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 $7$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 $14$:
 * $127 - 113 = 14$