Research on the Distribution of MersennePrimes Based on Zhou’s Conjecture

Wenlong DU, Bin SHEN, Yongqing ZHANG

Abstract


This paper presents an approximate expression of the number of Mersenne primes on the basis of Zhou’s conjecture, predicts the position of each Mersenne prime, and compares the number of Mersennes primes derived from this expression to the number of Mersennes primes derived from actual values and the four existing approximate expressions.


Keywords


Mersenne primes; Zhou’s conjecture; Distribution; Approximate expression

Full Text:

PDF

References


Zhang, S. B., & Chen, X. M. (2013). Mersenne primes and Zhou’s conjecture. Science & Technology Review, 31(3), 84.

Lehmer, D. H. (1935). On Lucas’test for primality of Mersenne’s numbers. J. of the London Math. Soc., 10, 162-165.

Zhang S. B. (2008). Review of research on Mersenne primes. Science & Technology Review, 26(18), 88-92.

Hurwitz, A. (1962). New Mersenne primes. Math.Comp,16, 249-51.

Gillies, D. B. (1964). Three new Mersenne primes and a statistical theory. Math Comp, 18, 93-97.

Wagstaff, S. S. (1983). Divisors of Mersenne numbers. Math Comp, 40, 385-397.

Zhou, H. Z. (1992). The distribution of Mersenne primes. Acta Scientiarum Naturalicm Universitatis Sunyatseni, 31(4), 121-122.




DOI: http://dx.doi.org/10.3968/3976

DOI (PDF): http://dx.doi.org/10.3968/g6166

Refbacks

  • There are currently no refbacks.


Copyright (c)




Share us to:   


Reminder

If you have already registered in Journal A and plan to submit article(s) to Journal B, please click the CATEGORIES, or JOURNALS A-Z on the right side of the "HOME".


We only use three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
caooc@hotmail.com; sms@cscanada.net; sms@cscanada.org

 Articles published in Studies in Mathematical Sciences are licensed under Creative Commons Attribution 4.0 (CC-BY).

 STUDIES IN MATHEMATICAL SCIENCES Editorial Office

Address: 9375 Rue de Roissy Brossard, Québec, J4X 3A1, Canada

Telephone: 1-514-558 6138
Http://www.cscanada.net
Http://www.cscanada.org
E-mail:caooc@hotmail.com

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures