167

Number
$167$ (one hundred and sixty-seven) is:


 * The $39$th prime number


 * The $13$th emirp after $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $107$, $113$, $149$, $157$


 * The $27$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$:
 * $167 \to 1^2 + 6^2 + 7^2 = 1 + 36 + 49 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$


 * The $3$rd of the $2$nd ordered triple of consecutive integers after $\left({105, 106, 107}\right)$ that have Euler $\phi$ values which are strictly increasing:
 * $\phi \left({165}\right) = 80$, $\phi \left({166}\right) = 82$, $\phi \left({167}\right) = 166$


 * The $33$rd positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.


 * The $10$th prime number after $53$, $71$, $103$, $107$, $109$, $149$, $151$, $157$, $163$ which cannot be expressed as the difference between a power of $2$ and a power of $3$.