71 (number)

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]

71 is a centered heptagonal number.^[3]

It is a regular prime,^[4] a Ramanujan prime,^[5] a Higgs prime,^[6] and a good prime.^[7]

It is a Pillai prime, since ${\displaystyle 9!+1}$ is divisible by 71, but 71 is not one more than a multiple of 9.^[8] It is part of the last known pair (71, 7) of Brown numbers, since ${\displaystyle 71^{2}=7!+1}$.^[9]

71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also Heegner numbers).^[10]

71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.^[11][12]

${\displaystyle F_{14}(71)={\frac {71^{16384}+1}{2}}}$ is the largest known generalized Fermat prime with base less than 1000.^[13][14]

• 71 (disambiguation)