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71 (number)
Encyclopedia
71 is the natural number
following 70
and preceding 72
.
degree of Conway's constant, a remarkable number arising in the study of look-and-say sequence
s.
It is the 20th prime number
. The next is 73
, with which it composes a twin prime
. It is also a permutable prime
with 17
. If we add up the primes less than 71 (2 through 67), we get 568, which is divisible by 71, 8 times. 71 is the largest (15th) supersingular prime
, which is also a Chen prime
. Also, 712 = 7! + 1, making it part of the last known pair of Brown numbers, as (71, 7). It is an Eisenstein prime
with no imaginary part and real part of the form 3n – 1. Since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9, 71 is a Pillai prime.
As 71 is the least prime factor of one more than the product of the first twenty-two terms of the Euclid–Mullin sequence, it is the twenty-third term. Also, 71 is the largest number which occurs as a prime factor of an order of a sporadic simple group.
71 is a centered heptagonal number
.
In astronomy
,
headquarters; it had 71 judges who judged cases where the criminal deserved the death penalty.
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 70
70 (number)
70 is the natural number following 69 and preceding 71.-In mathematics:Its factorization makes it a sphenic number. 70 is a Pell number and a generalized heptagonal number, one of only two numbers to be both. Also, it is the seventh pentagonal number and the fourth 13-gonal number, as well as the...
and preceding 72
72 (number)
72 is the natural number following 71 and preceding 73. It is half a gross or 6 dozen .-In mathematics:...
.
In mathematics
71 is the algebraicAlgebraic number
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental; almost all real numbers are transcendental...
degree of Conway's constant, a remarkable number arising in the study of look-and-say sequence
Look-and-say sequence
In mathematics, the look-and-say sequence is the sequence of integers beginning as follows:To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit...
s.
It is the 20th prime number
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...
. The next is 73
73 (number)
73 is the natural number following 72 and preceding 74. In English, it is the smallest integer with twelve letters in its spelled out name.- In mathematics :...
, with which it composes a twin prime
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
. It is also a 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...
with 17
17 (number)
17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70...
. If we add up the primes less than 71 (2 through 67), we get 568, which is divisible by 71, 8 times. 71 is the largest (15th) supersingular prime
Supersingular prime (moonshine theory)
In the mathematical branch of moonshine theory, a supersingular prime is a certain type of prime number.Namely, a supersingular prime is a prime divisor of the order of the Monster group M, the largest of the sporadic simple groups...
, which is also a 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....
. Also, 712 = 7! + 1, making it part of the last known pair of Brown numbers, as (71, 7). It is an 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 and real part of the form 3n – 1. Since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9, 71 is a Pillai prime.
As 71 is the least prime factor of one more than the product of the first twenty-two terms of the Euclid–Mullin sequence, it is the twenty-third term. Also, 71 is the largest number which occurs as a prime factor of an order of a sporadic simple group.
71 is a 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...
.
In science
- The atomic numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of lutetium, a lanthanide
In astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
,
- Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M71Messier 71Messier 71 is a globular cluster in the constellation Sagitta. It was discovered by Philippe Loys de Chéseaux in 1746 and included by Charles Messier in his catalog of comet-like objects in 1780...
, a magnitude 8.5 globular clusterGlobular clusterA globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
SagittaSagittaSagitta is a constellation. Its name is Latin for "arrow", and it should not be confused with the larger constellation Sagittarius, the archer. Although ancient, it is insignificant, for it has no star brighter than the 4th magnitude and is the third smallest of all constellations...
- The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 71, a magnitude 13.2 peculiarPeculiar galaxyA peculiar galaxy is a galaxy which is unusual in its size, shape, or composition. Peculiar galaxies come about as a result of interactions between galaxies, and they may contain atypical amounts of dust or gas, may have higher or lower surface brightness than a typical galaxy, or may have...
spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellation AndromedaAndromeda (constellation)Andromeda is a constellation in the northern sky. It is named after Andromeda, the princess in the Greek legend of Perseus who was chained to a rock to be eaten by the sea monster Cetus...
- The Saros number of the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
series which began on -702 October 8 and ended on 777777Year 777 was a common year starting on Wednesday of the Julian calendar. The denomination 777 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.- Europe :* Charlemagne defeats the Saxons; their...
March 14. The duration of Saros series 71 was 1478.4 years, and it contained 83 solar eclipses.
- The Saros number of the lunar eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
series which began on -472473 BCYear 473 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Year of the Consulship of Mamercus and Iullus...
June 4 and ended on 808808Year 808 was a leap year starting on Saturday of the Julian calendar.- Europe :* King Eardwulf is driven out of North-East England and succeeded by Alfwold II, but Eardwulf is restored following Alfwold’s death.- Births :* Gottschalk, German theologian* Walafrid Strabo, Swabian monk and...
July 11. The duration of Saros series 71 was 1280.1 years, and it contained 72 lunar eclipses.
