419

Number
$419$ (four hundred and nineteen) is:


 * The $81$st prime number


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


 * The upper end of the $7$th record-breaking gap between twin primes:
 * $419 - 349 = 70$


 * The $1$st of the $22$nd pair of twin primes:
 * $421 - 419 = 2$


 * The $22$nd Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$, $191$, $233$, $239$, $251$, $281$, $293$, $359$:
 * $2 \times 419 + 1 = 839$, which is prime.


 * The $30$th long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $269$, $313$, $337$, $367$, $379$, $383$, $389$