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741 (number) : ウィキペディア英語版
700 (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.
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
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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, area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index
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704 = 26 × 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), palindromic number
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708 = 22 × 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 = 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. 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.
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713 = 23 × 31, 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.
* 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.
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715 = 5 × 11 × 13, sphenic number, pentagonal number, pentatope number ( binomial coefficient \tbinom 4 ),
Harshad number, member of Ruth-Aaron pair (either definition)
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716 = 22 × 179
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717 = 3 × 239, palindromic number
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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 () 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
* 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 = 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 () 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, happy 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, palindromic number, Boeing 737 jet airliner.
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738 = 2 × 32 × 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 = 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 ''E''8.
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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, palindromic number, model number of the Boeing 747, perhaps the most famous Boeing aircraft
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748 = 22 × 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 () 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), 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.
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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, telephone number
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765 = 32 × 5 × 17
*a 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 (28 × 3 − 1), palindromic number
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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
*Holds special importance in the Chabad-Lubavitch Hasidic movement.
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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 \cos\left(\frac\right) can be written in terms of square roots.
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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, happy number
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776 = 23 × 97
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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''.
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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, 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 = 33 × 29
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784 = 24 × 72 = 282 = 1^3+2^3+3^3+4^3+5^3+6^3+7^3, 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 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, no of Partitions of 21, binomial coefficient \tbinom 5, 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 = 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

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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