71 (number)

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.{{cite journal

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.{{cite journal

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.{{cite journal | doi-access = free

References

References

1. {{cite OEIS. A006567. Emirps (primes whose reversal is a different prime)
2. {{Cite OEIS. A069099. Centered heptagonal numbers
3. "Sloane's A007703 : Regular primes". OEIS Foundation.
4. "Sloane's A104272 : a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x". OEIS Foundation.
5. "Sloane's A007459 : a(n+1) = smallest prime > a(n) such that a(n+1)-1 divides the product (a(1)...a(n))^2". OEIS Foundation.
6. "Sloane's A028388 : prime(n) such that prime(n)^2 > prime(n-i)*prime(n+i) for all 1 <= i <= n-1". OEIS Foundation.
7. {{Cite OEIS. A063980. Pillai primes
8. {{Cite OEIS. A046004. Discriminants of imaginary quadratic fields with class number 7 (negated).
9. {{Cite OEIS. A002267. The 15 supersingular primes