Number Theory

    

On the Existence of Infinitely Many Mersenne Primes and Finitely Many Fermat Primes

Authors: Pingyuan Zhou

Abstract: From existence of the intersection of the set of Mersenne primes and the set of Fermat primes being a set to contain only one element 3 to be the first Mersenne prime and also the first Fermat prime we fell there are connections between Mersenne and Fermat primes. In this paper, it is presented that two symmetric conjectures related to Mersenne and Fermat primes themselves will lead us to expect Mersenne primes to be infinite but Fermat primes to be finite.

Comments: 8 Pages. Author presents two symmetric conjectures related to Mersenne and Fermat primes themselves. It may imply that Mersenne primes are infinite but Fermat primes are finite.

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Submission history

[v1] 2014-07-11 03:55:10

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