PRP Records

(14*73^21369+1)/3



This (probable) prime is found to solve the generalized Sierpinski problem in base 73. This eliminated k=14 for the generalized Sierpinski problem in base 73 and proves that 47 is the smallest Sierpinski number in base 73.

Generalized Sierpinski problem in base b>=2: Finding and proving the smallest k such that (k*b^n+1)/gcd(k+1,b-1) is composite for all integers n>=1.

Generalized Riesel problem in base b>=2: Finding and proving the smallest k such that (k*b^n-1)/gcd(k-1,b-1) is composite for all integers n>=1.

To be completed...




Go back