Hmm... in games of chance, each game's outcome is independent of the results of past games, so that is a valid point.
In Mersenne Prime hunting though, I think it's safe to say that statistically there should be some prime numbers in the range we're checking, so the more we *don't* find, the higher the odds of the remaining ones being prime. :) In other words, there is a certain sort of dependence on previous outcomes. In gambling terms, that's like saying that perhaps you could guarantee winning one game out of every 50 hands of poker (alright, so he's a lousy player). If you lost 49 times, and you know you would win 1 out of 50 times, then yes, there's a 100% chance you'll win the next hand. :) What's a bigger issue here is whether or not the statistical model for how many primes we expect to find in a given range is accurate or not. Since the probabilities are based purely on the spread of previous primes, the sample data is pretty small, and there's already a jagged curve to the whole thing, so any probabilities are likely to be off by a good amount in practice. I know we did lots of analyses prior to finding the last one, and I'm curious how well that # fit any of the odds people had formulated. Aaron > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:mersenne-invalid- > [EMAIL PROTECTED]] On Behalf Of Nathan Russell > Sent: Sunday, November 04, 2001 5:49 PM > To: [EMAIL PROTECTED] > Subject: Re: Mersenne: Re: What will we do when anyone finds a number of > 10 million+ digits which is prime? > > On Sun, 04 Nov 2001 20:09:20 -0500, Jud McCranie > <[EMAIL PROTECTED]> wrote: > > > > >At 01:43 AM 11/5/2001 +0100, Steinar H. Gunderson wrote: > > > >>Speaking of which -- shouldn't we be (statistically) really close to > finding > >>a new prime soon? > > > >Yes, statistically. You'd "expect" the next one to be before 14,000,000 > >and I've got assignments in the 13,000,000 range. However, all exponents > >have been checked once only to a little past 8,000,000. > > Of course, this whole argument makes (as far as I can see) heavy use > of the gamblers' fallacy, aka the fallacy of maturation of > probabilities ("Hey, I lost the last 50 games - what are the odds > against me losing 51 5-man games in a row? I'm certain to win!") > > Nathan > ________________________________________________________________________ _ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
