521

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


 * The $98$th prime number


 * 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 $31$st minimal prime base $10$ after $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$, $61$, $67$, $71$, $73$, $79$, $83$, $89$, $97$, $227$, $251$, $257$, $277$, $281$, $349$, $409$, $449$, $499$