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-   -   GPU72 Largest 100 Factors Found (https://www.mersenneforum.org/showthread.php?t=26201)

LOBES 2020-11-17 05:40

GPU72 Largest 100 Factors Found
 
I was clicking around the site and found the "Largest 100 Factors Found" page interesting:


[URL]https://www.gpu72.com/reports/largest_factors/[/URL]


Is that up-to-date? If so, does it update automatically or is it something Chris updates manually?


I only ask because the largest as of this writing is:


734277451864747167510502805298930545450478445879


I found a factor today of exponent [URL="https://www.mersenne.org/report_exponent/default.php?exp_lo=105032111&full=1"]105032111[/URL]:



499400852887245323683941126088449355702834653807158087



Unless of course, I am completely reading that wrong, which is entirely possible. It is all just so fascinating, and I have such a small grasp of it.

chalsall 2020-11-17 05:49

[QUOTE=LOBES;563450]I was clicking around the site and found the "Largest 100 Factors Found" page interesting:

Unless of course, I am completely reading that wrong, which is entirely possible. It is all just so fascinating, and I have such a small grasp of it.[/QUOTE]

That list is automatically updated. And while your find is impressive, it is, unfortunately, a "composite factor".

BTW, it's a complete fluke that I'm at the top of the list. There are many others putting in far more P-1 efforts than myself; I just got lucky there.

paulunderwood 2020-11-17 05:50

[QUOTE=LOBES;563450]I was clicking around the site and found the "Largest 100 Factors Found" page interesting:


[URL]https://www.gpu72.com/reports/largest_factors/[/URL]


Is that up-to-date? If so, does it update automatically or is it something Chris updates manually?


I only ask because the largest as of this writing is:


734277451864747167510502805298930545450478445879


I found a factor today of exponent [URL="https://www.mersenne.org/report_exponent/default.php?exp_lo=105032111&full=1"]105032111[/URL]:



499400852887245323683941126088449355702834653807158087



Unless of course, I am completely reading that wrong, which is entirely possible. It is all just so fascinating, and I have such a small grasp of it.[/QUOTE]

Congrats! However:

[CODE]? factor(499400852887245323683941126088449355702834653807158087 )

[ 290582744822559701357207 1]

[1718618403140893608084889221841 1]
[/CODE]

LaurV 2020-11-17 09:44

Adding to it, that list only contains factors which are prime and were discovered for assignments taken with GPU-72 (if that's not understood).

To see a list with ever largest factors found, with the method used to find them, see [URL="https://www.mersenne.ca/userfactors/any/1/bits"]mersenne.ca[/URL] list.

LOBES 2020-11-17 14:35

Thanks so much for the responses. That is what I was expecting.


Me: See really long number, longer than the other numbers, think I'm onto something...


Reality: Nah. Not really.

ZFR 2020-11-24 15:28

Wow, those bit levels are way higher than anything that can be (reasonably) done on TF. Those top factors are all from P-1?

chalsall 2020-11-24 19:18

[QUOTE=ZFR;564207]Those top factors are all from P-1?[/QUOTE]

Yes.

ZFR 2020-11-24 20:21

[QUOTE=chalsall;564251]Yes.[/QUOTE]

And unlike TF, P-1 is better done on CPU than GPU, right?

So if I want to devote one of my CPU workers to P-1 instead of PRPs, I can just get a list from GPU72, copy it under that worker in mprime's worktodo, and that's it? B1 and B2 will be chosen automatically by mprime?

chalsall 2020-11-24 20:29

[QUOTE=ZFR;564259]And unlike TF, P-1 is better done on CPU than GPU, right?[/QUOTE]

There's some excellent GPU P-1 software available now. But Prime95/mprime (CPU) is by far the easiest to work with.

[QUOTE=ZFR;564259]So if I want to devote one of my CPU workers to P-1 instead of PRPs, I can just get a list from GPU72, copy it under that worker in mprime's worktodo, and that's it? B1 and B2 will be chosen automatically by mprime?[/QUOTE]

Contemporaneous P-1 work is available from both Primenet and GPU72. Know that GPU72 is currently working at higher ranges (105M) than Primenet (101M) for P-1 assignments. And so the work takes slightly more compute (and, thus, time).

ZFR 2020-11-24 21:07

Thanks. Going to grab some from GPU72 when the next PRP finishes next week. Let's see if I can get my name on that top 100 page.

LOBES 2021-05-13 19:55

[QUOTE=chalsall;564251]Yes.[/QUOTE]

Doh, nevermind.

chalsall 2021-05-13 21:01

[QUOTE=LOBES;578355]Doh, nevermind.[/QUOTE]

OK.

petrw1 2021-05-14 02:11

[QUOTE=chalsall;564260]There's some excellent GPU P-1 software available now. But Prime95/mprime (CPU) is by far the easiest to work with.[/QUOTE]

I agree with "easiest".

I am running GPUOwl under colab.
When I can get a P100 (which is virtually every day) I can do a 8GHz P-1 in 30 minutes.
Running a similar P-1 on all 8 cores of my i7-7820X takes about 75 minutes.

ewmayer 2021-05-14 22:36

(Somehow missed this when PaulU OPed it:)

[QUOTE=paulunderwood;563452]Congrats! However:

[CODE]? factor(499400852887245323683941126088449355702834653807158087 )

[ 290582744822559701357207 1]

[1718618403140893608084889221841 1]
[/CODE][/QUOTE]

Ha! Real men (a.k.a. execrable masochists) factor numbers like this using the world's slowest bignum code - I mean of course *nix 'bc', which IIRC uses base-10 emulation of your CPU's base-2 instructions or some such ludicrously inefficient bignum implementation - and crappy bc-based functions of their own writing:
[i]
n = 499400852887245323683941126088449355702834653807158087; p = 105032111;
pm1(n,p,10^4,5*10^6,5)
Stage 1 prime-powers seed = 105032111
Stage 1 residue A = 275242671610725931867172664303887659718570581548948384, gcd(A-1,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 prime-pairs and 113348 prime-singles [80.52 % paired].[/i]

Now back to work on my cutting-edge bc-based NFS implementation, with which I hope to someday factor numbers as large as the quantum-computer folks do: "the quantum factorization of the largest number to date, 56,153, smashing the previous record of 143 that was set in 2012."

ewmayer 2021-05-23 22:12

[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 general-modulus factoring machinery like ECM or QS on such (p-1)-found factor-product composites. Here's why: say we have some product of prime factors F = f1*f2*...*fn discovered by running p-1 to stage bounds b1 and b2 on an input Mersenne M(p) (or other bigum modulus with factors of a known form, allowing p-1 to be 'seeded' with a component of same). BY DEFINITION, each prime factor f1-fn will be b1/b2-smooth, in the sense than fj = 2*p*C + 1, where C is a composite all of whose prime factors are <= b1, save possibly one outlier-prime factor > b1 and <= b2. Thus if we again run p-1 to bounds b1/b2, but now with arithmetic modulo the relatively tiny factor product F, we are guaranteed to resolve all the prime factors f1-fn - 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 p-1 run modulo F again produce the same composite GCD = F which the original p-1 run mod M(p) did. Again, though, since in the followup p-1 run we are working mod F, all the arithmetic is trivially cheap, including the needed GCDs. And since the cost of a p-1 run is effectively akin to a single super-cheap ECM curve, we've reduced the work of resolving the composite F to just that equivalent.


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