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.
Varying both signs, there're four different types of numbers similiar to Williams numbers.
Lists of primes for bases b and n-values can be found here:
|PP: (b+1)•bn+1||here||here||here |
- The list table of any type contains only bases which are included as a separate page.
- The list of smallest primes of any base is an ASCII file for 2 ≤ b ≤ 1024. Any unknown value is given with the search range in brackets or empty.
- Values for bases b == 1 mod 3 are always divisible by 3, so not listed here.
- 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
- Mauro Fiorentini: Type MM, Type MP, Type PM, Type PP for 0 ≥ n ≥ 1000 (mostly) and 1 ≥ b ≥ 1000 (2016)
- Williams number