A generalized Sierpinski number base b is an integer k>1 for which gcd(k+1,b-1)=1, k is not a rational power of b, and kbn+1 is composite for all n>0. Given an integer k>0, we will seek a base b for which k is a generalized Sierpinski number base b. We will show that this is not possible if k is a Mersenne number. We will give an algorithm which will work for all other k provided that there exists a composite in the sequence {(k2m+1)/gcd(k+1,2)} for m ≥ 0.

Author Bio

Dan is originally from Chicago Illinois. For most of his undergraduate career he was on a sports scholarship as a football player. He wrote this paper while finishing his mathematics degree at the University of Tennessee at Martin and is now beginning a Masters in Statistics at Mississippi State University. After this Masters, Dan hopes to continue his education with a second Masters in Engineering Management. Dan uses the competitiveness and team attitudes that he learned in football while continuing in academia.