71 (number)

Template:Infobox number 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.

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.

See also

• 71 (disambiguation)