700 (number)

Template:Hatnote Template:Use dmy dates Template:Infobox number 700 (seven hundred) is the natural number following 699 and preceding 701.

It is a composite number and the sum of four consecutive primes (167 + 173 + 179 + 181).

Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 (i.e. nearly all numbers in this range that have both the hundreds and units digit be 7) are used as model numbers for Boeing Commercial Airplanes.

700s

• 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,<ref name=":0">Template:Cite web</ref> nontotient, Harshad number
• 703 = 19 × 37, the 37th triangular number,<ref name=":1">Template:Cite web</ref> a hexagonal number,<ref name=":2">Template:Cite web</ref> smallest number requiring 73 fifth powers for Waring representation, Kaprekar number,<ref>Template:Cite web</ref> area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index
• 704 = 2⁶ × 11, Harshad number, lazy caterer number Template:OEIS, area code for the Charlotte, NC area.
• 705 = 3 × 5 × 47, sphenic number, smallest Bruckman-Lucas pseudoprime Template:OEIS
• 706 = 2 × 353, nontotient, Smith number<ref name=":3">Template:Cite web</ref>
• 707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151), palindromic number, number of lattice paths from (0,0) to (5,5) with steps (0,1), (1,0) and, when on the diagonal, (1,1).<ref>Template:Cite OEIS</ref>
• 708 = 2² × 3 × 59, number of partitions of 28 that do not contain 1 as a part<ref>Template:Cite OEIS</ref>
• 709 = prime number; happy number. It is the seventh in the series 2, 3, 5, 11, 31, 127, 709 where each number is the nth prime with n being the number preceding it in the series, therefore, it is a prime index number.

710s

• 710 = 2 × 5 × 71, sphenic number, nontotient, number of forests with 11 vertices<ref>Template:Cite journal</ref><ref>Template:Cite OEIS</ref>
• 711 = 3² × 79, Harshad number, number of planar Berge perfect graphs on 7 nodes.<ref>Template:Cite OEIS</ref> Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.
• 712 = 2³ × 89, refactorable number, 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, Blum integer, main area code for Houston, TX. In Judaism there are 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, balanced number,<ref>Template:Cite OEIS</ref> member of Ruth–Aaron pair (either definition); area code for Orange County, California.
  • Flight 714 to Sidney is a Tintin graphic novel.
  • 714 is the badge number of Sergeant Joe Friday.
• 715 = 5 × 11 × 13, sphenic number, pentagonal number,<ref name=":4">Template:Cite web</ref> pentatope number ( binomial coefficient <math>\tbinom {13}4</math> ),<ref>Template:Cite web</ref> Harshad number, member of Ruth-Aaron pair (either definition)
• The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17)
• 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),<ref>Template:Cite web</ref> Sophie Germain prime,<ref name=":5">Template:Cite web</ref> safe prime,<ref>Template:Cite web</ref> sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

720s

• 720 = 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,<ref>Template:Cite web</ref> smallest number that is the difference of two positive cubes in two ways,
• 722 = 2 × 19², nontotient, number of odd parts in all partitions of 15,<ref>Template:Cite OEIS</ref> area of a square with diagonal 38<ref name = "area of a square with diagonal 2n">Template:Cite OEIS</ref>
  • G.722 is a freely available file format for audio file compression. The files are often named with the extension "722".
• 723 = 3 × 241, side length of an almost-equilateral Heronian triangle<ref>Template:Cite OEIS</ref>
• 724 = 2² × 181, sum of four consecutive primes (173 + 179 + 181 + 191), sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137), nontotient, side length of an almost-equilateral Heronian triangle,<ref>Template:Cite OEIS</ref> the number of n-queens problem solutions for n = 10,
• 725 = 5² × 29, side length of an almost-equilateral Heronian triangle<ref>Template:Cite OEIS</ref>
• 726 = 2 × 3 × 11², pentagonal pyramidal number<ref>Template:Cite web</ref>
• 727 = prime number, palindromic prime, lucky prime,<ref name=":6">Template:Cite web</ref>
• 728 = 2³ × 7 × 13, nontotient, Smith number,<ref name=":3" /> cabtaxi number,<ref>Template:Cite web</ref> 728!! - 1 is prime,<ref>Template:Cite OEIS</ref> number of cubes of edge length 1 required to make a hollow cube of edge length 12, 728⁶⁴ + 1 is prime, number of connected graphs on 5 labelled vertices
• 729 = 27² = 9³ = 3⁶.
  • the square of 27, and the cube of 9, the sixth power of three, and because of these properties, a perfect totient number.<ref>Template:Cite web</ref>
  • centered octagonal number,<ref>Template:Cite web</ref> Smith number<ref name=":3" />
  • the number of times a philosopher king'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 only three-digit sixth power. (3 x 3 x 3 x 3 x 3 x 3)

