De Polignac's Formula/Examples/13 in 1000

Example of Use of Multiplicity of Prime Factor in Factorial
The prime factor $13$ appears in $1000!$ to the power of $81$.

That is:
 * $13^{81} \mathrel \backslash 1000!$

but:
 * $13^{82} \nmid 1000!$

Proof
Let $\mu$ denote the power of $13$ which divides $1000!$