127

Number
$127$ (one hundred and twenty-seven) is:


 * The $31$st prime number


 * The $4$th Mersenne number and $4$th Mersenne prime after $3$, $7$, $31$:
 * $127 = 2^7 - 1$


 * The index of the $12$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$, $107$:
 * $M_{127} = 2^{127} - 1 = 170 \, 141 \, 183 \, 460 \, 469 \, 231 \, 731 \, 687 \, 303 \, 715 \, 884 \, 105 \, 728$


 * The $2$nd obstinate number after $1$.


 * The $7$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$:
 * $127 = 1 + 6 + 12 + 18 + 24 + 30 + 36 = 7^3 - 6^3$


 * The $26$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $93$, $99$, $105$, $111$, $115$, $127$, $\ldots$


 * The $8$th of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 7^2 + 29 = 127$


 * The larger of the smallest pair of primes whose prime gap is $14$:
 * $127 - 113 = 14$

Also see