71 (seventy-one) 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 n ...

following 70 and preceding 72. __TOC__

In mathematics

71 is: *the 20th

prime number 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 ...

. The next is 73, with which it composes a

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

. *a

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 th ...

and

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 ...

with 17. *is the largest number which occurs as a prime factor of an order of a

sporadic simple group In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...

. *the sum of three consecutive primes: 19, 23 and 29. *a

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 ...

. *an

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 and real part of the form 3''n'' – 1. *a

Pillai prime In number theory, a Pillai prime is a prime number ''p'' for which there is an integer ''n'' > 0 such that the factorial of ''n'' is one less than a multiple of the prime, but the prime is not one more than a multiple of ''n''. To put it algebraical ...

, since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9. *the largest (15th) supersingular prime, which is also a

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 Jin ...

. *part of the last known pair (71, 7) of

Brown number Brocard's problem is a problem in mathematics that asks to find integer values of n and m for which n!+1 = m^2, where n! is the factorial. It was posed by Henri Brocard in a pair of articles in 1876 and 1885, and independently in 1913 by Srinivasa ...

s, since 71² = 7! + 1. *the twenty-third term of the

Euclid–Mullin sequence The Euclid–Mullin sequence is an infinite sequence of distinct prime numbers, in which each element is the least prime factor of one plus the product of all earlier elements. They are named after the ancient Greek mathematician Euclid, because the ...

, as it is the least prime factor of one more than the product of the first twenty-two terms. *the smallest positive integer ''d'' such that the imaginary

quadratic field In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 an ...

Q() has class number = 7. *the algebraic degree of

Conway's constant In mathematics, the look-and-say sequence is the integer sequence, sequence of integers beginning as follows: : 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... . To generate a member of the sequence from the previous m ...

, a remarkable number arising in the study of

look-and-say sequence In mathematics, the look-and-say sequence is the integer sequence, sequence of integers beginning as follows: : 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... . To generate a member of the sequence from the previous m ...

s. *the sum of primes less than 71 (2 through 67) is 568, which is divisible by 71. *71 is the only number between 1 and 100 that is one less or one more than divisible by all numbers from 2 to 10 (70: 2, 5, 7, 10) (72: 2, 3, 4, 6, 8, 9). *71 is an index of a prime Lucas number.

In science

*The

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...

lutetium Lutetium is a chemical element with the symbol Lu and atomic number 71. It is a silvery white metal, which resists corrosion in dry air, but not in moist air. Lutetium is the last element in the lanthanide series, and it is traditionally counted am ...

, a lanthanide

In astronomy

Messier object The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters''). Because Messier was only int ...

M71, a

magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...

8.5

globular cluster A globular cluster is a spheroidal conglomeration of stars. Globular clusters are bound together by gravity, with a higher concentration of stars towards their centers. They can contain anywhere from tens of thousands to many millions of membe ...

in the

constellation A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the e ...

Sagitta Sagitta is a dim but distinctive constellation in the northern sky. Its name is Latin for 'arrow', not to be confused with the significantly larger constellation Sagittarius 'the archer'. It was included among the 48 constellations listed by t ...

* The

New General Catalogue The ''New General Catalogue of Nebulae and Clusters of Stars'' (abbreviated NGC) is an astronomical catalogue of deep-sky objects compiled by John Louis Emil Dreyer in 1888. The NGC contains 7,840 objects, including galaxies, star clusters and ...

br>object
NGC 71, a magnitude 13.2 peculiar

spiral galaxy Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''Andromeda

In other fields

Seventy-one is also: * The number of different characters that can be used with a standard English

keyboard Keyboard may refer to: Text input * Keyboard, part of a typewriter * Computer keyboard ** Keyboard layout, the software control of computer keyboards and their mapping ** Keyboard technology, computer keyboard hardware and firmware Music * Musi ...

, excluding uppercase letters * The registry of the U.S. Navy's nuclear aircraft carrier USS ''Theodore Roosevelt'' (CVN-71), named after U.S. President

Theodore Roosevelt Theodore Roosevelt Jr. ( ; October 27, 1858 – January 6, 1919), often referred to as Teddy or by his initials, T. R., was an American politician, statesman, soldier, conservationist, naturalist, historian, and writer who served as the 26t ...

* The number of the French department

Saône-et-Loire Saône-et-Loire (; Arpitan: ''Sona-et-Lêre'') is a department in the Bourgogne-Franche-Comté region in France. It is named after the rivers Saône and Loire, between which it lies, in the country's central-eastern part. Saône-et-Loire is Bo ...

