71 (number) explained

Number:	71
Factorization:	prime
Prime:	20th
Divisor:	1, 71

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.^[1]

71 is a centered heptagonal number.

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 .^[2]

71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner numbers).^[3]

71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.^[4]

See also

• 71 (disambiguation)

Notes and References

1. Baker . Alan . Alan Baker (philosopher) . January 2017 . 10.1080/00048402.2016.1262881 . 4 . Australasian Journal of Philosophy . 779–793 . Mathematical spandrels . 95. 218623812 .
2. Berndt . Bruce C. . Galway . William F. . 10.1023/A:1009873805276 . 1 . Ramanujan Journal . 1754629 . 41–42 . On the Brocard–Ramanujan Diophantine equation n! +1= m ^{2} . 4 . 2000. 119711158 .
3. 2024-08-03 .
4. Duncan . John F. R. . Ono . Ken . Ken Ono . 10.1016/j.jnt.2015.06.001 . Journal of Number Theory . 3435726 . 230–239 . The Jack Daniels problem . 161 . 2016. 117748466 . free .