> The chart ooked interesting. Approximately exponential. But it didn't fit > real cleanly. So I stared at it for a long time. > > I noticed that the last 6 mersenne primes appeared to be in pairs... <...> > Does anybody see what I'm talking about ? Is there any significance to > this ? Has somebody already written extensive papers on this ? > > I don't have access to a charting program this instant, or I'm sure I'd be > up the rest of the night playing with this. Hopefully I'll get some time > to do so tomorrow. I'm sure someone beat me to a reply already, but... This is what's known as Noll's Island Theorem, if I am remembering the name correctly (and someone is bound to correct me otherwise :-) A while back on this list, we had a discussion on just this very thing, but as it turns out, with some more notable examples, as you have seen, the deviation, in percent, between so called pairs is pretty far and wide. And then you have to ask, well, what constitutes a pair anyway? Within 10% of each other? 20%? Some pairs are ridiculously close when you look at 'em, and some are pretty far apart but still close enough that some would call it a pair still. And there's no real correlation to the size of the exponents either. The deviation grows and shrinks all along the list of primes. There does seem to be a general trend, but beyond that, nothing too notable. There are exceptions to the trend which makes me think it's just a case of we humans trying to place an order on something where no order can be found. We do the same thing when looking at clouds and we start to see shapes of actual things. Power of imagination is all, I suspect. But the only way to know for sure is to find more Mersenne Primes, so let's all keep looking! I'll take this opportunity to say this: Some of us have volunteered to pony up some dough to give to the next person who finds a Mersenne Prime. This goes back to the way it was *before* the EFF prize. Since it'll be a while before we find a 10M digit prime (unless someone gets REAL lucky), it's nice to have a small incentive for someone to find another one before that. Did we ever "elect" anyone to keep track of "donations"? Scott? George? :-) Once we figure that out, maybe a little pool could get going to add to the already pledged amounts. If you're really (and I mean *really*) excited about new discoveries, maybe you'd like to pledge $10 or $20 or however much. I've pledged more, but that's more of an atonement for things I did last year, besides the thrill of finding a new Mersenne prime. :-) Aaron _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
