# Selected Theorems and their Proofs

### By Chris Caldwell

This page indexes a number of theorems used on the prime pages. We will continue to add to it as time permits.

- A result of Euler and Lagrange on Mersenne Divisors
- All even perfect numbers are a power of two times a Mersenne prime
- Fermat's Little Theorem
- If 2
^{n}-1 is prime, then so is*n* - Lucas-Lehmer Test
- Mills' Theorem - a generalization
- Modular restrictions on Mersenne divisors
- Prime-square Mersenne divisors are Wieferich
- Repeated sums of the digits of a perfect number
- There are infinitely many primes
**(index)** - There are infinitely many pseudoprimes base a
- Wilson's Theorem

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