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 $1$st of the $8$th pair of twin primes, with $73$


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


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


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


 * 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