71 is the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences.
It is the 20th prime number. The next is 73, with which it composes a twin prime. It is also a permutable prime with 17. If we add up the primes less than 71 (2 through 67), we get 568, which is divisible by 71, 8 times. 71 is the largest supersingular prime. Also, 712 = 7! + 1, making it part of the last known pair of Brown numbers, as (71, 7). It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. Since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9, 71 is a Pillai prime.
71 is a centered heptagonal number.
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