Problems & Puzzles: Conjectures

Would you believe that there are some specific k values that makes composite k2ⁿ+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 k2ⁿ-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.