De Polignac's Formula/Examples/7 in 1000

Example of Use of Multiplicity of Prime Factor in Factorial
The prime factor $7$ appears in $1000!$ to the power of $164$.

That is:
 * $7^{164} \mathrel \backslash 1000!$

but:
 * $7^{165} \nmid 1000!$

Proof
Let $\mu$ denote the power of $7$ which divides $1000!$