De Polignac's Formula/Examples/3 in 1000

Example of Use of Multiplicity of Prime Factor in Factorial
The prime factor $3$ appears in $1000!$ to the power of $498$.

That is:
 * $3^{498} \mathrel \backslash 1000!$

but:
 * $3^{499} \nmid 1000!$

Proof
Let $\mu$ denote the power of $3$ which divides $1000!$