Theoretical question

[igor]

k=78557 is conjectured to give the smallest Sierpinski number.
What value of k is conjectured to give the second smallest Sierpinski number? I couldn't find any references.

Thanks

Igor

[eatmadustch]

how about 2*78557?
just a guess, don't know for sure!
I guess the range 78557 to 2*78557 hasn't been tested (yet?)because it isn't interessting from the mathematical point of view!

[smh]

Don't ask me about how and why, but the Sierpinski numbers belo 1*10^6 are:

78557
271129
271577
322523
327739
482719
575041
603713
903983
934909
965431

And yes, the range between 78557 and 2*78557 has been tested. In fact, there is an extended search which tries to eliminate all candidates below 1.000.000.

http://www.glasgowg43.freeserve.co.uk/siersurv.htm