1019

Number
$1019$ (one thousand and nineteen) is:


 * The $171$st prime number


 * The $8$th prime $p$ such that $p \# + 1$, where $p \#$ denotes primorial (product of all primes up to $p$) of $p$, is prime:
 * $2$, $3$, $5$, $7$, $11$, $31$, $379$, $1019$


 * The $26$th safe prime after $5$, $7$, $11$, $23$, $47$, $59$, $83$, $107$, $167$, $179$, $227$, $263$, $347$, $359$, $383$, $467$, $479$, $503$, $563$, $587$, $719$, $839$, $863$, $887$, $983$:
 * $1019 = 2 \times 509 + 1$


 * The $1$st of the $36$th pair of twin primes:
 * $1021 - 1019 = 2$


 * The $39$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $653$, $659$, $683$, $719$, $743$, $761$, $809$, $911$, $953$, $1013$:
 * $2 \times 1019 + 1 = 2039$, which is prime.