4583

Number
$4583$ (four thousand, five hundred and eighty-three) is:


 * The $620$th prime number


 * The $15$th prime $p$ such that $p \# - 1$, where $p \#$ denotes primorial (product of all primes up to $p$) of $p$, is prime:
 * $3$, $5$, $11$, $13$, $41$, $89$, $317$, $337$, $991$, $1873$, $2053$, $2377$, $4093$, $4297$, $4583$