The Numbers of Thousand Place of Mersenne Primes

Sibao Zhang, Lihang Zhou
DOI: 10.4236/am.2011.211190                

Abstract

Mersenne primes are a special kind of primes, which are an important content in number theory. The study of Mersenne primes becomes one of hot topics of the nowadays science. Searching for Mersenne primes is very challenging in scientific researches. In this paper, the numbers of thousand place of Mersenne primes are studied, and the conclusion is presented by using the Chinese remainder theorem.

Keywords

Mersenne Primes, The Chinese Remainder Theorem, The Number of Thousand Place

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. Z. Zhou, “The Distribution of Mersenne Primes,” in Chinese, Acta Scientiarum Naturalium Universitatis Sunyatseni, Vol. 31, No. 4, 1992, pp. 121-122.
[2]	S. B. Zhang, X. C. Ma and L. H. 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
[3]	Q. Cheng and L. Feng, “The Research of Mersenne Primes Based on Distributed Computing,” Frontier Science, Vol. 4, No. 14, 2010, pp. 59-67.
[4]	S. B. Zhang, “Review of Research on Mersenne Primes,” Science ＆ Technology Review, Vol. 26, No. 18, 2008, pp. 88-92.
[5]	Q. Chen and P. Zhang, “A Math Treasure: Mersenne Primes,” in Chinese, Encyclopedic Knowledge, Vol. 32, No. 5, 2009, p. 22.
[6]	S. B. Zhang and A. Yunus, “A Note on Mersenne Numbers,” in Chinese, Journal of Hebei North University, Vol. 26, No. 2, 2010, pp. 11-12.
[7]	S. B. Zhang, “The Mantissa of Mersenne Primes,” in Chinese, Journal of Jilin Normal University, Vol. 31, No. 2, 2010, pp. 92-94.
[8]	K. H. Rosen, “Elementary Number Theory and It’s Applications,” Pearson Education, Inc., Upper Saddle River, 2005.