700 (number)

This article is about the numbers 700 through 799; for each individual number, see its section below.

← 699 700 701 →
List of numbers Integers ←0100200300400500600700800900→
Cardinal	seven hundred
Ordinal	700th (seven hundredth)
Factorization	22× 52× 7
Greek numeral	Ψ´
Roman numeral	DCC
Binary	10101111002
Ternary	2212213
Senary	31246
Octal	12748
Duodecimal	4A412
Hexadecimal	2BC16
Armenian	Չ
Hebrew	ת "ש / ן
Babylonian cuneiform	𒌋𒐕𒐏
Egyptian hieroglyph	𓍨

700(seven hundred) is thenatural numberfollowing699and preceding701.

It is the sum of four consecutiveprimes(167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317)and aHarshad number.

Integers from 701 to 799

Nearly all of thepalindromic integersbetween 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 forBoeing Commercial Airplanes.

700s

• 701 = prime number, sum of three consecutive primes (229 + 233 + 239),Chen prime,Eisenstein primewith 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 codeforNorthern Virginiaalong with571,a number commonly found in the formula forbody mass index
• 704 = 2⁶× 11,Harshad number,lazy caterer number (sequenceA000124in theOEIS), area code for theCharlotte, NCarea.
• 705 = 3 × 5 × 47,sphenic number,smallestBruckman-Lucas pseudoprime(sequenceA005845in theOEIS)
• 706 = 2 × 353, nontotient,Smith number
• 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).
• 708 = 2²× 3 × 59, number of partitions of 28 that do not contain 1 as a part
• 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
• 711 = 3²× 79, Harshad number, number of planar Berge perfect graphs on 7 nodes.Also the phone number ofTelecommunications 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 codeforHouston, TX.InJudaismthere are 713 letters on aMezuzahscroll.
• 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,member ofRuth–Aaron pair(either definition); area code forOrange County, California.
  • Flight 714 to Sidneyis aTintingraphic novel.
  • 714 is the badge number of SergeantJoe Friday.
• 715 = 5 × 11 × 13, sphenic number, pentagonal number,pentatope number(binomial coefficient${\tbinom {13}{4}}$),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 forBuffalo, NY
• 717 = 3 × 239,palindromic number
• 718 = 2 × 359, area code forBrooklyn, NYandBronx, 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

720s

Main article:720 (number)

• 720 = 2⁴× 3²× 5.
  • 6factorial,highly composite number,Harshad numberin every base from binary to decimal,highly totient number.
  • tworound angles(= 2 ×360).
  • fivegross(= 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, number of odd parts in all partitions of 15,area of a square with diagonal 38
  • G.722is a freely available file format for audio file compression. The files are often named with the extension "722".
• 723 = 3 × 241, side length of analmost-equilateral Heronian triangle
• 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 analmost-equilateral Heronian triangle,the number ofn-queens problemsolutions forn= 10,
• 725 = 5²× 29, side length of analmost-equilateral Heronian triangle
• 726 = 2 × 3 × 11²,pentagonal pyramidal number
• 727 = prime number,palindromic prime,lucky prime,
• 728 = 2³× 7 × 13, nontotient,Smith number,cabtaxi number,728!! - 1 is prime,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.
  • thesquareof27,and thecubeof9,the sixthpower of three,and as a consequence of these properties, aperfect 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 inthe 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
• 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251), number of Euler trees with total weight 7
• 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
• 733 = prime number,emirp,balanced prime,permutable prime,sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
• 734 = 2 × 367, nontotient, number oftraceable graphson 7 nodes
• 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,happy number,niceFriedman numbersince 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,lucky prime,happy number,prime index prime

740s

• 740 = 2²× 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes
• 741 = 3 × 13 × 19, sphenic number, triangular number
• 742 = 2 × 7 × 53, sphenic number,decagonal number,icosahedral number.It is the smallest number that is one more than triple its reverse. Lazy caterer number (sequenceA000124in theOEIS). Number of partitions of 30 into divisors of 30.

