# 71 (number)

Short description: Natural number
 ← 70 71 72 →
Cardinalseventy-one
Ordinal71st
(seventy-first)
Factorizationprime
Prime20th
Divisors1, 71
Greek numeralΟΑ´
Roman numeralLXXI
Binary10001112
Ternary21223
Quaternary10134
Quinary2415
Senary1556
Octal1078
Duodecimal5B12
Hexadecimal4716
Vigesimal3B20
Base 361Z36

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

## In mathematics

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]

It is centered heptagonal number.[7]

## See also

• 71 (disambiguation)

## References

1. "Mathematical spandrels". Australasian Journal of Philosophy 95 (4): 779–793. January 2017. doi:10.1080/00048402.2016.1262881.
2. Sloane, N. J. A., ed. "Sequence A002267 (The 15 supersingular primes)". OEIS Foundation.
3. Duncan, John F. R. (2016). "The Jack Daniels problem". Journal of Number Theory 161: 230–239. doi:10.1016/j.jnt.2015.06.001.
4. Sloane, N. J. A., ed. "Sequence A063980 (Pillai primes)". OEIS Foundation.
5. 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.
6. Sloane, N. J. A., ed. "Sequence A069099 (Centered heptagonal numbers)". OEIS Foundation.