173

Number
$173$ (one hundred and seventy-three) is:


 * The $40$th prime number


 * The $13$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$:
 * $2 \times 173 + 1 = 347$, which is prime.


 * The $8$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$, $161$:
 * $\nexists n \in \Z_{>0}: n = 173 \times s_{10} \left({n}\right)$


 * The $4$th balanced prime after $5$, $53$, $157$:
 * $173 = \dfrac {167 + 179} 2$


 * The $34$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.


 * The $11$th prime number after $53$, $71$, $103$, $107$, $109$, $149$, $151$, $157$, $163$, $167$ which cannot be expressed as the difference between a power of $2$ and a power of $3$.


 * The $10$th of $11$ primes of the form $2 x^2 + 11$:
 * $2 \times 9^2 + 11 = 173$