409

Number
$409$ (four hundred and nine) is:


 * The $80$th prime number


 * The $2$nd after $199$ of the smallest $10$ primes in arithmetic sequence:
 * $409 = 1 \times 210 + 199$


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


 * The smaller of the $6$th pair of primes whose prime gap is $10$:
 * $419 - 409 = 10$


 * The $10$th minimal prime base $10$ after $2$, $3$, $5$, $7$, $11$, $19$, $41$, $61$, $89$

Also see