71 (seventy-one) is the natural number following 70 and preceding 72.
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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 <math>9!+1</math> 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 <math>71^{2}=7!+1</math>.
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.
<math>F_{14}(71) = \frac{71^{16384} + 1}{2}</math> is the largest known generalized Fermat prime with base less than 1000.
See also
- 71 (disambiguation)