Quote:
Originally Posted by MiniGeek
I wonder: can there be the fixedn equivalents of Riesel/Sierpinski numbers? (i.e. numbers n where all numbers k*2^n1 with k>0, n>0 are composite)

I think not!
Have a look
here and you can see there's not only a prime for any n for every k<10000, but also a twin for any n upto k=10000!
So it's only a matter of k to find a twin (and prime, too) for every n!