Re: Mersenne: Odds on finding a factor ?
- Original Message - From: Lucas Wiman [EMAIL PROTECTED] I think under windows that dos windows only run when they are "up". (I could be wrong, I've stopped using windows again) No. You can set a background priority. In Win 95, right-click on the icon, then click "Properties". Click on the "Misc" tab and move the slider for "Idle Priority" anywhere you want between Low and High. Click "OK". If I'm going to be away from a machine for a while, I quite often set a "B" priority task running in a Ubasic window and minimise it, then run an "A" priority task running in an active window. That way, I ensure that the machine won't be idle if the "A" task completes before my return. The downside is the reduction in resources available to the "A" task while both are running. HTH, Andy Steward Factorisations of 57,619 Generalised Repunits at: http://www.users.globalnet.co.uk/~aads/index.html _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Odds on finding a factor ?
Dear List-reader, I've been running Prime95 on my PII-400 at work, since December, and I'm currently on my second LL test ! And I've also been running it on my Celeron366 Laptop at home (When my wife isn't playing Settlers 3). I decided to make the Laptop do Factoring, and I've factored five numbers, all in the 1165-1166 range, as allocated by Primenet, without finding a factor. So my question is, What are the odds on finding a factor ? I've looked in all the FAQ's, including the mailing list one, and can't find it anywhere. I know that the odds for a LL test are 1 in 6, but I can't find out what the odds on finding a factor are ? Presumably all the non-prime numbers have a factor so the odds should be 1 in 5, but most of these factors must be higher than 2^64 (Yes/No) ? So what are the odds on a factor that prime95 will find ? Alex Phillips Campaign for Unmetered Telecommunications http://www.unmetered.org.uk Campaigning for a fair choice in telecommunications _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Odds on finding a factor ?
From a quick browse through the top 101-500 producer list (it's the one I'm in:) it looks like the odds say you can expect 10-15 factors per P90 year spent on factoring. Based on my own stats, I've got 13.959 P90 years spent factoring, with 177 factors found. That's 12-13 per P90 year, so you're estimate fits in my case at least. Currently, I'm #8 in the factoring, but slipping fast. :-) My quick checks on the top 10 factorers show that *usually*, the ratio is the same, but for some of those top factorers, the ratios are much higher (20-23 per P90 year). I would guess that since those folks concentrate more on factoring, they got some numbers that were not tested even up to 52-55 bits yet, so probably found more small factors than the rest of us will. Aaron _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Odds on finding a factor ?
Hi, At 02:28 PM 1/23/00 -, Alex Phillips wrote: I've factored five numbers, all in the 1165-1166 range, as allocated by Primenet, without finding a factor. So my question is, What are the odds on finding a factor ? Since these exponents are already factored to 2^52 and you will be factoring to 2^64, your chance of NOT finding a factor is about 52/64. Thus, your chance of finding a factor is about 1 in 5.3. Regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Re: Mersenne: Odds on finding a factor ?
If you're factoring numbers in the 1165-1166 (bit) range, the first factor could be anywhere in the root(1165) - root(1166) range i.e. 3413 - 3414 bits long !! George's system prechecks to 2^52, and you are checking 2^52 - 2^64. There's still a long way from 2^64 to 2^3413 !! I'd have thought your odds of finding a factor are a lot smaller than 12 / 64 - probably closer to 12/3361 - and that's only if we pretend that the power series 2^n is a linear series he he he. Ala UBASIC, I estimate your real odds might be 4096 / 32989426643240701483986993770935879632714536463200834099702279000990323400845506277491238625469065799538799279719128688693415406076675530724056704926101784285634753285319263538813063962473878985845765797845382055337410440541344284339559168809418760420390481478282631414197807485742686389211555474213360120263991042780466426554289607050263290603052932269781896923601167447335692297055310057722218974401098206912973223458043228893199068964860334959883380891047401094866827202436849064674042859442415444909323924665551800675608529710402787571709270778808353338056583984539214599795637132555384173747564573799652452887403289984970168150936830142761015018525288690378571739745875603105853883771805379459256782614783580420623573859821949368686420256825421270831663687631501030074365192655752808545130451931636125256136601341096259794595447757151468551319326463387407612700784225723686398209046372801607655715856866505731790293078961776887506795295596160507661321192454505544316814816212744874172554054248307360609913496327637545196093414411166298407300058885128192 Sorry to be the Grim Reaper, but I've spent months with UBASIC eliminating factors in the 32,000,000 to 48,000,000 range - I'm only on about 24% eliminated using multiples 2pk+1 where k is 1 to 2^16 - and there's no doubt that the density of factors decreases as the multiplier increases. Finding the first few % is easy - finding the last 1% might take forever !! However I am using DaveNET - One P133 Laptop only, shared with the wife's chatting and E-Mail, and the kid's games !! Dave
Re: Re: Mersenne: Odds on finding a factor ?
If you're factoring numbers in the 1165-1166 (bit) range, the first factor could be anywhere in the root(1165) - root(1166) range i.e. 3413 - 3414 bits long !! No, in the x-y bit range (remember that n bit integers are about 2^n) the first factor could be x/2 to y/2 bits long (powers of a power multiply). I'd have thought your odds of finding a factor are a lot smaller than 12 / 64 - probably closer to 12/3361 - and that's only if we pretend that the power series 2^n is a linear series he he he. see http://www.utm.edu/research/primes/glossary/MertensTheorem.html Ala UBASIC, I estimate your real odds might be 4096 / 3298942664324070148398699377093587963271453646320083409970227900099032340084550 [...] Abreviate! Use scientific notation... Sorry to be the Grim Reaper, but I've spent months with UBASIC eliminating factors in the 32,000,000 to 48,000,000 range - I'm only on about 24% eliminated using multiples 2pk+1 where k is 1 to 2^16 - and there's no doubt that the density of factors decreases as the multiplier increases. Finding the first few % is easy - finding the last 1% might take forever !! Why are you only setting k==1 mod 2^16? (I'm probably missing something obvious) I think under windows that dos windows only run when they are "up". (I could be wrong, I've stopped using windows again) You would probably get better results with Will Edgington's mersfacgmp program, and DJGPP (a port of g++ to dos). -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
