Factorizations of Cunningham numbers with bases 13 to 99
Richard P. Brent, Peter L. Montgomery, Herman J. J. te Riele
TL;DR
This paper updates and extends tables of factorizations for Cunningham numbers a^n ± 1 with bases from 14 to 99, providing 951 new factorizations and complete data for n < 76.
Contribution
It provides the most recent and comprehensive factorizations for Cunningham numbers in the specified range, improving previous tables and confirming the absence of small composite cofactors.
Findings
951 new factorizations added
Complete factorizations for n < 76
No composite cofactors smaller than 10^102
Abstract
This Report updates the tables of factorizations of a^n +- 1 for 13 < a < 100, previously published as CWI Report NM-R9212 (June 1992) and updated in CWI Report NM-R9419 (Update 1, September 1994) and CWI Report NM-R9609 (Update 2, March 1996). A total of 951 new entries in the tables are given here. The factorizations are now complete for n < 76, and there are no composite cofactors smaller than 10^102.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Coding theory and cryptography · Geometric and Algebraic Topology