730s

• 730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, number of generalized weak orders on 5 points <ref>Template:Cite OEIS</ref>
• 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251), number of Euler trees with total weight 7 <ref>Template:Cite OEIS</ref>
• 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, number of collections of subsets of {1, 2, 3, 4} that are closed under union and intersection <ref>Template:Cite OEIS</ref>
• 733 = prime number, emirp, balanced prime,<ref>Template:Cite web</ref> permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
• 734 = 2 × 367, nontotient, number of traceable graphs on 7 nodes <ref>Template:Cite OEIS</ref>
• 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,<ref>Template:Cite web</ref> happy number, nice Friedman number since 736 = 7 + 3⁶, Harshad number
• 737 = 11 × 67, palindromic number, blum integer.
• 738 = 2 × 3² × 41, Harshad number.
• 739 = prime number, strictly non-palindromic number,<ref>Template:Cite web</ref> lucky prime,<ref name=":6" /> happy number, prime index prime

740s

• 740 = 2² × 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes <ref>Template:Cite OEIS</ref>
• 741 = 3 × 13 × 19, sphenic number, 38th triangular number<ref name=":1" />
• 742 = 2 × 7 × 53, sphenic number, decagonal number,<ref>Template:Cite web</ref> icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number Template:OEIS. Number of partitions of 30 into divisors of 30.<ref>Template:Cite OEIS</ref>
• 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, and the zeroth degree term of the Laurent series of the J-invariant. Furthermore, 744 = 3 × 248 where 248 is the dimension of the Lie algebra E₈.
• 745 = 5 × 149 = 2⁴ + 3⁶, number of non-connected simple labeled graphs covering 6 vertices<ref>Template:Cite OEIS</ref>
• 746 = 2 × 373 = 1⁵ + 2⁴ + 3⁶ = 1⁷ + 2⁴ + 3⁶, nontotient, number of non-normal semi-magic squares with sum of entries equal to 6<ref>Template:Cite OEIS</ref>
• 747 = 3² × 83 = <math>\left\lfloor {\frac {4^{23}}{3^{23}}} \right\rfloor</math>,<ref>Template:Cite OEIS</ref> palindromic number.
• 748 = 2² × 11 × 17, nontotient, happy number, primitive abundant number<ref>Template:Cite web</ref>
• 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), blum integer

750s

• 750 = 2 × 3 × 5³, enneagonal number.<ref>Template:Cite web</ref>
• 751 = prime number with a prime number of prime digits,<ref>Template:Cite OEIS</ref> Chen prime, emirp,
• 752 = 2⁴ × 47, nontotient, number of partitions of 11 into parts of 2 kinds<ref>Template:Cite OEIS</ref>
• 753 = 3 × 251, blum integer
• 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers, number of different ways to divide a 10 × 10 square into sub-squares <ref>Template:Cite OEIS</ref>
• 755 = 5 × 151, number of vertices in a regular drawing of the complete bipartite graph K_9,9.<ref>Template:Cite OEIS</ref>
• 756 = 2² × 3³ × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,<ref name=":0" /> 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, prime number of measurement <ref>Template:Cite OEIS</ref>
• 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163), a q-Fibonacci number for q=3 <ref>Template:Cite OEIS</ref>

