Supriya Ghosh (Editor)

700 (number)

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700
  
701 →

Factorization
  
2× 5× 7

Binary
  
10101111002

Cardinal
  
seven hundred

Roman numeral
  
DCC

Ordinal
  
700th(seven hundredth)

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.

    In Judaism there is 713 letters on a Mezuzah scroll.

    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 ( 13 4 ) ), Harshad number, member of Ruth-Aaron pair (either definition)

    716 = 22 × 179, area code for Buffalo, NY

    717 = 3 × 239, palindromic number

    718 = 2 × 359, area code for Brooklyn, NY and Bronx, NY

    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 [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.

    • 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 [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, 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 E8.

    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 [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), 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 Six nines in pi

    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 cos ⁡ ( 2 π 771 ) 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 (191, 193, 197, and 199); 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 = 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

    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, number of partitions of 21, binomial coefficient ( 12 5 ) , 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

    References

    700 (number) Wikipedia
    (Text) CC BY-SA


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