700 (seven hundred) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...

following

699 __NOTOC__ Year 699 ( DCXCIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. The denomination 699 for this year has been used since the early medieval period, when the Anno Domini calendar e ...

and preceding 701. It is the sum of four consecutive

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317) and a Harshad number.

Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 are used as model numbers for Boeing Commercial Airplanes, and the only one not officially used by Boeing, 797, is commonly speculated to be the number of the next new Boeing commercial airplane.

700s

* 701 = prime number, sum of three consecutive primes (229 + 233 + 239),

Chen prime A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingru ...

Eisenstein prime In mathematics, an Eisenstein prime is an Eisenstein integer : z = a + b\,\omega, \quad \text \quad \omega = e^, that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...

with no imaginary part * 702 = 2 × 3³ × 13,

pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...

, Harshad number * 703 = 19 × 37,

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...

hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...

, smallest number requiring 73 fifth powers for Waring representation,

Kaprekar number In mathematics, a natural number in a given number base is a p-Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p digits, that add up to the original number. The numbers are n ...

, area code for

Northern Virginia Northern Virginia, locally referred to as NOVA or NoVA, comprises several counties and independent cities in the Commonwealth of Virginia in the United States. It is a widespread region radiating westward and southward from Washington, D.C. Wit ...

along with 571, a number commonly found in the formula for body mass index * 704 = 2⁶ × 11, Harshad number, lazy caterer number , area code for the Charlotte, NC area. * 705 = 3 × 5 × 47,

sphenic number In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definit ...

, smallest Bruckman-Lucas pseudoprime * 706 = 2 × 353, nontotient,

Smith number In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-f ...

* 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). Model number for the Boeing 707 * 708 = 2² × 3 × 59, number of partitions of 28 that do not contain 1 as a part * 709 = prime number;

happy number In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...

. 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 proceeding 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 of

Telecommunications Relay Service A telecommunications relay service, also known as TRS, relay service, or IP-relay, or Web-based relay service, is an operator service that allows people who are deaf, hard of hearing, deafblind, or have a speech disorder to place calls to st ...

, 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. 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 In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/tal ...

, main area code for

Houston, TX Houston (; ) is the most populous city in Texas, the most populous city in the Southern United States, the fourth-most populous city in the United States, and the sixth-most populous city in North America, with a population of 2,304,580 ...

. In

Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in t ...

there is 713 letters on a

Mezuzah A ''mezuzah'' ( he, מְזוּזָה "doorpost"; plural: ''mezuzot'') is a piece of parchment, known as a '' klaf'', contained in a decorative case and inscribed with specific Hebrew verses from the Torah ( and ). These verses consist of the ...

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, member of

Ruth–Aaron pair In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: :714 = 2 × 3 × 7 × 17, :715 = 5 × 11 × 13, and : 2 + 3 + 7 + 17 = 5 + 11 + 13 ...

(either definition); area code for

Orange County, California Orange County is located in the Los Angeles metropolitan area in Southern California. As of the 2020 census, the population was 3,186,989, making it the third-most-populous county in California, the sixth-most-populous in the United States, a ...

. ** 714 is the number of career

home run In baseball, a home run (abbreviated HR) is scored when the ball is hit in such a way that the batter is able to circle the bases and reach home plate safely in one play without any errors being committed by the defensive team. A home run i ...

s hit by

Babe Ruth George Herman "Babe" Ruth Jr. (February 6, 1895 – August 16, 1948) was an American professional baseball player whose career in Major League Baseball (MLB) spanned 22 seasons, from 1914 through 1935. Nicknamed "the Bambino" and "the Su ...

, a record that stood from his last home run on May 25, 1935, until being broken by

Hank Aaron Henry Louis Aaron (February 5, 1934 – January 22, 2021), nicknamed "Hammer" or "Hammerin' Hank", was an American professional baseball right fielder who played 23 seasons in Major League Baseball (MLB), from 1954 through 1976. One of the gre ...

on April 8, 1974. ** ''Flight 714 to Sidney'' is a

Tintin Tintin or Tin Tin may refer to: ''The Adventures of Tintin'' * ''The Adventures of Tintin'', a comics series by Belgian cartoonist Hergé ** Tintin (character), a fictional character in the series ** ''The Adventures of Tintin'' (film), 2011, ...

graphic novel. ** 714 is the badge number of Sergeant

Joe Friday Joe Friday is a fictional character created and portrayed by Jack Webb as the lead for his series '' Dragnet''. Friday is a detective in the Los Angeles Police Department. The character first appeared on June 3, 1949 in the premiere of the NBC ...

. * 715 = 5 × 11 × 13, sphenic number, pentagonal 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 , either from left to right or from right to left. The first few numbers of this kind are: : 1, 5, 15, 35, 70, 126, 210, 330, 4 ...

( binomial coefficient

\tbinom 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 for

Buffalo, NY Buffalo is the second-largest city in the U.S. state of New York (behind only New York City) and the seat of Erie County. It is at the eastern end of Lake Erie, at the head of the Niagara River, and is across the Canadian border from South ...

