700 (number) - AbsoluteAstronomy.com

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

700 (seven hundred) is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

following 699 and preceding 701.


Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...	700 seven hundred
Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...	700th seven hundredth
Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...
Roman numeral	DCC
Roman numeral (Unicode)	DCC, dcc
Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...	1010111100
Octal Octal The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...	1274
Duodecimal Duodecimal The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...	4A4
Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...	2BC
Vigesimal Vigesimal The vigesimal or base 20 numeral system is based on twenty .- Places :...	1F0

It is the sum of four consecutive prime

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

s (167 + 173 + 179 + 181). It is a Harshad number

Harshad number

A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...

.

700 is also:

The year AD, see 700
700
Year 700 was a leap year starting on Thursday of the Julian calendar. The denomination 700 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.- North America :* The Mount Edziza volcanic complex...

.
The decade beginning in the year 700 BC, see 700s BC
700s BC
-Events and trends:* 706 BC—Spartan immigrants found Taras colony in southern Italy.* 706 BC—Sargon II dies.* 705 BC—Sennacherib succeeds his father Sargon II as king of Assyria....

.
A television show aired on the Christian Broadcasting Network
Christian Broadcasting Network
The Christian Broadcasting Network, or CBN, is a fundamentalist Christian television broadcasting network in the United States. Its headquarters and main studios are in Virginia Beach, Virginia.-Background:...

, see The 700 Club
The 700 Club
The 700 Club is the flagship news talk show of the Christian Broadcasting Network, airing in syndication throughout the United States and Canada. In production since 1966, it is currently hosted by Pat Robertson, Terry Meeuwsen, Kristi Watts, and Gordon P. Robertson, two of whom will host on any...

.

700s

700 — see above
----
701 prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime

Chen prime

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem....

, Eisenstein prime

Eisenstein prime

In mathematics, an Eisenstein prime is an Eisenstein integerz = a + b\,\omega\qquadthat is irreducible in the ring-theoretic sense: its only Eisenstein divisors are the units , a + bω itself and its associates.The associates and the complex conjugate...

with no imaginary part
----
702 = 2 × 3³ × 13, pronic number

Pronic number

A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...

, nontotient

Nontotient

In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...

, Harshad number
----
703 = 19 × 37, triangular number

Triangular number

A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

, hexagonal number

Hexagonal number

A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...

, smallest number requiring 73 fifth powers for Waring representation, Kaprekar number

Kaprekar number

In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45. The Kaprekar numbers are...

----
704 = 2⁶ × 11, Harshad number

Harshad number

.
----
705 = 3 × 5 × 47, sphenic number

Sphenic number

In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...

, smallest Lucas pseudoprime

Lucas pseudoprime

In number theory, the classes of Lucas pseudoprime and Fibonacci pseudoprime comprise sequences of composite integers that passes certain tests that all primes pass: in this case, criteria relative to some Lucas sequence.-Definition:...

----
706 = 2 × 353, nontotient, Smith number

Smith number

A Smith number is a composite number for which, in a given base , the sum of its digits is equal to the sum of the digits in its prime factorization. For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 =...

----
707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151)
----
708 = 2² × 3 × 59
----
709 prime number
----
710 = 2 × 5 × 71, sphenic number, nontotient
----
711 = 3² × 79, Harshad number. Also the phone number of Telecommunications Relay Service

Telecommunications Relay Service

Telecommunications Relay Service, also known as TRS, Relay Service, or IP-Relay, or Web-based relay services, is an operator service that allows people who are Deaf, Hard-of-Hearing, Speech-Disabled, or DeafBlind to place calls to standard telephone users via a keyboard or assistive device...

, 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, the number of the ambulance on the TV show Saved

Saved (TV series)

Saved is a medical drama television series, which was broadcast on Turner Network Television in 2006. The series was created by David Manson....

. It is the largest known number such that it and its 8^th power have no common digits.
----
713 = 23 × 31, main area code for Houston, TX, vault containing the philosopher's stone

Philosopher's stone

The philosopher's stone is a legendary alchemical substance said to be capable of turning base metals into gold or silver. It was also sometimes believed to be an elixir of life, useful for rejuvenation and possibly for achieving immortality. For many centuries, it was the most sought-after goal...

in Harry Potter and the Philosopher's Stone

Harry Potter and the Philosopher's Stone

Harry Potter and the Philosopher's Stone is the first novel in the Harry Potter series written by J. K. Rowling and featuring Harry Potter, a young wizard...

