Re: Re: Mersenne: Odds on finding a factor ?

[Dave Mullen]

If you're factoring numbers in the 11650000-11660000 (bit) range, the first factor could be anywhere in the root(11650000) - root(11660000) 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 /  3298942664324070148398699377093587963271453646320083409970227900099032340084550 62774912386254690657995387992797191286886934154060766755307240567049261017842856 34753285319263538813063962473878985845765797845382055337410440541344284339559168 80941876042039048147828263141419780748574268638921155547421336012026399104278046 64265542896070502632906030529322697818969236011674473356922970553100577222189744 01098206912973223458043228893199068964860334959883380891047401094866827202436849 06467404285944241544490932392466555180067560852971040278757170927077880835333805 65839845392145997956371325553841737475645737996524528874032899849701681509368301 42761015018525288690378571739745875603105853883771805379459256782614783580420623 57385982194936868642025682542127083166368763150103007436519265575280854513045193 16361252561366013410962597945954477571514685513193264633874076127007842257236863 98209046372801607655715856866505731790293078961776887506795295596160507661321192 45450554431681481621274487417255405424830736060991349632763754519609341441116629 8407300058885128192   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