* The year

AD 71 AD 71 ( LXXI) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Vespasian and Nerva (or, less frequently, year 824 '' Ab urbe condita' ...

71 BC __NOTOC__ Year 71 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Lentulus and Orestes (or, less frequently, year 683 ''Ab urbe condita''). The denomination 71 BC for this year has been u ...

, or

1971 * The year 1971 had three partial solar eclipses ( February 25, July 22 and August 20) and two total lunar eclipses (February 10, and August 6). The world population increased by 2.1% this year, the highest increase in history. Events Ja ...

* In the Mexican television sitcom, ''

El Chavo del Ocho ''El Chavo'' (English: ''The Kid''); — also known as ''El Chavo del Ocho'' (English: ''The Kid from number Eight'') during its earliest episodes —, is a Mexico, Mexican television sitcom created by Roberto Gómez Bolaños, produced by Tele ...

'', Doña Clotilde lives in the apartment number 71, being therefore known as "La Bruja del 71" (

Spanish Spanish might refer to: * Items from or related to Spain: **Spaniards are a nation and ethnic group indigenous to Spain **Spanish language, spoken in Spain and many Latin American countries **Spanish cuisine Other places * Spanish, Ontario, Cana ...

: "The Witch from Number 71") * Lockheed

SR-71 Blackbird The Lockheed SR-71 "Blackbird" is a long-range, high-altitude, Mach 3+ strategic reconnaissance aircraft developed and manufactured by the American aerospace company Lockheed Corporation. It was operated by the United States Air Force ...

long-range, Mach 3 strategic reconnaissance aircraft * '' 71 Fragments of a Chronology of Chance'', a film by

Michael Haneke Michael Haneke (; born 23 March 1942) is an Austrian film director and screenwriter. His work often examines social issues and depicts the feelings of estrangement experienced by individuals in modern society. Haneke has made films in French, G ...

* '' 71: Into the Fire'', South Korean film about the

Korean War , date = {{Ubl, 25 June 1950 – 27 July 1953 (''de facto'')({{Age in years, months, weeks and days, month1=6, day1=25, year1=1950, month2=7, day2=27, year2=1953), 25 June 1950 – present (''de jure'')({{Age in years, months, weeks a ...

* The form number for the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

Office of Personnel Management for requesting a leave of absence * The

Irish Rail Irish may refer to: Common meanings * Someone or something of, from, or related to: ** Ireland, an island situated off the north-western coast of continental Europe ***Éire, Irish language name for the isle ** Northern Ireland, a constituent unit ...

071 Class diesel locomotive * In the

Jason Bourne Jason Bourne () is the title character and the protagonist in a series of novels and subsequent film adaptations. The character was created by novelist Robert Ludlum. He first appeared in the novel '' The Bourne Identity'' (1980), which was a ...

novels by American author

Robert Ludlum Robert Ludlum (May 25, 1927 – March 12, 2001) was an American author of 27 thriller novels, best known as the creator of Jason Bourne from the original '' The Bourne Trilogy'' series. The number of copies of his books in print is estimated b ...

the department within the

CIA The Central Intelligence Agency (CIA ), known informally as the Agency and historically as the Company, is a civilian intelligence agency, foreign intelligence service of the federal government of the United States, officially tasked with gat ...

which made Bourne and the other super agents is called Treadstone Seventy-One. *

SR-71 The Lockheed SR-71 "Blackbird" is a Range (aeronautics), long-range, high-altitude, Mach number, Mach 3+ military strategy, strategic reconnaissance aircraft developed and manufactured by the American aerospace company Lockheed Corporati ...

, an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

alternative rock Alternative rock, or alt-rock, is a category of rock music that emerged from the independent music underground of the 1970s and became widely popular in the 1990s. "Alternative" refers to the genre's distinction from Popular culture, mainstre ...

band * The number of the laps of the

Austrian Grand Prix The Austrian Grand Prix (german: Großer Preis von Österreich) is a Fédération Internationale de l'Automobile sanctioned motor racing event that was held in , –, –, and then returned to the Formula One calendar in . History The A ...

Mexican Grand Prix The Mexican Grand Prix ( es, Gran Premio de México), currently held under the name Mexico City Grand Prix ( es, Gran Premio de la Ciudad de México), is a motor racing event held at the Autódromo Hermanos Rodríguez in Mexico City. It first a ...

, and

Brazilian Grand Prix The Brazilian Grand Prix ( pt, Grande Prêmio do Brasil), currently held under the name São Paulo Grand Prix ( pt, Grande Prêmio de São Paulo), is a Formula One championship race which is currently held at the Autódromo José Carlos Pace ...

References

{{Integers, zero Integers