Thread: N Weights
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Old 2010-04-17, 00:19   #1
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

102538 Posts
Default N Weights

I remember reading some passing comments on the apparent 'weights' of n's in files with many k's, (like NPLB's drive 11, or drive 1, where I think it was first noticed) and that we chalked it up to random chance. But then I looked at some (e.g. k*2^333333-1) with, and it looks pretty obvious to me that, just like with fixed k's, (e.g. 349*2^n-1) k*2^n-1 with fixed n has factors repeating periodically (just like with fixed k, this can mean that the number of candidates remaining after trivial factorization can be a small or large proportion of the candidates).
I wonder: can there be the fixed-n equivalents of Riesel/Sierpinski numbers? (i.e. numbers n where all numbers k*2^n-1 with k>0, n>0 are composite) If so, what is the smallest such? And is this mathematically any more or less interesting than Riesel/Sierpinski numbers?
I can see that, for practical purposes of proving such a conjecture, it'd be easier. Because you can test near-countless candidates before the digit length of the candidates you're testing grows much larger than the original 1*2^n-1.
(I figured CRUS would be the best subforum for this, since it's not serious enough for the likes of the Math forum, and is more CRUS-like with the vague consideration of covering sets, etc. than NPLB)

Last fiddled with by Mini-Geek on 2010-04-17 at 00:34
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