20210513, 21:01  #12 
If I May
"Chris Halsall"
Sep 2002
Barbados
9,887 Posts 

20210514, 02:11  #13  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2^{2}·3·5·79 Posts 
Quote:
I am running GPUOwl under colab. When I can get a P100 (which is virtually every day) I can do a 8GHz P1 in 30 minutes. Running a similar P1 on all 8 cores of my i77820X takes about 75 minutes. 

20210514, 22:36  #14  
∂^{2}ω=0
Sep 2002
República de California
11,657 Posts 
(Somehow missed this when PaulU OPed it:)
Quote:
n = 499400852887245323683941126088449355702834653807158087; p = 105032111; pm1(n,p,10^4,5*10^6,5) Stage 1 primepowers seed = 105032111 Stage 1 residue A = 275242671610725931867172664303887659718570581548948384, gcd(A1,n) = 1 Stage 2 interval = [10000,5000000]: Using base= 3; Initializing M*24 = 120 [base^(A^(b^2)) % n] buffers for Stage 2... Stage 2 q0 = 10080, k0 = 48 At q = 209790 At q = 419790 At q = 629790 At q = 839790 At q = 1049790 At q = 1259790 At q = 1469790 At q = 1679790 At q = 1889790 At q = 2099790 At q = 2309790 At q = 2519790 At q = 2729790 At q = 2939790 At q = 3149790 At q = 3359790 At q = 3569790 At q = 3779790 At q = 3989790 At q = 4199790 At q = 4409790 At q = 4619790 At q = 4829790 Stage 2: did 23762 loop passes. Residue B = 409059575611368065569985294315721920104412510081096652, gcd(B,n) = 290582744822559701357207 This factor is a probable prime. Processed 581936 stage 2 primes, including 234294 primepairs and 113348 primesingles [80.52 % paired]. Now back to work on my cuttingedge bcbased NFS implementation, with which I hope to someday factor numbers as large as the quantumcomputer folks do: "the quantum factorization of the largest number to date, 56,153, smashing the previous record of 143 that was set in 2012." Last fiddled with by ewmayer on 20210514 at 22:37 

20210523, 22:12  #15 
∂^{2}ω=0
Sep 2002
República de California
11,657 Posts 
[We open our next scene with a hand slapping the owner's forehead, accompanied by the utterance "doh!"]
Re above: In fact it seems silly to use powerful generalmodulus factoring machinery like ECM or QS on such (p1)found factorproduct composites. Here's why: say we have some product of prime factors F = f1*f2*...*fn discovered by running p1 to stage bounds b1 and b2 on an input Mersenne M(p) (or other bigum modulus with factors of a known form, allowing p1 to be 'seeded' with a component of same). BY DEFINITION, each prime factor f1fn will be b1/b2smooth, in the sense than fj = 2*p*C + 1, where C is a composite all of whose prime factors are <= b1, save possibly one outlierprime factor > b1 and <= b2. Thus if we again run p1 to bounds b1/b2, but now with arithmetic modulo the relatively tiny factor product F, we are guaranteed to resolve all the prime factors f1fn  the only trick is that we will need to do multiple GCDs along the way in order to capture the individual prime factors f1,...,fn, rather than have this secondary p1 run modulo F again produce the same composite GCD = F which the original p1 run mod M(p) did. Again, though, since in the followup p1 run we are working mod F, all the arithmetic is trivially cheap, including the needed GCDs. And since the cost of a p1 run is effectively akin to a single supercheap ECM curve, we've reduced the work of resolving the composite F to just that equivalent. Last fiddled with by ewmayer on 20210523 at 22:17 
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