Speech Around the Twin Primes Conjecture, the Mersenne Primes Conjecture, and the Sophie Germain Primes Conjecture

Abstract

Here, we state a simple Assertion (A), we introduce an original method of induction, and we use it to give a simple and detailed proof that (A) is stronger than the twin primes conjecture, the Mersenne primes conjecture and the Sophie Germain primes conjecture; this helps us to explain why it is not surprising to conjecture that the Mersenne primes conjecture and the Sophie Germain primes conjecture are all special cases of the twin primes conjecture.