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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.
- The New General Catalogue object NGC 71, a magnitude 13.2 peculiar spiral galaxy in the constellation Andromeda
- The Saros number of the solar eclipse series which began on -702 October 8 and ended on 777 March 14. The duration of Saros series 71 was 1478.4 years, and it contained 83 solar eclipses.
- The Saros number of the lunar eclipse series which began on -472 June 4 and ended on 808 July 11. The duration of Saros series 71 was 1280.1 years, and it contained 72 lunar eclipses.
- NASCAR TRG Motorsports #71 driven by Bobby Labonte
In other fields
Seventy-one is also:
- The number of different characters that can be used with a standard English Keyboard, excluding uppercase letters.
- The designation of USA Interstate 71, which runs from Kentucky to Ohio.
- The registry of the U.S. Navy's nuclear aircraft carrier USS Theodore Roosevelt (CVN-71), named after U.S. President Theodore Roosevelt.
- The number of the French department Saône-et-Loire.
- The year AD 71, 71 BC, 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".
- Lockheed SR-71 Blackbird long-range, Mach 3 strategic reconnaissance aircraft
- "71 Fragments of a Chronology of Chance," a film by Michael Haneke
- 71: Into the Fire, South Korean film about the Korean War
- The form number for the United States Office of Personnel Management for requesting a leave of absence.
- Municipal Okrug #71, name of Volkovskoye Municipal Okrug of Frunzensky District of Saint Petersburg, Russia, before 2008
- The Irish Rail 071 Class diesel locomotive.
- In the Jason Bourne novels by American author Robert Ludlum the department within the CIA which made Bourne and the other super agents is called Treadstone Seventy-One.
- SR-71 is an American Alternative Rock band.