71 (number)

71 (seventy-one) is the natural number following 70 and preceding 72.

← 70 71 72 →
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Cardinal	seventy-one
Ordinal	71st (seventy-first)
Factorization	prime
Prime	20th
Divisors	1, 71
Greek numeral	ΟΑ´
Roman numeral	LXXI
Binary	10001112
Ternary	21223
Octal	1078
Duodecimal	5B12
Hexadecimal	4716

In mathematics

71 is:

• the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences.
• the 20th prime number. The next is 73, with which it composes a twin prime.
• a permutable prime with 17.
• is the largest number which occurs as a prime factor of an order of a sporadic simple group.
• the sum of three consecutive primes: 19, 23 and 29.
• a centered heptagonal number.[1]
• an Eisenstein prime with no imaginary part and real part of the form 3n – 1.
• a Pillai prime, since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9.[2]
• the largest (15th) supersingular prime, which is also a Chen prime.[3]
• part of the last known pair (71, 7) of Brown numbers, since 71² = 7! + 1.
• the twenty-third term of the Euclid–Mullin sequence, as it is the least prime factor of one more than the product of the first twenty-two terms.[4]
• the smallest positive integer d such that the imaginary quadratic field Q(√–d) has class number = 7.[5]

In science

• The atomic number of lutetium, a lanthanide

In astronomy

• Messier object M71, a magnitude 8.5 globular cluster in the constellation Sagitta
• The New General Catalogue object NGC 71, a magnitude 13.2 peculiar spiral galaxy in the constellation Andromeda

In other fields

See also: List of highways numbered 71

Seventy-one is also:

• The number of different characters that can be used with a standard English keyboard, 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
• 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 "La Bruja del 71" (Spanish: "The Witch from Number 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
• 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, an American alternative rock band
• The number of the laps of the Austrian Grand Prix, Mexican Grand Prix, and Brazilian Grand Prix

References

1. "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
3. "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
4. "Sloane's A000945 : Euclid-Mullin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
5. "Tables of imaginary quadratic fields with small class number". numbertheory.org.