RE: estimating primes (was: Re: Mersenne: Islands of Truth)
> I'd also guess that the skipped prime may have been pretty close to > 2^5014947-1, and have a number of digits close to 1408773. <...> > Hmm... I just changed my worktodo.ini to Test=5014947,63 (where's the 63 > come from ? it was used for the last number I was assigned). > > It's saying "Error: Work-to-do file contained composite exponent: 5014947" > > I suppose that means it's already been tested & found to be non-prime ? > (composite = non-prime, right?) That's because the exponent itself needs to be prime, and 5014947 is not. Divides by 3 in fact. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: estimating primes (was: Re: Mersenne: Islands of Truth)
> Hmm... I just changed my worktodo.ini to Test=5014947,63 (where's the 63 > come from ? it was used for the last number I was assigned). > > It's saying "Error: Work-to-do file contained composite exponent: 5014947" > > I suppose that means it's already been tested & found to be non-prime ? > (composite = non-prime, right?) This is for the number of bits the Mersenne number has been trial factored to. I.E. your last number was factored to 2^63. the reason that it reported a problem was that the exponent was composite. This means that the corisponding Mersenne number is composite, thus we only check prime exponents. The number 5014947=3*7*47*5081. Thus 2^3-1, 2^7-1, 2^47-1, and 2^5081-1 all divide 2^5014947-1 (though they do not factor it completely!). -Lucas _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: estimating primes (was: Re: Mersenne: Islands of Truth)
On Thu, 14 Oct 1999, Darxus wrote: > On Thu, 14 Oct 1999, Darxus wrote: > > > On Thu, 14 Oct 1999 [EMAIL PROTECTED] wrote: > > > > > conjectures. <<(#1: That there's a prime around the 4M range that we're > > > missing. #2: That the discovered M38, which all we knew about was that it was > > > in the 6M range, was actually around 6.9M, which I was correct about, and #3: >Pdigits > #38 5,014,947 1,408,773 > #39 7,414,614 2,070,471 Wow... I recalculated my estimates of P as # of digits * 3.321928094887 -- based on #5.6 from the faq (I really must read that whole thing some time so I stop asking stuff in it). They came out as: #38 4679842.61 #39 6877955.78 At some point I had a vague recollection that STL had believed there was a number missing, and I was quite happy to see that it basically matched what I got. And rounded, my estimate for #39 equals his. So now I'd estimate we're missing a prime near 2^4679842-1.. but of course when I try to do that manually, I'm getting told it's composite. __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
estimating primes (was: Re: Mersenne: Islands of Truth)
On Thu, 14 Oct 1999, Darxus wrote: > On Thu, 14 Oct 1999 [EMAIL PROTECTED] wrote: > > > missing. #2: That the discovered M38, which all we knew about was that it was > > in the 6M range, was actually around 6.9M, which I was correct about, and #3: > > How did you make this estimate ? Fit an exponential curve to the known > primes, and extrapolate the 1st one that should have at least 1m digits ? Okay, I figured out how to do exponential extrapolation in Excel. Omitting the 38th prime (p=6,972,593), and exponentially extrapolating from the 1st through 37th primes, I got the folowing: Pdigits #38 5,014,947 1,408,773 #39 7,414,614 2,070,471 Which is... intresting. The # of digits extrapolated for #39 (p=7414614) is only 1.36% different from the actual number of digits in 2^6972593-1. I wish I had time tonight to remove more entries and see if this extrapolation continued to be this accurate. Also, if this extrapolation of the number of digits is accurate, there is another prime between the 37th & 38th(p=6972593) discovered primes. Unfortunately, the extrapolation of P just didn't go well. Actually, the extrapolated 39th mersenne prime is 6.34% off of 2^6972593-2. I suppose that's not so bad. That would also mean one was skipped. So it is currently my fairly strong opinion that a mersenne prime was skipped between the 37th & 38th discovered primes. I reserve the right to change my mind at any instant :) I'd also guess that the skipped prime may have been pretty close to 2^5014947-1, and have a number of digits close to 1408773. So does any of this sound at all valid ? Most people seem to agree that the distribution of mersenne primes is at least roughly exponential, and that the variances are truly random. The above is based on these asumptions. I don't actually agree with those asumptions, but the distribution fits an exponential curve better with those assumptions than if you graph them as pairs. [EMAIL PROTECTED]: I'm really looking forward to hearing how you made your estimates. Hmm... I just changed my worktodo.ini to Test=5014947,63 (where's the 63 come from ? it was used for the last number I was assigned). It's saying "Error: Work-to-do file contained composite exponent: 5014947" I suppose that means it's already been tested & found to be non-prime ? (composite = non-prime, right?) I think that manual & primenet should not be seperate optinos on the test menu. I think manual should be another option on the "type of work to request" box. __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
