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.<ref>Template:Cite OEIS</ref><ref>Template:Cite journal</ref>
71 is a centered heptagonal number.<ref>Template:Cite OEIS</ref>
It is a regular prime,<ref>Template:Cite web</ref> a Ramanujan prime,<ref>Template:Cite web</ref> a Higgs prime,<ref>Template:Cite web</ref> and a good prime.<ref>Template:Cite web</ref>
It is a Pillai prime, since <math>9!+1</math> is divisible by 71, but 71 is not one more than a multiple of 9.<ref>Template:Cite OEIS</ref> It is part of the last known pair (71, 7) of Brown numbers, since <math>71^{2}=7!+1</math>.<ref>Template:Cite journal</ref>
71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also Heegner numbers).<ref>Template:Cite OEIS</ref>
71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.<ref>Template:Cite OEIS</ref><ref>Template:Cite journal</ref>