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Which of the following statements about prime factorization is true?

Select ALL that apply.

The number of distinct prime factors of $2^7-1$ is $1$.

The number of distinct prime factors of $2^p-1$ is $\ll \frac{p}{\log p}$ where $p$ is a prime.

The number of distinct prime factors of $2^{pq}-1$ is at least $2$ where $p$ and $q$ are distinct primes.

A prime $p$ always divides $2^p -1$.