In number theory, a Williams number base b is a natural number of the form for integers b ≥ 2 and n ≥ 1.[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.[2]

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

See also

References

  1. ^ Williams primes
  2. ^ See Table 1 in the last page of the paper: Williams, H. C. (1981). "The primality of certain integers of the form 2 A rn – 1". Acta Arith. 39: 7–17. doi:10.4064/aa-39-1-7-17.