# 173

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## Number

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

- The $40$th prime number

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

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

- 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 $13$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 $34$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.