← 70 71 72 →
Cardinalseventy-one
Ordinal71st
(seventy-first)
Factorizationprime
Prime20th
Divisors1, 71
Greek numeralΟΑ´
Roman numeralLXXI
Binary10001112
Ternary21223
Senary1556
Octal1078
Duodecimal5B12

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

## In mathematics

71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime.[1][2] It is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.[3][4]

It is a Pillai prime, since ${\displaystyle 9!+1}$ is divisible by 71, but 71 is not one more than a multiple of 9.[5] It is part of the last known pair (71, 7) of Brown numbers, since ${\displaystyle 71^{2}=7!+1}$.[6]

6. ^ Berndt, Bruce C.; Galway, William F. (2000). "On the Brocard–Ramanujan Diophantine equation ${\displaystyle n!+1=m^{2))$". Ramanujan Journal. 4 (1): 41–42. doi:10.1023/A:1009873805276. MR 1754629. S2CID 119711158.