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Difference between revisions of "Williams prime"
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==External links== | ==External links== | ||
| − | *H. C. Williams: [http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf "The primality of certain integers of the form 2Ar^n-1"], Acta Arith. 39 (1981), 7-17. | + | *H. C. Williams: [http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf "The primality of certain integers of the form 2Ar^n-1"], Acta Arith. 39 (1981), 7-17 |
| − | *[http://harvey563.tripod.com/wills.txt Search for original Williams primes] | + | *A. Stein, H. C. Williams: [https://www.ams.org/journals/mcom/2000-69-232/S0025-5718-00-01212-6/S0025-5718-00-01212-6.pdf "Explicit primality criteria for (p−1)p<sup>n</sup>−1"], Math. Comp. 69 (2000), 1721-1734 |
| + | *Steven Harvey: [http://harvey563.tripod.com/wills.txt Search for original Williams primes] | ||
*[[Wikipedia:Williams number|Williams number]] | *[[Wikipedia:Williams number|Williams number]] | ||
{{Navbox NumberClasses}} | {{Navbox NumberClasses}} | ||
[[Category:Williams prime| ]] | [[Category:Williams prime| ]] | ||
Revision as of 11:36, 15 April 2019
Definition
A Williams number is a natural number of the form (b-1)•bn-1 for integers b ≥ 2 and n ≥ 1.
A Williams prime is a Williams number which is prime.
Generalization
Varying both signs, there're four different types of Williams primes:
External links
- H. C. Williams: "The primality of certain integers of the form 2Ar^n-1", Acta Arith. 39 (1981), 7-17
- A. Stein, H. C. Williams: "Explicit primality criteria for (p−1)pn−1", Math. Comp. 69 (2000), 1721-1734
- Steven Harvey: Search for original Williams primes
- Williams number
Number classes
| General numbers |
| Special numbers |
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| Prime numbers |
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