Williams number

In number theory, a Williams number base b is a natural number of the form for integers b ≥ 2 and n ≥ 1. The Williams numbers base 2 are exactly the Mersenne numbers.

A Williams prime is a Williams number that is prime. They were considered by Hugh C. Williams.

It is conjectured that for every b ≥ 2, there are infinitely many Williams primes for base b.

See also

• Thabit number

References

External links

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