Quote:
Originally Posted by sweety439
Extended to base 539
Note: I only searched the k <= 5000000, if there are <16 Sierpinski/Riesel k's <= 5000000, then this text file only show the Sierpinski/Riesel k's <= 5000000 for this Sierpinski/Riesel base (if there are no Sierpinski/Riesel k's <= 5000000, then this text file do not show any Sierpinski/Riesel k's <= 5000000 for this Sierpinski/Riesel base), also, I only searched the exponent n <= 2000 (for (k*b^n+1)/gcd(k+1,b1), + for Sierpinski,  for Riesel) and only searched the primes <= 100000 (for the prime factor of (k*b^n+1)/gcd(k+1,b1), + for Sierpinski,  for Riesel), thus this text file wrongly shows 1 as Sierpinski number base 125, although (1*125^n+1)/gcd(1+1,1251) has no covering set, but since (1*125^n+1)/gcd(1+1,1251) has a prime factor <= 100000 for all n <= 2000

These are the conjectures in the thread
https://mersenneforum.org/showthread.php?t=11061 (conjectured smallest
prime Sierpinski/Riesel numbers), for the extended Sierpinski/Riesel conjectures (k*b^n+1)/gcd(k+1,b1) (+ for Sierpinski,  for Riesel) for bases 2<=b<=128 and 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536