71 (number)

71 (seventy-one) is the natural number following 70 and preceding 72.

← 70 71 72 →
← 70 71 72 73 74 75 76 77 78 79 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventy-one
Ordinal	71st (seventy-first)
Factorization	prime
Prime	20th
Divisors	1, 71
Greek numeral	ΟΑ´
Roman numeral	LXXI, lxxi
Binary	10001112
Ternary	21223
Senary	1556
Octal	1078
Duodecimal	5B12
Hexadecimal	4716

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][2]

71 is a centered heptagonal number.^[3]

It is a regular prime^[4], a Ramanujan prime^[5], a Higgs prime^[6], and a good prime^[7].

It is a Pillai prime, since ${\displaystyle 9!+1}$ is divisible by 71, but 71 is not one more than a multiple of 9.^[8] It is part of the last known pair (71, 7) of Brown numbers, since ${\displaystyle 71^{2}=7!+1}$.^[9]

71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner numbers).^[10]

71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.^[11][12]

See also

• 71 (disambiguation)