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. 71 is a
centered heptagonal number. It is a
regular prime, a
Ramanujan prime, a
Higgs prime, and a
good prime. It is a
Pillai prime, since 9!+1 is divisible by 71, but 71 is not one more than a multiple of 9. It is part of the last known pair (71, 7) of
Brown numbers, since 71^{2}=7!+1. 71 is the smallest of thirty-one discriminants of imaginary
quadratic fields with class number of 7, negated (see also
Heegner numbers). 71 is the largest number which occurs as a prime factor of an order of a
sporadic simple group, the largest (15th)
supersingular prime. F_{14}(71) = \frac{71^{16384} + 1}{2} is the largest known
generalized Fermat prime with base less than 1000. == See also ==