521

Number

$521$ (five hundred and twenty-one) is:

The $8$th Lucas prime after $2$, $3$, $7$, $11$, $29$, $47$, $199$.

The $13$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$, $47$, $76$, $123$, $199$, $322$:

$521 = 199 + 322$

The index of the $13$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$, $107$, $127$:

$M_{521} = 2^{521} - 1 \approx 6 \cdotp 865 \times 10^{156}$

The smaller of the $25$th pair of twin primes:

$523 - 521 = 2$

The Mersenne number $2^{521} - 1$ was proven to be the $13$th Mersenne prime on $30$th January $1952$, on the Standards Western Automatic Computer.

The program used was written by Raphael Mitchel Robinson over the Christmas period of $1951$, using an implementation of the Lucas-Lehmer Test.

This and the $14$th Mersenne prime $2^{607} - 1$ were thus discovered after a mere few hours.