TITLE: Find five prime factors of $3^{140 }- 1$
QUESTION [9 upvotes]: I tried to simplify $3^{140}$ but I couldn't go past $81^{35}$, any help would be greatly appreciated.

REPLY [2 votes]: He asks for primes. So any prime $p\neq 3$ for which $p-1$ divides $140$ is such a prime.
This includes $2,5,11,29,71$. The are not the only prime factors, but they are the first five that we can find.
For example, $4^3\equiv 3\pmod {61}$, so $3^{20}=4^{60}\equiv 1\pmod {61}$. So $61$ is another prime factor.