# How fact, that $n^p-(n-1)^p\equiv0\pmod{pk+1}$, using in prime numbers computing?

If $n^p-(n-1)^p=m$ and $p$ - prime, then all prime factors of $m$ have form $pk+1$. If we take small $p$, there are a lot of primes which having form $pk+1$, but when we take large $p$ it less and less. How is it using for computing large prime numbers or factorization large numbers?

If I made some mistakes, sorry for my English.