760s

• 760 = 2³ × 5 × 19, centered triangular number,<ref>Template:Cite web</ref> number of fixed heptominoes.
• 761 = prime number, emirp, Sophie Germain prime,<ref name=":5" /> Chen prime, Eisenstein prime with no imaginary part, centered square number<ref>Template:Cite web</ref>
• 762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number,<ref name=":3" /> admirable number, number of 1's in all partitions of 25 into odd parts,<ref>Template:Cite OEIS</ref> see also Six nines in pi
• 763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), number of degree-8 permutations of order exactly 2 <ref>Template:Cite OEIS</ref>
• 764 = 2² × 191, telephone number<ref>Template:Cite web</ref>
• 765 = 3² × 5 × 17, octagonal pyramidal number <ref>Template:Cite OEIS</ref>
  • a Japanese word-play for Namco;
• 766 = 2 × 383, centered pentagonal number,<ref>Template:Cite web</ref> nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)
• 767 = 13 × 59, Thabit number (2⁸ × 3 − 1), palindromic number.
• 768 = 2⁸ × 3,<ref>Template:Cite OEIS</ref> sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109)
• 769 = prime number, Chen prime, lucky prime,<ref name=":6" /> Proth prime<ref>Template:Cite web</ref>

770s

• 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
  • <Math>\sum_{n=0}^{10} 770^{n}</math> is prime<ref>Template:Cite OEIS</ref>
  • 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 <math>\cos\left(\frac{2\pi}{771}\right)</math> can be written in terms of square roots.
• 772 = 2² × 193, 772!!!!!!+1 is prime<ref>Template:Cite OEIS</ref>
• 773 = prime number, Eisenstein prime with no imaginary part, tetranacci number,<ref>Template:Cite web</ref> prime index prime, sum of the number of cells that make up the convex, regular 4-polytopes
• 774 = 2 × 3² × 43, nontotient, totient sum for first 50 integers, Harshad number
• 775 = 5² × 31, member of the Mian–Chowla sequence<ref>Template:Cite web</ref>
• 776 = 2³ × 97, refactorable number, number of compositions of 6 whose parts equal to q can be of q² kinds<ref>Template:OEIS</ref>

• 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.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>
• 778 = 2 × 389, nontotient, Smith number<ref name=":3" />
• 779 = 19 × 41, highly cototient number<ref>Template:Cite web</ref>

780s

• 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), 39th triangular number,<ref name=":1" /> a hexagonal number,<ref name=":2" /> 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. 781 is the sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0, lazy caterer number Template:OEIS
• 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,<ref name=":4" /> Harshad number, also, 782 gear used by U.S. Marines
• 783 = 3³ × 29, heptagonal number
• 784 = 2⁴ × 7² = 28² = <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 positive integers, happy number
• 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors<ref>Template:Cite OEIS</ref>

• 786 = 2 × 3 × 131, sphenic number, admirable 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,<ref name=":6" /> palindromic prime.
• 788 = 2² × 197, nontotient, number of compositions of 12 into parts with distinct multiplicities<ref>Template:Cite OEIS</ref>
• 789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269), Blum integer

790s

• 790 = 2 × 5 × 79, sphenic number, nontotient, a Harshad number in bases 2, 7, 14 and 16, an aspiring number,<ref>Template:Cite OEIS</ref> the aliquot sum of 1574.
• 791 = 7 × 113, centered tetrahedral number, 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 integer partitions of 21,<ref>Template:Cite OEIS</ref> binomial coefficient <math>\tbinom {12}5</math>, Harshad number, sum of the nontriangular numbers between successive triangular numbers
• 793 = 13 × 61, Mertens function(793) = 0, star number,<ref>Template:Cite OEIS</ref> happy number
• 794 = 2 × 397 = 1⁶ + 2⁶ + 3⁶,<ref>Template:Cite OEIS</ref> nontotient
• 795 = 3 × 5 × 53, sphenic number, Mertens function(795) = 0, number of permutations of length 7 with 2 consecutive ascending pairs <ref>Template:Cite OEIS</ref>
• 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, two-sided prime, prime index prime.
• 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient, product of primes indexed by the prime exponents of 10! <ref>Template:Cite OEIS</ref>
• 799 = 17 × 47, smallest number with digit sum 25 <ref>Template:Cite OEIS</ref>