Number Theory

    

A Conjecture on Near-square Prime Number Sequence of Mersenne Primes

Authors: Pingyuan Zhou

Abstract: In this paper we present a conjecture that there is a near-square prime number sequence of Mersenne primes to arise from the near-square number sequence Wp=2(Mp)^2-1 generated from all Mersenne primes Mp, in which every term is larger prime number than corresponding perfect number. The conjecture has been verified for the first few prime terms in the near-square prime number sequence and we may expect appearing of near-square prime numbers of some known Mersenne primes with large p-values will become larger primes to be searched than the largest known Mersenne prime M57885161.

Comments: 4 Pages. Aothor presents a near-sguare number sequence of all Mersenne primes, which seems to be an accptable awy in searching for larger primes by known Mersenne primes themselves than the largest known Mersenne prime M57885161.

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Submission history

[v1] 2014-07-15 22:13:12

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