* 717 = 3 × 239, palindromic number, model number for the

Boeing 717 The Boeing 717 is an American five-abreast single-aisle airliner produced by Boeing Commercial Airplanes. The twin-engine airliner was developed for the 100-seat market and originally marketed by McDonnell Douglas as the MD-95. It was a shor ...

* 718 = 2 × 359, area code for Brooklyn, NY and

Bronx, NY The Bronx () is a borough of New York City, coextensive with Bronx County, in the state of New York. It is south of Westchester County; north and east of the New York City borough of Manhattan, across the Harlem River; and north of the New Yor ...

* 719 = prime number,

factorial prime A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! +&n ...

(6! − 1),

Sophie Germain prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

safe prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

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

720s

* 720 (''seven hundred ndtwenty'')= 2⁴ × 3² × 5. ** 6 factorial,

highly composite number __FORCETOC__ A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...

, 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, 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.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 * 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, the number of ''n''-queens problem solutions for ''n'' = 10, * 725 = 5² × 29, side length of an almost-equilateral Heronian triangle * 726 = 2 × 3 × 11²,

pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...

* 727 = prime number, palindromic prime,

lucky prime In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...

, ** model number for the

Boeing 727 The Boeing 727 is an American narrow-body airliner that was developed and produced by Boeing Commercial Airplanes. After the heavy 707 quad-jet was introduced in 1958, Boeing addressed the demand for shorter flight lengths from smaller airpo ...

* 728 = 2³ × 7 × 13, nontotient,

cabtaxi number In mathematics, the ''n''-th cabtaxi number, typically denoted Cabtaxi(''n''), 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. Such numbers exist for all ''n'', whi ...

, 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 * 729 = 27² = 9³ = 3⁶. ** the

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...

of 27, and the cube of 9, the sixth

power of three In mathematics, a power of three is a number of the form where is an integer – that is, the result of exponentiation with number three as the base and integer as the exponent. Applications The powers of three give the place values in ...

, and as a consequence of these properties, a perfect totient 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.. The centered octagonal numbers are the same as the od ...

, 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 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 that are closed under union and intersection * 733 = prime number,

emirp An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as e ...

, balanced prime,

permutable prime A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to study the ...

, sum of five consecutive primes (137 + 139 + 149 + 151 + 157) * 734 = 2 × 367, nontotient, number of traceable graphs on 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 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. The centered heptagonal number for ''n'' is given by ...

, nice

Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, pa ...

since 736 = 7 + 3⁶, Harshad number * 737 = 11 × 67, palindromic number,

, model number of the

Boeing 737 The Boeing 737 is a narrow-body aircraft produced by Boeing at its Boeing Renton Factory, Renton Factory in Washington (state), Washington. Developed to supplement the Boeing 727 on short and thin routes, the twinjet retains the Boeing 707, 7 ...

jet airliner. * 738 = 2 × 3² × 41, Harshad number, designation for a

Boeing 737-800 The Boeing 737 Next Generation, commonly abbreviated as 737NG, or 737 Next Gen, is a narrow-body aircraft powered by two jet engines and produced by Boeing Commercial Airplanes. Launched in 1993 as the third generation derivative of the Boein ...

jet airliner. * 739 = prime number, strictly non-palindromic number, lucky prime,

, 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 A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal number ...

, icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number . Number of partitions of 30 into divisors of 30. * 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 In mathematics, Felix Klein's -invariant or function, regarded as a function of a complex variable , is a modular function of weight zero for defined on the upper half-plane of complex numbers. It is the unique such function which is hol ...

. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra ''E''₈. * 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 =

\lfloor  \rfloor

, palindromic number, model number of the Boeing 747 jet airliner * 748 = 2² × 11 × 17, nontotient,

, primitive abundant number * 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257),

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,

* 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 th
complete bipartite graph K_n,n
In 1976, Major League Baseball player

ended his career with a Major League record 755 home runs (record now held by Barry 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),

, model number for the

Boeing 757 The Boeing 757 is an American narrow-body airliner designed and built by Boeing Commercial Airplanes. The then-named 7N7, a twinjet successor for the 727 (a trijet), received its first orders in August 1978. The prototype completed its mai ...

** "The 757" is a local nickname for the Hampton Roads area in the U.S. state of

Virginia Virginia, officially the Commonwealth of Virginia, is a state in the Mid-Atlantic and Southeastern regions of the United States, between the Atlantic Coast and the Appalachian Mountains. The geography and climate of the Commonwealth ar ...

, derived from the telephone area code that 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 numbers for q=3

760s

* 760 = 2³ × 5 × 19,

centered triangular number A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers. The followin ...

, number of fixed heptominoes. * 761 = prime number,

, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part,

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 cen ...

* 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 also

Six nines in pi A sequence of six consecutive nines occurs in the decimal representation of the number pi (), starting at the 762nd decimal place.. It has become famous because of the mathematical coincidence and because of the idea that one could memorize the d ...

* 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 A telephone number is a sequence of digits assigned to a landline telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices f ...

