Williams prime

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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.

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Number classes
General numbers
Special numbers
  • Mersenne (2n-1)
  • Fermat (22n+1)
  • Proth (k*2n+1)
  • Riesel (k*2n-1)
  • Double Mersenne (22p-1-1)
  • Perfect (2n-1(2n-1))
  • Prime numbers
  • Mersenne
  • Proth
  • Riesel
  • Williams ((b-1)*bn-1)
  • Carol ((bn-1)2-2)
  • Kynea ((bn+1)2-2)