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 $2$, $3$, $5$, $7$, $11$, $19$, $41$, $61$, $89$