401

Number
$401$ (four hundred and one) is:


 * The $79$th prime number


 * The $8$th prime number of the form $n^2 + 1$ after $2$, $5$, $17$, $37$, $101$, $197$, $257$:
 * $401 = 20^2 + 1$


 * The smaller of the $4$th pair of primes whose prime gap is $8$:
 * $409 - 401 = 8$