71 (number)

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70 71 72
Cardinal seventy-one
Ordinal 71st
Factorization prime
Prime 20th
Divisors 1, 71
Roman numeral LXXI
Binary 10001112
Ternary 21223
Quaternary 10134
Quinary 2415
Senary 1556
Octal 1078
Duodecimal 5B12
Hexadecimal 4716
Vigesimal 3B20
Base 36 1Z36

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

In mathematics[edit]

71 is the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences.

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 science[edit]

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
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.

In sports[edit]

  • NASCAR TRG Motorsports #71 driven by Bobby Labonte

In other fields[edit]

Seventy-one is also: