Problems & Puzzles: Conjectures Conjecture 13. Sierpinski numbersWould you believe that there are some specific k values that makes composite k2^{n}+1 for all n ? Those k numbers exists, were theoretically discovered by Sierpinski in 1960. It’s is believed that k=78557 is the least of such numbers but the coin is still in the air… There is a similar problem for the k2^{n}1 numbers and the also believed least "Riesel" number is k=509203. Several prime hunters are working to discard the smaller candidates to be Sierpinski or Riesel numbers, mainly J. Young & W. Keller. 




