Available in electronic format
Available in print format
Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

Large Sophie Germain primes

Author(s): Harvey Dubner.
Journal: Math. Comp. 65 (1996), 393-396.
MSC (1991): Primary 11A41
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: If $P$ is a prime and $2P+1$ is also prime, then $P$ is a Sophie Germain prime. In this article several new Sophie Germain primes are reported, which are the largest known at this time. The search method and the expected search times are discussed.


References:

1
J. Brillhart, D. H. Lehmer, and J. L. Selfridge, New primality criteria and factorizations of $2^m\pm1$, Math. Comp. 29 (1975), 620--647. MR 52:5546

2
C. Caldwell, Review of the Cruncher PC plug-in board, J. Recreational Math. 25 (1993), 56--57.

3
------, The largest known primes, updated regularly and is available on request. Tel. (901) 587--7360, E-mail: caldwell@UTmartn.bitnet

4
G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 5th ed., Oxford Univ. Press, New York, 1979. MR 81i:10002

5
P. Ribenboim, The book of prime number records, 2nd ed., Springer-Verlag, New York, 1989. MR 90g:11127

6
H. Riesel, Prime numbers and computer methods for factorization, Birkhäuser, Boston, 1958.


Similar Articles:

Retrieve articles in Mathematics of Computation with MSC (1991): 11A41

Retrieve articles in all Journals with MSC (1991): 11A41


Additional Information:

Harvey Dubner
Affiliation: 449 Beverly Road, Ridgewood, New Jersey 07450
Email: 70372.1170@compuserve.com

DOI: 10.1090/S0025-5718-96-00670-9
PII: S 0025-5718(96)00670-9
Received by editor(s): March 7, 1994
Received by editor(s) in revised form: April 26, 1994
Copyright of article: Copyright 1996, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google