View source for 700 (number)

{{Hatnote|This article is about the numbers 700 through 799; for each individual number, see its section below.}}
{{Infobox number
| number = 700
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Չ|lang2=[[Hebrew numerals|Hebrew]]|lang2 symbol=<span style="font-size:150%;">ת"ש / ן</span>|lang3=[[Babylonian cuneiform numerals|Babylonian cuneiform]]|lang3 symbol=𒌋𒐕𒐏|lang4=[[Egyptian numerals|Egyptian hieroglyph]]|lang4 symbol=<span style="font-size:200%;">𓍨</span>}}
'''700''' ('''seven hundred''') is the [[natural number]] following [[600 (number)#690s|699]] and preceding [[#700s|701]].

It is the sum of four consecutive [[Prime number|prime]]s (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317)<ref>{{cite OEIS|A024364|Ordered perimeters of primitive Pythagorean triangles|access-date=2022-05-31}}</ref> and a [[Harshad number]].

==Integers from 701 to 799==
Nearly all of the [[Palindromic number|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 × 3<sup>3</sup> × 13, [[pronic number]],<ref name=":0">{{Cite web|url=https://oeis.org/A002378|title=Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[nontotient]], Harshad number
* 703 = 19 × 37, the 37th [[triangular number]],<ref name=":1">{{Cite web|url=https://oeis.org/A000217|title=Sloane's A000217 : Triangular numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> a [[hexagonal number]],<ref name=":2">{{Cite web|url=https://oeis.org/A000384|title=Sloane's A000384 : Hexagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> smallest number requiring 73 fifth powers for Waring representation, [[Kaprekar number]],<ref>{{Cite web|url=https://oeis.org/A006886|title=Sloane's A006886 : Kaprekar numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[703 area code|area code]] for [[Northern Virginia]] along with [[571 area code|571]], a number commonly found in the formula for [[body mass index]]
* 704 = 2<sup>6</sup> × 11, [[Harshad number]], lazy caterer number {{OEIS|id=A000124}}, area code for the [[Charlotte, NC]] area.
* 705 = 3 × 5 × 47, [[sphenic number]], smallest [[Lucas pseudoprime|Bruckman-Lucas pseudoprime]] {{OEIS|id=A005845}}
* 706 = 2 × 353, nontotient, [[Smith number]]<ref name=":3">{{Cite web|url=https://oeis.org/A006753|title=Sloane's A006753 : Smith numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</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>{{cite OEIS|A026671|Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when on the diagonal, (1,1)|access-date=2022-05-22}}</ref>
* 708 = 2<sup>2</sup> × 3 × 59, number of partitions of 28 that do not contain 1 as a part<ref>{{cite OEIS|A002865|Number of partitions of n that do not contain 1 as a part|access-date=2022-06-02}}</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>{{Cite journal|title=Classes of perfect graphs - ScienceDirect|journal=Discrete Mathematics |series=Creation and Recreation: A Tribute to the Memory of Claude Berge |date=6 October 2006 |volume=306 |issue=19 |pages=2529–2571 |doi=10.1016/j.disc.2006.05.021 |last1=Hougardy |first1=Stefan |doi-access=free }}</ref><ref>{{cite OEIS|A005195|Number of forests with n unlabeled nodes|access-date=2022-05-22}}</ref>
* 711 = 3<sup>2</sup> × 79, Harshad number, number of planar Berge perfect graphs on 7 nodes.<ref>{{cite OEIS|A123449|Number of planar Berge perfect graphs on n nodes}}</ref> Also the phone number of [[Telecommunications Relay Service]], commonly used by the deaf and hard-of-hearing.
* 712 = 2<sup>3</sup> × 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]], [[Area codes 281, 713, and 832|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>{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}}</ref> member of [[Ruth–Aaron pair]] (either definition); area code for [[Orange County, California]].
** ''Flight 714 to Sidney'' is a [[The Adventures of Tintin|Tintin]] graphic novel.
** 714 is the badge number of Sergeant [[Joe Friday]].
* 715 = 5 × 11 × 13, sphenic number, pentagonal number,<ref name=":4">{{Cite web|url=https://oeis.org/A000326|title=Sloane's A000326 : Pentagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[pentatope number]] ( [[binomial coefficient]] <math>\tbinom {13}4</math>  ),<ref>{{Cite web|url=https://oeis.org/A000332|title=Sloane's A000332 : Binomial coefficient binomial(n,4)|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</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 = 2<sup>2</sup> × 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>{{Cite web|url=https://oeis.org/A088054|title=Sloane's A088054 : Factorial primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[Sophie Germain prime]],<ref name=":5">{{Cite web|url=https://oeis.org/A005384|title=Sloane's A005384 : Sophie Germain primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[safe prime]],<ref>{{Cite web|url=https://oeis.org/A005385|title=Sloane's A005385 : Safe primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

