Factors of Fermat numbers and large primes of the form

Author:
Wilfrid Keller

Journal:
Math. Comp. **41** (1983), 661-673

MSC:
Primary 11Y05; Secondary 11A41, 11Y11

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717710-7

MathSciNet review:
717710

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Abstract | References | Similar Articles | Additional Information

Abstract: A new factor is given for each of the Fermat numbers , and . In addition, a factor of discovered by Gary Gostin is presented. The current status for all is shown in a table. Primes of the form odd, are listed for , , and for , . Some primes for even larger values of *n* are included, the largest one being . Also, a survey of several related questions is given. In particular, values of *k* such that is composite for every *n* are considered, as well as odd values of *h* such that never yields a twin prime pair.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717710-7

Keywords:
Fermat numbers,
numbers of Ferentinou-Nicolacopoulou,
factoring,
trial division,
large primes,
covering set of divisors,
twin primes

Article copyright:
© Copyright 1983
American Mathematical Society