71

Number
$71$ (seventy-one) is:


 * The $20$th prime number, after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$, $61$, $67$


 * The $2$nd prime number after $53$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$.


 * The $3$rd prime number after $2, 5$ which divides the sum of all smaller primes:
 * $8 \times 71 = 568 = 2 + 3 + 5 + \cdots + 61 + 67$


 * The $5$th emirp after $13$, $17$, $31$, $37$


 * The smaller of the $8$th pair of twin primes, with $73$


 * The $10$th permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$


 * The $11$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$, $47$, $53$, $59$, $67$ such that the Mersenne number $2^p - 1$ is composite


 * The $16$th minimal prime base $10$ after $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$, $61$, $67$


 * Its square is the sum of two factorials:
 * $71^2 = 7! + 1!$


 * Its cube is the odd integers from $3$ to $11$ written in sequence:
 * $71^3 = 357 \, 911$

Also see

 * Brocard's Problem
 * Cube of 71 is Odd Integers in Sequence