* 765 = 3² × 5 × 17, octagonal pyramidal number ** a

Japanese Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspor ...

word-play for

Namco was a Japanese multinational video game and entertainment company, headquartered in Ōta, Tokyo. It held several international branches, including Namco America in Santa Clara, California, Namco Europe in London, Namco Taiwan in Kaohsiung, ...

; * 766 = 2 × 383,

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. The centered pentagonal number for ''n'' is given by th ...

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

Thabit number In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 \cdot 2^n - 1 for a non-negative integer ''n''. The first few Thabit numbers are: : 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 61 ...

(2⁸ × 3 − 1), palindromic number, model number for the Boeing 767 * 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 A Proth number is a natural number ''N'' of the form N = k \times 2^n +1 where ''k'' and ''n'' are positive integers, ''k'' is odd and 2^n > k. A Proth prime is a Proth number that is prime. They are named after the French mathematician François ...

770s

* 770 = 2 × 5 × 7 × 11, nontotient, Harshad number **

\sum_^ 770^

is prime ** Famous room party in New Orleans hotel room 770, giving the name to a well known

science fiction fanzine A science-fiction fanzine is an amateur or semi-professional magazine published by members of science-fiction fandom, from the 1930s to the present day. They were one of the earliest forms of fanzine, within one of which the term "''fanzine''" wa ...

called

File 770 ''File 770'' is a long-running science fiction fanzine, newszine, and blog site published/administered by Mike Glyer. It has been published every year since 1978, and has won a record eight Hugo Awards for Best Fanzine, with the first win in ...

** Holds special importance in the

Chabad Chabad, also known as Lubavitch, Habad and Chabad-Lubavitch (), is an Orthodox Jewish Hasidic dynasty. Chabad is one of the world's best-known Hasidic movements, particularly for its outreach activities. It is one of the largest Hasidic grou ...

-Lubavitch

Hasidic movement Hasidism, sometimes spelled Chassidism, and also known as Hasidic Judaism (Ashkenazi Hebrew: חסידות ''Ḥăsīdus'', ; originally, "piety"), is a Jewish religious group that arose as a spiritual revival movement in the territory of conte ...

. * 771 = 3 × 257, sum of three consecutive primes in

arithmetic progression An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common differ ...

(251 + 257 + 263). Since 771 is the product of the distinct

Fermat prime In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 429496 ...

s 3 and 257, a

regular polygon In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence ...

with 771 sides can be constructed using compass and straightedge, and

\cos\left(\frac\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 * 774 = 2 × 3² × 43, nontotient, totient sum for first 50 integers, Harshad number * 775 = 5² × 31, member of the

Mian–Chowla sequence In mathematics, the Mian–Chowla sequence is an integer sequence defined recursively in the following way. The sequence starts with :a_1 = 1. Then for n>1, a_n is the smallest integer such that every pairwise sum :a_i + a_j is distinct, for ...

* 776 = 2³ × 97, number of compositions of 6 whose parts equal to q can be of q² kinds * 777 = 3 × 7 × 37, sphenic number, Harshad number, palindromic number, model number of the

Boeing 777 The Boeing 777, commonly referred to as the Triple Seven, is an American long-range wide-body airliner developed and manufactured by Boeing Commercial Airplanes. It is the world's largest twinjet. The 777 was designed to bridge the gap betw ...

jet airliner, 3333 in

senary A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two co ...

(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 consecutive

primes A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

in a

quadruplet A multiple birth is the culmination of one multiple pregnancy, wherein the mother gives birth to two or more babies. A term most applicable to vertebrate species, multiple births occur in most kinds of mammals, with varying frequencies. Such bi ...

(191, 193, 197, and 199); sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101),

, 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, sum of powers of 5/repdigit in base 5 (11111),

Mertens function In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...

(781) = 0, lazy caterer number * 782 = 2 × 17 × 23, sphenic number, nontotient,

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...

, Harshad number, also, 782 gear used by U.S. Marines * 783 = 3³ × 29,

heptagonal number A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula :H_n=\frac. The first few heptagonal numbers are: : 0, 1, 7, 18, 34, 55, 81, 112 ...

* 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,

* 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors * 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,

, palindromic prime, model number for the

Boeing 787 Dreamliner The Boeing 787 Dreamliner is an American wide-body jet airliner developed and manufactured by Boeing Commercial Airplanes. After dropping its unconventional Sonic Cruiser project, Boeing announced the conventional 7E7 on January 29, 2003, ...

* 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),

790s

* 790 = 2 × 5 × 79, sphenic number, nontotient * 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 partitions of 21, binomial coefficient

\tbinom 5

, Harshad number, sum of the nontriangular numbers between successive triangular numbers * 793 = 13 × 61, Mertens function(793) = 0,

star number A star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n'' − 1) + 1. The ...

* 794 = 2 × 397 = 1⁶ + 2⁶ + 3⁶, nontotient * 795 = 3 × 5 × 53, 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, speculated model number for the Boeing New Midsize Airplane * 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

References

{{Authority control Integers