# 719

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## Number

$719$ (seven hundred and nineteen) is:

The $128$th prime number.

The $3$rd prime number after $5$, $23$ of the form $n! - 1$ for integer $n$:
$719 = 6! - 1$
where $n!$ denotes $n$ factorial

The $4$th term after $89$, $179$, $359$ of the smallest Cunningham chain of the first kind of length $6$:
$\tuple {89, 179, 359, 719, 1439, 2879}$

The smaller of the $10$th pair of primes whose prime gap is $8$:
$727 - 719 = 8$

The larger of the $12$th pair of primes whose prime gap is $10$:
$719 - 709 = 10$

The $21$st safe prime after $5$, $7$, $11$, $23$, $47$, $59$, $83$, $107$, $167$, $179$, $227$, $263$, $347$, $359$, $383$, $467$, $479$, $503$, $563$, $587$:
$719 = 2 \times 359 + 1$

The $32$nd Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $233$, $239$, $251$, $281$, $293$, $359$, $419$, $431$, $443$, $491$, $509$, $593$, $641$, $653$, $659$, $683$:
$2 \times 719 + 1 = 1439$, which is prime.