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 In mathematics, 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 in base are also known as -harshad (or -Niven) numbers. 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 Boeing Commercial Airplanes (BCA) is a division of The Boeing Company. It designs, assembles, markets, and sells jet airliners and business jets (Boeing Business Jets), and also provides product-related maintenance and training to customers ...

, 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,

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,

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, 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 A telephone numbering plan is a type of numbering scheme used in telecommunication to assign telephone numbers to subscriber telephones or other telephony endpoints. Telephone numbers are the addresses of participants in a telephone network, r ...

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 __NOTOC__ Year 571 ( DLXXI) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. The denomination 571 for this year has been used since the early medieval period, when the Anno Domini calendar er ...

, a number commonly found in the formula for

body mass index Body mass index (BMI) is a value derived from the mass ( weight) and height of a person. The BMI is defined as the body mass divided by the square of the body height, and is expressed in units of kg/m2, resulting from mass in kilograms and ...

* 704 = 2⁶ × 11,

, lazy caterer number , area code for the

Charlotte, NC Charlotte ( ) is the most populous city in the U.S. state of North Carolina. Located in the Piedmont region, it is the county seat of Mecklenburg County. The population was 874,579 at the 2020 census, making Charlotte the 16th-most populo ...

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 A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palin ...

, 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 The Boeing 707 is an American, long-range, narrow-body airliner, the first jetliner developed and produced by Boeing Commercial Airplanes. Developed from the Boeing 367-80 prototype first flown in 1954, the initial first flew on December 2 ...

* 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 th ...

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 (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, ...

. ** 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 (

binomial coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...

\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,

, model number for the Boeing 717 * 718 = 2 × 359, area code for

Brooklyn, NY Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, beh ...

and Bronx, NY * 719 = prime number, factorial prime (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 In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \ ...

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 ...

in every base from binary to decimal,

highly totient number A highly totient number k is an integer that has more solutions to the equation \phi(x) = k, where \phi is Euler's totient function, than any integer below it. The first few highly totient numbers are 1, 2, 4, 8, 12, 24, 48, 72, 144, 240, 4 ...

. ** two round angles (= 2 ×

360 360 may refer to: * 360 (number) * 360 AD, a year * 360 BC, a year * 360 degrees, a circle Businesses and organizations * 360 Architecture, an American architectural design firm * Ngong Ping 360, a tourism project in Lantau Island, Hong Kong ...

). ** five gross (= 500 duodecimal, 5 ×

144 144 may refer to: * 144 (number), the natural number following 143 and preceding 145 * AD 144, a year of the Julian calendar, in the second century AD * 144 BC, a year of the pre-Julian Roman calendar * ''144'' (film), a 2015 Indian comedy * ''14 ...

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

centered hexagonal number In mathematics and combinatorics, 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. The following ...

, 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 In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the Radix, base of the number system and its notational conventions, while primality is independent of ...

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 air ...

* 728 = 2³ × 7 × 13, nontotient,

, 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 * 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 In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only ...

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 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, ...

. ** centered octagonal number, 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,

balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p_n, where is it ...

, permutable prime, 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,

, 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,

* 737 = 11 × 67,

, model number of the

Boeing 737 The Boeing 737 is a narrow-body aircraft produced by Boeing at its Renton Factory in Washington. Developed to supplement the Boeing 727 on short and thin routes, the twinjet retains the 707 fuselage width and six abreast seating with two u ...

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 An icosahedral number is a figurate number that represents an icosahedron. The ''n''th icosahedral number is given by the formula : The first such numbers are 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, … . History The fi ...

. 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

, model number of the

Boeing 747 The Boeing 747 is a large, long-range wide-body airliner designed and manufactured by Boeing Commercial Airplanes in the United States between 1968 and 2022. After introducing the 707 in October 1958, Pan Am wanted a jet times its size, ...

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 Barry Lamar Bonds (born July 24, 1964) is an American former professional baseball left fielder who played 22 seasons in Major League Baseball (MLB). Bonds was a member of the Pittsburgh Pirates from 1986 to 1992 and the San Francisco Gian ...

). * 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 maid ...

** "The 757" is a local nickname for the

Hampton Roads Hampton Roads is the name of both a body of water in the United States that serves as a wide channel for the James, Nansemond and Elizabeth rivers between Old Point Comfort and Sewell's Point where the Chesapeake Bay flows into the Atlantic ...

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 are ...

, 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, 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 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 * 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 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 Kaohsiun ...

; * 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 (2⁸ × 3 − 1),

, model number for the

Boeing 767 The Boeing 767 is an American wide-body aircraft developed and manufactured by Boeing Commercial Airplanes. The aircraft was launched as the 7X7 program on July 14, 1978, the prototype first flew on September 26, 1981, and it was certified o ...

* 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 group ...

-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 In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...

, 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,

, 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 c ...

(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 In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient f ...

780s

* 780 = 2² × 3 × 5 × 13, sum of four consecutive primes 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 bir ...

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

, hexagonal 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 * 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 aircraft, wide-body jet airliner developed and manufactured by Boeing Commercial Airplanes. After dropping its unconventional Boeing Sonic Cruiser, Sonic Cruiser project, Boeing announced th ...

* 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 A centered tetrahedral number is a centered figurate number that represents a tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular ...

, 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 Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of ...

of 21,

\tbinom 5

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

* 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 The New Midsize Airplane (NMA), or New Midsize Aircraft, (culturally referred to as the Boeing 797) is a concept airliner proposed by Boeing to fill the middle of the market segment. In 2015, Boeing determined the market was large enough to lau ...

* 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