83

Number
$83$ (eighty-three) is:


 * The $23$rd prime number


 * The $7$th safe prime after $5$, $7$, $11$, $23$, $47$, $59$:
 * $83 = 2 \times 41 + 1$


 * The $7$th of $11$ primes of the form $2 x^2 + 11$:
 * $2 \times 6^2 + 11 = 83$


 * The $9$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$:
 * $2 \times 83 + 1 = 167$, which is prime.


 * The $14$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$, $47$, $53$, $59$, $67$, $71$, $73$, $79$ such that the Mersenne number $2^p - 1$ is composite


 * The $19$th minimal prime base $10$ after $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$, $61$, $67$, $71$, $73$, $79$


 * The $33$rd odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
 * $1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $\ldots$