8191

Number
$8191$ (eight thousand, one hundred and ninety-one) is:


 * The $1028$th prime number


 * The $2$nd of the $2$ known numbers (with $31$) expressible as the sum of successive powers starting from $1$ in in $2$ different ways:
 * $8191 = 1 + 90 + 90^2 = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^{10} + 2^{11} + 2^{12}$


 * The $5$th Mersenne prime after $3$, $7$, $31$, $127$:
 * $8191 = 2^{13} - 1$


 * The $6$th Mersenne number after $3$, $7$, $31$, $127$, $2047$:
 * $8191 = 2^{13} - 1$