113
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Number
$113$ (one hundred and thirteen) is:
- The $30$th prime number
- The $1$st $3$-digit permutable prime:
- $113$, $131$, $311$
- The $2$nd near-repdigit prime after $101$
- The $7$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$:
- $113 = 7 \times 2^4 + 1$
- The $10$th emirp after $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $107$
- The $11$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$:
- $2 \times 113 + 1 = 227$, which is prime.
- The $11$th long period prime after $7$, $17$, $19$, $23$, $29$, $47$, $59$, $61$, $97$, $109$
- The $14$th permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$
- The $16$th left-truncatable prime after $2$, $3$, $5$, $7$, $13$, $17$, $23$, $37$, $43$, $47$, $53$, $67$, $73$, $83$, $97$
Also see
- Previous ... Next: Permutable Prime
- Previous ... Next: Left-Truncatable Prime
- Previous ... Next: Proth Prime
- Previous ... Next: Prime Number
- Previous ... Next: Long Period Prime
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $113$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $113$