===720s===

{{Main|720 (number)}}
* 720 = 2<sup>4</sup> × 3<sup>2</sup> × 5.
** [[6 (number)|6]] [[factorial]], [[highly composite number]], [[Harshad number]] in every base from binary to decimal, [[highly totient number]].
** two [[turn (geometry)|round angle]]s (= 2 × [[360 (number)|360]]).
** five [[Gross (unit)|gross]] (= 500 duodecimal, 5 × [[144 (number)|144]]).
** 241-[[polygonal number|gonal number]].
* 721 = 7 × 103, sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), [[centered hexagonal number]],<ref>{{Cite web|url=https://oeis.org/A003215|title=Sloane's A003215 : Hex (or centered hexagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> smallest number that is the difference of two positive cubes in two ways, 
* 722 = 2 × 19<sup>2</sup>, nontotient, number of odd parts in all partitions of 15,<ref>{{cite OEIS|A066897|Total number of odd parts in all partitions of n|access-date=2022-05-22}}</ref> area of a square with diagonal 38<ref name = "area of a square with diagonal 2n">{{cite OEIS|A001105|a(n) = 2*n^2}}</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 [[Heronian triangle#Almost-equilateral Heronian triangles|almost-equilateral Heronian triangle]]<ref>{{cite OEIS|A016064|Smallest side lengths of almost-equilateral Heronian triangles|access-date=2022-05-22}}</ref>
* 724 = 2<sup>2</sup> × 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 [[Heronian triangle#Almost-equilateral Heronian triangles|almost-equilateral Heronian triangle]],<ref>{{cite OEIS|A003500|a(n) = 4*a(n-1) - a(n-2) with a(0) = 2, a(1) = 4|access-date=2022-05-22}}</ref> the number of [[Eight queens puzzle|''n''-queens problem]] solutions for&nbsp;''n''&nbsp;=&nbsp;10,
* 725 = 5<sup>2</sup> × 29, side length of an [[Heronian triangle#Almost-equilateral Heronian triangles|almost-equilateral Heronian triangle]]<ref>{{cite OEIS|A335025|Largest side lengths of almost-equilateral Heronian triangles|access-date=2022-05-22}}</ref>
* 726 = 2 × 3 × 11<sup>2</sup>, [[pentagonal pyramidal number]]<ref>{{Cite web|url=https://oeis.org/A002411|title=Sloane's A002411 : Pentagonal pyramidal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 727 = prime number, [[palindromic prime]], [[lucky prime]],<ref name=":6">{{Cite web|url=https://oeis.org/A031157|title=Sloane's A031157 : Numbers that are both lucky and prime|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> 
* 728 = 2<sup>3</sup> × 7 × 13, nontotient, [[Smith number]],<ref name=":3" /> [[cabtaxi number]],<ref>{{Cite web|url=https://oeis.org/A047696|title=Sloane's A047696 : Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) cubes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> 728!! - 1 is prime,<ref>{{cite OEIS|A007749|Numbers k such that k!! - 1 is prime|access-date=2022-05-24}}</ref> [[oeis:A005897|number of cubes of edge length 1 required to make a hollow cube of edge length 12]], [[oeis:A006316|728<sup>64</sup> + 1 is prime]], [[oeis:A001187|number of connected graphs on 5 labelled vertices]]
* 729 = 27<sup>2</sup> = 9<sup>3</sup> = 3<sup>6</sup>.
** the [[square number|square]] of [[27 (number)|27]], and the [[cube (arithmetics)|cube]] of [[9 (number)|9]], the sixth [[power of three]], and because of these properties, a [[perfect totient number]].<ref>{{Cite web|url=https://oeis.org/A082897|title=Sloane's A082897 : Perfect totient numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
** [[centered octagonal number]],<ref>{{Cite web|url=https://oeis.org/A016754|title=Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> Smith number<ref name=":3" />
** the number of times a philosopher's pleasure is greater than a tyrant's pleasure according to Plato in [[The Republic (Plato)|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>{{cite OEIS|A004123|Number of generalized weak orders on n points|access-date=2022-05-22}}</ref>
* 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251), number of Euler trees with total weight 7 <ref>{{cite OEIS|A007317|Binomial transform of Catalan numbers}}</ref>
* 732 = 2<sup>2</sup> × 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>{{cite OEIS|A306445|Number of collections of subsets of {1, 2, ..., n} that are closed under union and intersection|access-date=2022-05-22}}</ref>
* 733 = prime number, [[emirp]], [[balanced prime]],<ref>{{Cite web|url=https://oeis.org/A006562|title=Sloane's A006562 : Balanced primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[permutable prime]], sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
* 734 = 2 × 367, nontotient, number of [[hamiltonian path#Definitions|traceable graphs]] on 7 nodes <ref>{{cite OEIS|A057864|Number of simple traceable graphs on n nodes|access-date=2022-05-22}}</ref>
* 735 = 3 × 5 × 7<sup>2</sup>, [[Harshad number]], Zuckerman number, smallest number such that uses same digits as its distinct prime factors
* 736 = 2<sup>5</sup> × 23, [[centered heptagonal number]],<ref>{{Cite web|url=https://oeis.org/A069099|title=Sloane's A069099 : Centered heptagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[happy number]], nice [[Friedman number]] since 736 = 7 + 3<sup>6</sup>, [[Harshad number]]
* 737 = 11 × 67, [[palindromic number]], [[blum integer]].
* 738 = 2 × 3<sup>2</sup> × 41, Harshad number.
* 739 = prime number, strictly non-palindromic number,<ref>{{Cite web|url=https://oeis.org/A016038|title=Sloane's A016038 : Strictly non-palindromic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> lucky prime,<ref name=":6" /> [[happy number]], [[oeis:A006450|prime index prime]]

