113

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 $7$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 $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$

Also see

 * Smallest 3-Digit Permutable Prime