Some Notes on the Distribution of Mersenne Primes

Abstract

Mersenne primes are a special kind of primes, which are always an important content in number theory. The study of Mersenne primes becomes one of hot topics of the nowadays science. It has not settled that whether there exist infinite Mersenne primes. And several of conjectures on the distribution of it provided by scholars. Starting from the Mersenne primes known about, in this paper we study the distribution of Mersenne primes and argued against some suppositions by data analyzing.

Mersenne primes are a special kind of primes, which are always an important content in number theory. The study of Mersenne primes becomes one of hot topics of the nowadays science. It has not settled that whether there exist infinite Mersenne primes. And several of conjectures on the distribution of it provided by scholars. Starting from the Mersenne primes known about, in this paper we study the distribution of Mersenne primes and argued against some suppositions by data analyzing.

Cite this paper

nullS. Zhang, X. Ma and L. Zhou, "Some Notes on the Distribution of Mersenne Primes,"*Applied Mathematics*, Vol. 1 No. 4, 2010, pp. 312-315. doi: 10.4236/am.2010.14041.

nullS. Zhang, X. Ma and L. Zhou, "Some Notes on the Distribution of Mersenne Primes,"

References

[1] Q. Chen and P. Zhang, “A Math Treasure: Mersenne Primes,” Encyclopedic Knowledge, Vol. 32, No. 5, 2009, p. 22.

[2]
K. H. Rosen, “Elementary Number Theory and it’s Applications,” Published by arrangement with the original publisher, Pearson Education, Inc., publishing as Addision-Wesley, 2005.

[3] H. Z. Zhou, “The Distribution of Mersenne Primes,” Acta Scientiarum Naturalium Universitatis Sunyatseni, Vol. 31, No. 4, 1992, pp. 121-122.

[4]
J. Z. Zhang, “Zhou Conjecture Reveals the Beauty of Mathematics,” In: J. Z. Zhang, et al., Ed., 100 Cases of Scientific and Technological Achievements in Three Decades: 1978-2008, Children’s Press, Wuhan: Hubei, 2008, pp. 8-9.

[5]
S. W. Chen, “Conjecture on Distribution of Mersenne Primes,” Huanghuai Journal, Vol. 11, No. 4, 1995, pp. 44-46.

[6]
C. Pomerance, “Recent Developments in Primality Testing,” Mathematical Intelligencer, Vol. 3, No. 3, 1980, pp. 97-105.

[7]
S. Wagstaff, “Divisors of Mersenne Numbers,” Mathematics and Computation, Vol. 40, No. 38, 1983, pp. 385 -397.