Number Theory

    

Two Conjectures Which Generalize the Conjecture on the Infinity of Sophie Germain Primes

Authors: Marius Coman

In a previous paper (“Five conjectures on Sophie Germain primes and Smarandache function and the notion of Smarandache-Germain primes”) I defined two notions: the Smarandache-Germain pairs of primes and the Coman-Germain primes of the first and second degree. The few conjectures that I made on these particular types of primes inspired me to make two other conjectures regarding two sets of primes that are generalizations of the set of Sophie Germain primes. And, based on the observation of the first few primes from these two possible infinite sets of primes, I also made a conjecture regarding the primes q of the form q = p*2^n + 31 = r*2^m + 3, where p, r are primes an m, n are non-null positive integers.

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[v1] 2014-01-18 05:00:59

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