419

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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 smaller 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 $7$, $17$, $19$, $23$, $29$, $\ldots$, $269$, $313$, $337$, $367$, $379$, $383$, $389$

Also see

• Previous  ... Next: Twin Primes
• Previous  ... Next: Record Gaps between Twin Primes
• Previous  ... Next: Sophie Germain Prime
• Previous  ... Next: Long Period Prime
• Previous  ... Next: Prime Number
• Previous  ... Next: Prime Gaps of 10