 700 Club''. ==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, 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 ---- 707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151), palindromic number ---- 708 = 22 × 3 × 59 ---- 709 is a prime number. It is also a happy 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. 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. ---- 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. ---- 715 = 5 × 11 × 13, sphenic number, pentagonal number, pentatope number ( binomial coefficient ), Harshad number, member of Ruth-Aaron pair (either definition) ---- 716 = 22 × 179 ---- 717 = 3 × 239, palindromic number ---- 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 ---- 720 (''seven hundred () 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. ---- 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 * 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 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 ---- 729 (''seven hundred () 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, 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, 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, palindromic number, 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, Lucky prime, happy number ---- 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 ''E''8. ---- 745 = 5 × 149 ---- 746 = 2 × 373, nontotient 746 = 17 + 24 + 36 ---- 747 = 32 × 83, palindromic number, model number of the Boeing 747, perhaps the most famous Boeing aircraft ---- 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number ---- 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257) ---- 750 (''seven hundred () 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), happy number * "The 757" is a local nickname for the Hampton Roads area in the U.S. state of Virginia, derived from the telephone area code that covers almost all of the metropolitan area. ---- 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, telephone number ---- 765 = 32 × 5 × 17 *a Japanese word-play for Namco; ---- 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 ---- 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, 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 *Holds special importance in the Chabad-Lubavitch Hasidic movement. ---- 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 ---- 774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number ---- 775 = 52 × 31, member of the Mian–Chowla sequence, happy number ---- 776 = 23 × 97 ---- 777 = 3 × 7 × 37, sphenic number, Harshad number, palindromic number, 3333 in senary (base 6) counting. *The numbers 3 and 7 are considered both "perfect numbers" under Hebrew tradition. 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, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0 ---- 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number, 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, 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, no of Partitions of 21, binomial coefficient , Harshad number ---- 793 = 13 × 61, Mertens function(793) = 0, star number, 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 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「700 (number)」の詳細全文を読む スポンサード リンク
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