===740s===
* 740 = 2<sup>2</sup> × 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes <ref>{{cite OEIS|
A077269|Number of connected squarefree graphs on n nodes|access-date=2022-05-23}}</ref>
* 741 = 3 × 13 × 19, sphenic number, 38th [[triangular number]]<ref name=":1" />
* 742 = 2 × 7 × 53, sphenic number, [[decagonal number]],<ref>{{Cite web|url=https://oeis.org/A001107|title=Sloane's A001107 : 10-gonal (or decagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[icosahedral number]]. It is the smallest number that is one more than triple its reverse. Lazy caterer number {{OEIS|id=A000124}}. Number of partitions of 30 into divisors of 30.<ref>{{cite OEIS|A018818|Number of partitions of n into divisors of n}}</ref>
* [[743 (number)|743]] = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part
* [[744 (number)|744]] = 2<sup>3</sup> × 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 (mathematics)|''E''<sub>8</sub>]].
* 745 = 5 × 149 = 2<sup>4</sup> + 3<sup>6</sup>, number of non-connected simple labeled graphs covering 6 vertices<ref>{{cite OEIS|A327070|Number of non-connected simple labeled graphs covering n vertices|access-date=2022-05-23}}</ref>
* 746 = 2 × 373 = 1<sup>5</sup> + 2<sup>4</sup> + 3<sup>6</sup> = 1<sup>7</sup> + 2<sup>4</sup> + 3<sup>6</sup>, nontotient, number of non-normal semi-magic squares with sum of entries equal to 6<ref>{{cite OEIS|A321719|Number of non-normal semi-magic squares with sum of entries equal to n|access-date=2022-05-30}}</ref>
* 747 = 3<sup>2</sup> × 83 = <math>\left\lfloor {\frac {4^{23}}{3^{23}}} \right\rfloor</math>,<ref>{{cite OEIS|A064628|Floor(4^n / 3^n)|access-date=2022-05-30}}</ref> [[palindromic number]].
* 748 = 2<sup>2</sup> × 11 × 17, nontotient, [[happy number]], primitive abundant number<ref>{{Cite web|url=https://oeis.org/A091191|title=Sloane's A091191 : Primitive abundant numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), [[blum integer]]

