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 2ⁿ-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