In Judaism
In ancient Israel there was a SanhedrinSanhedrin
The Sanhedrin was an assembly of twenty-three judges appointed in every city in the Biblical Land of Israel.The Great Sanhedrin was the supreme court of ancient Israel made of 71 members...
headquarters; it had 71 judges who judged cases where the criminal deserved the death penalty.
In other fields
Seventy-one is also:- The number of different characters that can be used with a standard English KeyboardKeyboard (computing)In computing, a keyboard is a typewriter-style keyboard, which uses an arrangement of buttons or keys, to act as mechanical levers or electronic switches...
, excluding uppercase letters. - The designation of USAUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
Interstate 71Interstate 71Interstate 71 is an Interstate Highway in the Great Lakes/Midwestern and Southeastern region of the United States. Its southern terminus is at an interchange with Interstate 64 and Interstate 65 in Louisville, Kentucky. Its northern terminus is at an interchange with Interstate 90 in Cleveland,...
, which runs from KentuckyKentuckyThe Commonwealth of Kentucky is a state located in the East Central United States of America. As classified by the United States Census Bureau, Kentucky is a Southern state, more specifically in the East South Central region. Kentucky is one of four U.S. states constituted as a commonwealth...
to OhioOhioOhio is a Midwestern state in the United States. The 34th largest state by area in the U.S.,it is the 7th‑most populous with over 11.5 million residents, containing several major American cities and seven metropolitan areas with populations of 500,000 or more.The state's capital is Columbus...
. - The registry of the U.S. Navy's nuclear aircraft carrier USS Theodore Roosevelt (CVN-71)USS Theodore Roosevelt (CVN-71)USS Theodore Roosevelt is the fourth Nimitz-class supercarrier. Her radio call sign is Rough Rider, the name of President Theodore Roosevelt's volunteer cavalry unit during the Spanish-American War...
, named after U.S. President Theodore RooseveltTheodore RooseveltTheodore "Teddy" Roosevelt was the 26th President of the United States . He is noted for his exuberant personality, range of interests and achievements, and his leadership of the Progressive Movement, as well as his "cowboy" persona and robust masculinity...
. - The number of the French department Saône-et-LoireSaône-et-LoireSaône-et-Loire is a French department, named after the Saône and the Loire rivers between which it lies.-History:When it was formed during the French Revolution, as of March 4, 1790 in fulfillment of the law of December 22, 1789, the new department combined parts of the provinces of southern...
. - The year AD 7171Year 71 was a common year starting on Tuesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Augustus and Nerva...
, 71 BC71 BCYear 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 1971. - In the Mexican television sitcom, El Chavo del Ocho, Doña Clotilde lives in the apartment number 71, being therefore known as "Bruja del 71" (Witch of 71).
- Lockheed SR-71 BlackbirdSR-71 BlackbirdThe Lockheed SR-71 "Blackbird" was an advanced, long-range, Mach 3+ strategic reconnaissance aircraft. It was developed as a black project from the Lockheed A-12 reconnaissance aircraft in the 1960s by the Lockheed Skunk Works. Clarence "Kelly" Johnson was responsible for many of the...
long-range, Mach 3 strategic reconnaissance aircraft - "71 Fragments of a Chronology of Chance71 Fragments of a Chronology of Chance71 Fragments of a Chronology of Chance is a 1994 Austrian drama film directed by Michael Haneke. It has a fragmented storyline as the title suggests, and chronicles several unrelated stories in parallel. Separate narrative lines intersect in an incident at the last of the film: a mass killing at...
," a film by Michael HanekeMichael HanekeMichael Haneke is a German born Austrian filmmaker and writer best known for his bleak and disturbing style. His films often document problems and failures in modern society. Haneke has worked in television‚ theatre and cinema. He is also known for raising social issues in his work... - 71: Into the Fire, South Korean film about the Korean WarKorean WarThe Korean War was a conventional war between South Korea, supported by the United Nations, and North Korea, supported by the People's Republic of China , with military material aid from the Soviet Union...
- The form number for the United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
Office of Personnel Management for requesting a leave of absence. - Municipal Okrug #71, name of Volkovskoye Municipal Okrug of Frunzensky District of Saint PetersburgSaint PetersburgSaint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
, Russia, before 2008 - The Irish Rail 071 Class diesel locomotive.
- In the Jason BourneJason BourneJason Charles Bourne is a fictional character and the main protagonist in the novels of Robert Ludlum and subsequent film adaptations. He first appeared in the novel The Bourne Identity...
novels by American author Robert LudlumRobert LudlumRobert Ludlum was an American author of 23 thriller novels. The number of his books in print is estimated between 290–500 million copies. They have been published in 33 languages and 40 countries. Ludlum also published books under the pseudonyms Jonathan Ryder and Michael Shepherd.-Life and...
the department within the CIA which made Bourne and the other super agents is called Treadstone Seventy-One. - SR-71 is an AmericanUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
Alternative RockAlternative rockAlternative rock is a genre of rock music and a term used to describe a diverse musical movement that emerged from the independent music underground of the 1980s and became widely popular by the 1990s...
band.