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Originally Posted by Citrix
Can b-1 ever be a sierpinki or riesel number for base b?
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I've proved that if b-1 is a Sierpinski or a Riesel number for base b then it must have an infinite covering set. I can post the proof here if someone wants it.
It might be possible to find a b such that (b-1)*b^n+/-1 factorises nicely for some n (e.g. 4*5^6-1=(2*5^3-1)*(2*5^3+1)) with the rest of the n's having a finite covering set, but I haven't managed yet. I'm still looking into it.
Also, I'm working on the 5*6^n-1 sequence:
5*6^11233-1 & 5*6^13363-1 are both prime with no further primes below 14500