===750s===
* 750 = 2 × 3 × 5<sup>3</sup>, [[nonagonal number|enneagonal number]].<ref>{{Cite web|url=https://oeis.org/A001106|title=Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 751 = prime number, Chen prime, emirp
* 752 = 2<sup>4</sup> × 47, nontotient, number of partitions of 11 into parts of 2 kinds<ref>{{cite OEIS|A000712|Generating function = Product_{m>=1} 1/(1 - x^m)^2; a(n) = number of partitions of n into parts of 2 kinds|access-date=2022-05-30}}</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>{{cite OEIS|A034295|Number of different ways to divide an n X n square into sub-squares|access-date=2022-05-23}}</ref>
* 755 = 5 × 151, number of vertices in a regular drawing of the [https://oeis.org/A331755/a331755_10.png complete bipartite graph K<sub>9,9</sub>].<ref>{{cite OEIS|A331755|Number of vertices in a regular drawing of the complete bipartite graph K_{9,9}|access-date=2022-05-23}}</ref>
* 756 = 2<sup>2</sup> × 3<sup>3</sup> × 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 [[Area code 757|the telephone area code]] that covers almost all of the metropolitan area
* 758 = 2 × 379, nontotient, prime number of measurement <ref>{{cite OEIS|A002049|Prime numbers of measurement|access-date=2022-05-23}}</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>{{cite OEIS|A015474|q-Fibonacci numbers for q=3|access-date=2022-05-23}}</ref>

===760s===
* 760 = 2<sup>3</sup> × 5 × 19, [[centered triangular number]],<ref>{{Cite web|url=https://oeis.org/A005448|title=Sloane's A005448 : Centered triangular numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</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>{{Cite web|url=https://oeis.org/A001844|title=Sloane's A001844 : Centered square numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number,<ref name=":3" /> [[oeis:A111592|admirable number]], number of 1's in all partitions of 25 into odd parts,<ref>{{cite OEIS|A036469|Partial sums of A000009 (partitions into distinct parts)}}</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>{{cite OEIS|A001189|Number of degree-n permutations of order exactly 2|access-date=2022-05-23}}</ref>
* 764 = 2<sup>2</sup> × 191, [[Telephone number (mathematics)|telephone number]]<ref>{{Cite web|url=https://oeis.org/A000085|title=Sloane's A000085 : Number of self-inverse permutations on n letters, also known as involutions|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 765 = 3<sup>2</sup> × 5 × 17, octagonal pyramidal number <ref>{{cite OEIS|A002414|Octagonal pyramidal numbers|access-date=2022-05-23}}</ref>
** a [[Japanese language|Japanese]] word-play for [[Namco]]; 
* 766 = 2 × 383, [[centered pentagonal number]],<ref>{{Cite web|url=https://oeis.org/A005891|title=Sloane's A005891 : Centered pentagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)
* 767 = 13 × 59, [[Thabit number]] (2<sup>8</sup> × 3  − 1), [[palindromic number]].
* 768 = 2<sup>8</sup> × 3,<ref>{{cite OEIS|A007283|a(n) = 3*2^n|access-date=2022-05-30}}</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>{{Cite web|url=https://oeis.org/A080076|title=Sloane's A080076 : Proth primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>

===770s===
* 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
** <Math>\sum_{n=0}^{10} 770^{n}</math> is prime<ref>{{cite OEIS|A162862|Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime|access-date=2022-05-30}}</ref>
**  Famous room party in New Orleans hotel room 770, giving the name to a well known [[science fiction fanzine]] called [[File 770]]
** [[770 Eastern Parkway#Symbolism of "770"|Holds special importance]] in the [[Chabad]]-Lubavitch [[Hasidic Judaism|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 prime]]s 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 = 2<sup>2</sup> × 193, 772!!!!!!+1 is prime<ref>{{cite OEIS|A085150|Numbers n such that n!!!!!!+1 is prime|access-date=2022-05-30}}</ref>
* 773 = prime number, Eisenstein prime with no imaginary part, [[tetranacci number]],<ref>{{Cite web|url=https://oeis.org/A000078|title=Sloane's A000078 : Tetranacci numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[oeis:A006450|prime index prime]], sum of the number of cells that make up the convex, regular 4-polytopes
* 774 = 2 × 3<sup>2</sup> × 43, nontotient, totient sum for first 50 integers, Harshad number
* 775 = 5<sup>2</sup> × 31, member of the [[Mian–Chowla sequence]]<ref>{{Cite web|url=https://oeis.org/A005282|title=Sloane's A005282 : Mian-Chowla sequence|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> 
* 776 = 2<sup>3</sup> × 97, [[refactorable number]], number of compositions of 6 whose parts equal to q can be of q<sup>2</sup> kinds<ref>{{OEIS|A033453|access-date=2022-05-30}}</ref>

