700 (number)

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{{#invoke:Hatnote|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">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> nontotient, Harshad number

  • 703 = 19 × 37, the 37th triangular number,<ref name=":1">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> a hexagonal number,<ref name=":2">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> smallest number requiring 73 fifth powers for Waring representation, Kaprekar number,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index

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  • 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

|CitationClass=web }}</ref> pentatope number ( binomial coefficient <math>\tbinom {13}4</math> ),<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Harshad number, member of Ruth-Aaron pair (either definition)

|CitationClass=web }}</ref> Sophie Germain prime,<ref name=":5">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> safe prime,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

720s

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}

|CitationClass=web }}</ref> smallest number that is the difference of two positive cubes in two ways,

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|CitationClass=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

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    • 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>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)

|CitationClass=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>{{#invoke:citation/CS1|citation

|CitationClass=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>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number (sequence A000124 in the 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>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), blum integer

750s

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  • 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 K9,9.<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.
  • 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

|CitationClass=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>{{#invoke:citation/CS1|citation

|CitationClass=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>{{#invoke:citation/CS1|citation

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|CitationClass=web }}</ref> nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)

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770s

|CitationClass=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>{{#invoke:citation/CS1|citation

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{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}

  • 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>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

  • 778 = 2 × 389, nontotient, Smith number<ref name=":3" />
  • 779 = 19 × 41, highly cototient number<ref>{{#invoke:citation/CS1|citation

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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 (sequence A000124 in the 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>

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790s

References

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