.
----
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 number of home runs Babe Ruth

Babe Ruth

George Herman Ruth, Jr. , best known as "Babe" Ruth and nicknamed "the Bambino" and "the Sultan of Swat", was an American Major League baseball player from 1914–1935...

scored in his career; see also 714 (disambiguation)

714 (disambiguation)

714 can refer to:* 714, the year AD 714* 714 BC* The number 714* Area code 714 was the telephone area code for most of Southern California beyond Los Angeles County during the 1960s and 1970s. It would later be reduced in size until it essentially only covered portions of Orange County....

. 714 is the smallest number that uses the same digits in bases 2 and 5.
----
715 = 5 × 11 × 13, sphenic number, pentatope number

Pentatope number

A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left.The first few numbers of this kind are :...

, Harshad number, member of Ruth-Aaron pair (either definition)
----
716 = 2² × 179
----
717 = 3 × 239
----
718 = 2 × 359
----
719 prime number, factorial prime

Factorial prime

A factorial prime is a prime number that is one less or one more than a factorial . The first few factorial primes are:n! − 1 is prime for :n! + 1 is prime for :...

(6! − 1), Sophie Germain prime

Sophie Germain prime

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number...

, safe prime

Safe prime

A safe prime is a prime number of the form 2p + 1, where p is also a prime. The first few safe primes are...

, sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part
----
720

720 (number)

Seven hundred twenty is the natural number following 719 and preceding 721.It is 6! , a composite number with thirty divisors, more than any number below, making it a highly composite number...

（seven hundred [and] twenty）= 2⁴ × 3² × 5.

6 factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...

, highly composite number
Highly composite number
A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....

, Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...

in every base from binary to decimal, highly totient number
Highly totient number
A highly totient number k is an integer that has more solutions to the equation φ = k, where φ is Euler's totient function, than any integer below it. The first few highly totient numbers are...

.
two round angle
Turn (geometry)
A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....

s (= 2 × 360
360 (number)
360 or three sixty is the natural number following 359 and preceding 361.-In mathematics:*Divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. *360 makes a highly composite number...

).
five gross
Gross (unit)
A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...

(= 500 duodecimal, 5 × 144
144 (number)
144 is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.-In mathematics:It is the twelfth Fibonacci number, and the largest one to also be a square, as the square of 12 , following 89 and preceding 233.144 is the smallest number with exactly 15 divisors.144 is...

).
241-gonal number
Polygonal number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...

.

----
721 = 7 × 103, sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), centered hexagonal number

Centered hexagonal number

A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice....

, smallest number that is the difference of two positive cubes in two ways
----
722 = 2 × 19², nontotient
----
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

Eight queens puzzle

The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal...

solutions for n = 10,
----
725 = 5² × 29
----
726 = 2 × 3 × 11², pentagonal pyramidal number

Pentagonal pyramidal number

A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base. The nth pentagonal pyramidal number is equal to the sum of the first n pentagonal numbers....

----
727 prime number, palindromic prime

Palindromic prime

A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns...

, Lucky prime
----
728 = 2³ × 7 × 13, nontotient, Smith number

Smith number

, cabtaxi number

Cabtaxi number

In mathematics, the n-th cabtaxi number, typically denoted Cabtaxi, is defined as the smallest positive integer that can be written as the sum of two positive or negative or 0 cubes in n ways...

----
729（seven hundred [and] twenty-nine） = 3⁶ = 27².

the square
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

of 27
27 (number)
27 is the natural number following 26 and preceding 28.- In mathematics :Twenty-seven is a perfect cube, being 33 = 3 × 3 × 3. 27 is also 23 . There are exactly 27 straight lines on a smooth cubic surface, which give a basis of the fundamental representation of the E6 Lie algebra...

, and the cube of 9, and as a consequence of these properties, a perfect totient number
Perfect totient number
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers;...

.
centered octagonal number
Centered octagonal number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers...

, 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
----
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

Permutable prime

A permutable prime is a prime number, which, in a given base, can have its digits' positions switched through any permutation and still spell a prime number. H. E...

, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
----
734 = 2 × 367, nontotient
----
735 = 3 × 5 × 7², Harshad number

Harshad number

, Zuckerman number, smallest number such that uses same digits as its distinct prime factors
----
736 = 2⁵ × 23, centered heptagonal number

Centered heptagonal number

A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers...

