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
- Previous ... Next: Twin Primes
- Previous ... Next: Sequence of Indices of Composite Mersenne Numbers
- Previous ... Next: Prime Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $71$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $71$