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Difference between revisions of "Williams prime"
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==Definition== | ==Definition== | ||
| − | A '''Williams number''' is a [[natural number]] of the form | + | A '''Williams number''' is a [[natural number]] of the form {{Kbn|(b-1)|b|n}} for integers ''b ≥ 2'' and ''n ≥ 1. |
A '''Williams prime''' is a Williams number which is [[prime]]. | A '''Williams prime''' is a Williams number which is [[prime]]. | ||
| + | |||
| + | ==Generalization== | ||
| + | Varying both signs, there're four different types of Williams primes: | ||
| + | *[[:Category:Williams prime MM|Type {{Kbn|(b-1)|b|n}}]] | ||
| + | *[[:Category:Williams prime MP|Type {{Kbn|+|(b-1)|b|n}}]] | ||
| + | *[[:Category:Williams prime PM|Type {{Kbn|(b+1)|b|n}}]] | ||
| + | *[[:Category:Williams prime PP|Type {{Kbn|+|(b+1)|b|n}}]] | ||
==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] maintaind by Steven Harvey | ||
*[[Wikipedia:Williams number|Williams number]] | *[[Wikipedia:Williams number|Williams number]] | ||
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{{Navbox NumberClasses}} | {{Navbox NumberClasses}} | ||
[[Category:Williams prime| ]] | [[Category:Williams prime| ]] | ||
Revision as of 17:27, 14 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.
- Search for original Williams primes maintaind by Steven Harvey
- Williams number
Number classes
| General numbers |
| Special numbers |
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| Prime numbers |
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