Innumber theory, aWilliams number baseb is anatural number of the form${\displaystyle (b-1)\cdot b^n-1}$ for integersb ≥ 2 andn ≥ 1.^[1] The Williams numbers base 2 are exactly theMersenne numbers.

AWilliams prime is a Williams number that isprime. They were considered byHugh C. Williams.^[2]

It is conjectured that for everyb ≥ 2, there are infinitely many Williams primes for baseb.

• Thabit number

• The primality of certain integers of the form 2Arⁿ − 1
• Some prime numbers of the forms 2·3ⁿ + 1 and 2·3ⁿ − 1
• Williams prime at PrimeWiki

• Classes of prime numbers
• Mersenne primes

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• Short description matches Wikidata
• Wikipedia indefinitely semi-protected pages