, nice Friedman number

Friedman number

A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators and sometimes exponentiation. For example, 347 is a Friedman number since 347 = 73 + 4...

since 736 = 7 + 3⁶, Harshad number

Harshad number

----
737 = 11 × 67, name of a Boeing plane
----
738 = 2 × 3² × 41, Harshad number
----
739 prime number, strictly non-palindromic number

Strictly non-palindromic number

A strictly non-palindromic number is an integer n that is not palindromic in any numeral system with a base b in the range 2 ≤ b ≤ n − 2...

, Lucky prime
----
740 = 2² × 5 × 37, nontotient
----
741 = 3 × 13 × 19, sphenic number, triangular number
----
742 = 2 × 7 × 53, sphenic number, decagonal number

Decagonal number

A decagonal number is a figurate number that represents a decagon. The n-th decagonal number is given by the formulaThe first few decagonal numbers are:...

. 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

J-invariant

In mathematics, Klein's j-invariant, regarded as a function of a complex variable τ, is a modular function defined on the upper half-plane of complex numbers.We haveThe modular discriminant \Delta is defined as \Delta=g_2^3-27g_3^2...

. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra E₈

E8 (mathematics)

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...

.
----
745 = 5 × 149
----
746 = 2 × 373, nontotient
746 = 1⁷ + 2⁴ + 36
----
747 = 3² × 83, model number of the Boeing 747

Boeing 747

The Boeing 747 is a wide-body commercial airliner and cargo transport, often referred to by its original nickname, Jumbo Jet, or Queen of the Skies. It is among the world's most recognizable aircraft, and was the first wide-body ever produced...

, perhaps the most famous Boeing aircraft
----
748 = 2² × 11 × 17, nontotient
----
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

Barry Bonds

Barry Lamar Bonds is an American former Major League Baseball outfielder. Bonds played from 1986 to 2007, for the Pittsburgh Pirates and San Francisco Giants. He is the son of former major league All-Star Bobby 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)
----
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

Centered triangular number

A centered triangular number is a centered figurate number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers...

----
761 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, centered square number

Centered square number

In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a...

----
762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number, see also Feynman point

Feynman point

The Feynman point is a sequence of six 9s that begins at the 762nd decimal place of the decimal representation of . It is named after physicist Richard Feynman, who once stated during a lecture he would like to memorize the digits of until that point, so he could recite them and quip "nine nine...

----
763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103)
----
764 = 2² × 191
----
765 = a Japanese

Japanese language

is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...

word-play for Namco

Namco

is a Japanese corporation best known as a former video game developer and publisher. Following a merger with Bandai in September 2005, the two companies' game production assets were spun off into Namco Bandai Games on March 31, 2006. Namco Ltd. was re-established to continue domestic operation of...

; 3² × 5 × 17
----
766 = 2 × 383, centered pentagonal number

Centered pentagonal number

A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers...

, nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)
----
767 = 13 × 59, Thabit number

Thabit number

In number theory, a Thabit number, Thâbit ibn Kurrah number, or 321 number is an integer of the form 3·2n−1 for a non-negative integer n...

(2⁸ × 3 − 1)
----
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
Fanzine
A fanzine is a nonprofessional and nonofficial publication produced by fans of a particular cultural phenomenon for the pleasure of others who share their interest...

called File 770
File 770
File 770 is a long running science fiction fanzine and newszine published by Mike Glyer; it is named after the now legendary party held in Room 770 at Nolacon, the 9th World Science Fiction Convention in New Orleans, Louisiana, that ran continuously for nearly two days and upstaged all the other...

----
771 = 3 × 257, sum of three consecutive primes (251 + 257 + 263)
----
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
----
776 = 2³ × 97
----
777 = 3 × 7 × 37, sphenic number, Harshad number, 3333 in senary

Senary

In mathematics, a senary numeral system is a base- numeral system.Senary may be considered useful in the study of prime numbers since all primes other than 2 and 3, when expressed in base-six, have 1 or 5 as the final digit...

(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

Highly cototient number

In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation...

----
780 = 2² × 3 × 5 × 13, sum of four consecutive primes

Prime number

in a quadruplet; sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number

Triangular number

, hexagonal number

Hexagonal number

A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...

, Harshad 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, Mertens function(781) = 0
----
782 = 2 × 17 × 23, sphenic number, nontotient, Harshad number, also, 782 gear used by U.S. Marines
----
783 = 3³ × 29
----
784 = 2⁴ × 7² = 28² =

, the sum of the cubes of the first seven integers.
----
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, Harshad number
----
793 = 13 × 61, Mertens function(793) = 0, star number

Star number

A star number is a centered figurate number that represents a centered hexagram, such as the one that Chinese checkers is played on.The nth star number is given by the formula 6n + 1...

----
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

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