{{Main|777 (number)}}
* 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>{{cite web | last=Posner | first=Eliezer | title=On the Meaning of Three | url=http://www.chabad.org/library/article_cdo/aid/608781/jewish/On-the-Meaning-of-Three.htm | publisher=Chabad | access-date=2 July 2016}}</ref><ref>{{cite web | last=Dennis | first=Geoffrey | title=Judaism & Numbers | url=http://www.myjewishlearning.com/beliefs/Issues/Magic_and_the_Supernatural/Practices_and_Beliefs/Incantations/Names_and_Numbers/Numbers.shtml | publisher=My Jewish Learning | access-date=2 July 2016}}</ref>
* 778 = 2 × 389, nontotient, Smith number<ref name=":3" />
* 779 = 19 × 41, [[highly cototient number]]<ref>{{Cite web|url=https://oeis.org/A100827|title=Sloane's A100827 : Highly cototient numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>

===780s===
* 780 = 2<sup>2</sup> × 3 × 5 × 13, sum of four consecutive [[prime number|primes]] in a [[Prime quadruplet|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 {{OEIS|id=A000124}}
* 782 = 2 × 17 × 23, sphenic number, nontotient, [[pentagonal number]],<ref name=":4" /> Harshad number, also, 782 gear used by U.S. Marines
* 783 = 3<sup>3</sup> × 29, [[heptagonal number]]
* 784 = 2<sup>4</sup> × 7<sup>2</sup> = 28<sup>2</sup> = <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>{{cite OEIS|A050381|Number of series-reduced planted trees with n leaves of 2 colors|access-date=2022-05-24}}</ref>

{{Main|786 (number)}}
* 786  = 2 × 3 × 131, sphenic number, [[oeis:A111592|admirable number]]. See also [[Basmala#Numerology|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 = 2<sup>2</sup> × 197, nontotient, number of compositions of 12 into parts with distinct multiplicities <ref>{{cite OEIS|A242882|Number of compositions of n into parts with distinct multiplicities|access-date=2022-05-24}}</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>{{cite OEIS|A063769|Aspiring numbers}}</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 = 2<sup>3</sup> × 3<sup>2</sup> × 11, number of [[integer partition]]s of 21,<ref>{{Cite OEIS|A000041|2=a(n) = number of partitions of n}}</ref> [[binomial coefficient]] <math>\tbinom {12}5</math>, Harshad number, [[oeis:A006002|sum of the nontriangular numbers between successive triangular numbers]]
* 793 = 13 × 61, Mertens function(793) = 0, [[star number]],<ref>{{Cite OEIS|A003154|Centered 12-gonal numbers. Also star numbers}}</ref> [[happy number]]
* 794 = 2 × 397 = 1<sup>6</sup> + 2<sup>6</sup> + 3<sup>6</sup>,<ref>{{cite OEIS|A001550|2=a(n) = 1^n + 2^n + 3^n}}</ref> nontotient
* 795 = 3 × 5 × 53, [[sphenic number]], Mertens function(795) = 0, number of permutations of length 7 with 2 consecutive ascending pairs <ref>{{cite OEIS|A000274|Number of permutations of length n with 2 consecutive ascending pairs|access-date=2022-05-24}}</ref>
* 796 = 2<sup>2</sup> × 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]], [[oeis:A006450|prime index prime]].
* 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient, product of primes indexed by the prime exponents of 10! <ref>{{cite OEIS|A325508|Product of primes indexed by the prime exponents of n!|access-date=2022-05-24}}</ref>
* 799 = 17 × 47, smallest number with digit sum 25 <ref>{{cite OEIS|A051885|Smallest number whose sum of digits is n|access-date=2022-05-24}}</ref>

==References==
{{Reflist}}

{{Integers|7}}
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[[Category:Integers]]