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 smaller of the $1$st pair of primes whose prime gap is $14$:
$127 - 113 = 14$


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



Sources