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 2020-10-24, 16:28 #1 sweety439   Nov 2016 22·691 Posts Cullen-Williams primes and Woodall-Williams primes The Cullen-Williams number base b is (b-1)*b^(b-1)+1, which is both Cullen number base b (n*b^n+1, some author requires n>=b-1, and for this number n is exactly b-1) and 2nd Williams number base b ((b-1)*b^n+1) The Woodall-Williams number base b is (b-1)*b^(b-1)-1, which is both Woodall number base b (n*b^n-1, some author requires n>=b-1, and for this number n is exactly b-1) and 1st Williams number base b ((b-1)*b^n-1) The Cullen-Williams number base b, (b-1)*b^(b-1)+1 is prime for b = 2, 3, 4, 10, 11, 15, 34, 37, ... (they are exactly the smallest Cullen prime base b for b = 2, 3, 11, 37, and they are exactly the smallest 2nd Williams prime base b for b = 2 and 11) The Woodall-Williams number base b, (b-1)*b^(b-1)-1 is prime for 3, 4, 8, 15, 44, 82, ... (they are exactly the smallest Woodall prime base b for b = 82, and they are exactly the smallest 2nd Williams prime base b for b = 15 and 82) What are the next Cullen-Williams prime and the next Woodall-Williams prime?