71

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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 $11$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$, $37$, $53$, $59$

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

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $71$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $71$