Main article:743 (number)

• 743 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part

Main article:744 (number)

• 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'sj-invariant.Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebraE₈.
• 745 = 5 × 149 = 2⁴+ 3⁶,number of non-connected simple labeled graphs covering 6 vertices
• 746 = 2 × 373 = 1⁵+ 2⁴+ 3⁶= 1⁷+ 2⁴+ 3⁶,nontotient, number of non-normal semi-magic squares with sum of entries equal to 6
• 747 = 3²× 83 =$\left\lfloor {\frac {4^{23}}{3^{23}}}\right\rfloor$,palindromic number.
• 748 = 2²× 11 × 17, nontotient,happy number,primitive abundant number
• 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257),blum integer

750s

• 750 = 2 × 3 × 5³,enneagonal number.
• 751 = prime number, Chen prime, emirp
• 752 = 2⁴× 47, nontotient, number of partitions of 11 into parts of 2 kinds
• 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
• 755 = 5 × 151, number of vertices in a regular drawing of thecomplete bipartite graph K_9,9.
• 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 theHampton Roadsarea in the U.S. state ofVirginia,derived fromthe telephone area codethat covers almost all of the metropolitan area
• 758 = 2 × 379, nontotient, prime number of measurement
• 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163), a q-Fibonacci number for q=3

760s

• 760 = 2³× 5 × 19,centered triangular number,number of fixedheptominoes.
• 761 = prime number,emirp,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,admirable number,number of 1's in all partitions of 25 into odd parts,see alsoSix 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
• 764 = 2²× 191,telephone number
• 765 = 3²× 5 × 17, octagonal pyramidal number
  • aJapaneseword-play forNamco;
• 766 = 2 × 383,centered pentagonal number,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,sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109)
• 769 = prime number, Chen prime, lucky prime,Proth prime

770s

• 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
  • $\sum _{n=0}^{10}770^{n}$is prime
  • Famous room party in New Orleans hotel room 770, giving the name to a well knownscience fiction fanzinecalledFile 770
  • Holds special importancein theChabad-LubavitchHasidic movement.
• 771 = 3 × 257, sum of three consecutive primes inarithmetic progression(251 + 257 + 263). Since 771 is the product of the distinctFermat primes3 and 257, aregular polygonwith 771 sides can be constructed usingcompass and straightedge,and$\cos \left({\frac {2\pi }{771}}\right)$can be written in terms of square roots.
• 772 = 2²× 193, 772!!!!!!+1 is prime
• 773 = prime number, Eisenstein prime with no imaginary part,tetranacci number,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 theMian–Chowla sequence
• 776 = 2³× 97,refactorable number,number of compositions of 6 whose parts equal to q can be of q²kinds

Main article:777 (number)

• 777 = 3 × 7 × 37, sphenic number, Harshad number,palindromic number,3333 insenary(base 6) counting.
  • The numbers 3 and 7 are considered both "perfect numbers" under Hebrew tradition.
• 778 = 2 × 389, nontotient, Smith number
• 779 = 19 × 41,highly cototient number

780s

• 780 = 2²× 3 × 5 × 13, sum of four consecutiveprimesin aquadruplet(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. 781 is the sum of powers of 5/repdigit in base 5 (11111),Mertens function(781) = 0, lazy caterer number (sequenceA000124in theOEIS)
• 782 = 2 × 17 × 23, sphenic number, nontotient,pentagonal number,Harshad number, also, 782 gear used by U.S. Marines
• 783 = 3³× 29,heptagonal number
• 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 positive integers,happy number
• 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors

Main article:786 (number)

• 786 = 2 × 3 × 131, sphenic number,admirable number.See alsoits 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, number of compositions of 12 into parts with distinct multiplicities
• 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, anaspiring number,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 ofinteger partitionsof 21,binomial coefficient${\tbinom {12}{5}}$,Harshad number,sum of the nontriangular numbers between successive triangular numbers
• 793 = 13 × 61, Mertens function(793) = 0,star number,happy number
• 794 = 2 × 397 = 1⁶+ 2⁶+ 3⁶,nontotient
• 795 = 3 × 5 × 53,sphenic number,Mertens function(795) = 0, number of permutations of length 7 with 2 consecutive ascending pairs
• 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!
• 799 = 17 × 47, smallest number with digit sum 25