CEMPLLA: An alternative to GIMPS ?

[Uncwilly]

Originally Posted by CEMPLLA Author

Thanks again, Optimus ;)

Looks like I've got my work cut out for me.

The .info site is out dated.
You may want to check out Mersenne.ca
e.g. http://www.mersenne.ca/exponent/brow...0001/332229999
Everything from 332192831 to 332459011 has been trial factored to at least the 74 bit depth (except those that have had a lower factor found).

In the range to 332999959:
Everything has been taken to 73 bits.
Of those over 1,500 are at a depth of 77 bits or higher.
Over 640 have had P-1 factoring done on them.
With P-1 factoring, factors have been found in the range above 84 bits (many lower ones too) out to 106.9 (call it 107).
We have found over 1200 factors that your program is not capable of finding.

[chalsall]

Originally Posted by Madpoo

I just installed this on my sandbox and watched the network traffic. I guess it's not encouraging to me that everything happened over SSH. Yes... SSH, port 22.

LOL... What an idiot.

At least use port 443. Or port 80 with a less-than-obvious data-path within.

[Uncwilly]

Originally Posted by science_man_88

I tried roughly timing the second one on my PC trying it out anonymously ( avast didn't seem to detect anything after download or after install but it did do a deep scan when it loaded it) p=332,290,529 had something like 223 candidates per minute without screen updates disabled and roughly 227 per minute with it disabled. though like you said no obvious k were skipped as far as I could tell.

There is a 51 bit known factor of that number.

I checked 332,290,807 (the next number with no known factor). It took Prime95 (32 bit version) 15 minutes to get through all bit levels up to (and including) 65, running on a single core on my 2.4 GHz Core2Duo laptop.

[science_man_88]

Originally Posted by Uncwilly

There is a 51 bit known factor of that number.

I checked 332,290,807 (the next number with no known factor). It took Prime95 (32 bit version) 15 minutes to get through all bit levels up to (and including) 65, running on a single core on my 2.4 GHz Core2Duo laptop.

I stopped it and it seems a new exponent was given every time I loaded it so other than playing around with it I'm not really sure what I want to try with it.edit: I mean actually reloading the program but this last time I played around it took four tries just to select optimal exponent.

[Primeinator]

Originally Posted by CEMPLLA Author

"Bilirubin" is a little-known neural antioxidant - it inhibits the growth of viruses in the human brain.

Not related to the current discussion BUT

I found this claim very interesting especially considering bilirubin is widely considered in the medical literature to be neurotoxic particularly cases of kernicterus in newborns. I found a couple of papers that seem to support the idea of it acting as an antioxidant in the central nervous system involved in a redox reaction with biliverdin to prevent excess oxidation of lipids- a parallel to the glutathione system that protects proteins from excess oxidation. At least one paper was in a fairly respected journal. I've not had the time to read the methods section yet. The cited sources are also interesting and may provide additional supporting evidence. The cited example of Gilbert Syndrome is especially interesting. That paper is cited from Atherosclerosis and indicates that these individuals have a 1/3 reduced incidence of cardiovascular events compared to the general population. I would like to read that paper as well when I find the time. I was also able to find a couple of papers that support at least in vitro evidence of antiviral activity of bilirubin- at least against some herpes viruses and enteroviruses; however, it goes without saying that even good in vitro studies do not always translate well to in vivo studies. This will definitely require more reading! Thank you for this interesting bit of potentially paradigm-challenging information. Whether further research supports a physiologic and clinical significance for bilirubin's antioxidant effects remains to be seen but it is nonetheless intriguing.

If anyone is interested I can provide names for some of the papers I found. A couple are free text articles while others require subscription to the journal itself or membership at an institution that provides access.


Back to topic:

I do not mean to disbelieve your good intents with your program; however, I would like to inquire as to why you have yet to answer these questions from Gordon. These seem like perfectly reasonable questions even if they are presented in a manner that could be perceived as mistrusting. If you have noticed these questions then your failure to address them is suspicious. If you have not noticed them before then here is your chance to address them. I won't pretend to know the significance of Madpoo's post about port 22. I will be the first to confess that I am ignorant when it comes to computer science, coding, and networks- so ignorant, in fact, that I am almost assuredly using the wrong terms!

1. Explain why it must be run as administator
2. Explain why virus checking must be disabled
3. Explain why wddm whatever must be turned off. - especially when Nvidia recommend you leave it turned on.
4. What web sites the software will try to connect to, where it is hosted and who the registrant is[
5. SOURCE code - because at the moment you simply come across as trying to get us to install your bitcoin mining software or even who knows what.

[owftheevil]

The author of this software has either written his own ffts, is using some unknow new method to perform the squaring step of an LL iteration, or is exagerating the capabilities of his software. NVIDIA's ffts are capable of handling LL tests for Mersenne numbers up to around 200,000,000 decimal digits (as far as I can remember,) but definitely not 1 billion digit numbers.

[kladner]

This exchange is fascinating.

[Madpoo]

Originally Posted by Batalov

...One can only imagine if CEMPLLA is implemented with equally profound thinking as MPCG.

I for one would LOVE to see some benchmarks of CEMPLLA on 5 GPUs doing that first 100M digit exponent.

To the program author: Check out a thread on here, the 100M benchmark discussion:
http://www.mersenneforum.org/showthread.php?t=13185

My personal best is a time of 45 days for M332220523, but that's on a dual 14-core Xeon with pretty good DDR4 memory. All 14 cores on CPU #1 and I think it was 4-5 cores on CPU #2 thrown in.

There was someone else who did even better (I think) with a similar setup but dual 18-core Xeons.

If CEMPLLA could beat that, even on a "modestly priced $25,000 Nvidia times 5 system", you might be off to a good start.

Remember though that not all Nvidia GPU's are equal. Besides requiring 5 of them (why 5?) you might also understand that some of the newer ones don't do so well at FP64. They'd be better suited to eliminating Mersenne #'s through factoring which they are still wicked awesome at.

[LaurV]

Originally Posted by CEMPLLA Author

Each of these "K Factors" are tried, one by one, in numerical order by the MPCG program. It starts with a K Factor of one, and increments the "Current K Factor" by one for each "iteration". And, of course, it keeps track of the "Current K Factor" for each candidate.

[just to make it clear, I have read all the posts in the thread that were posted after OP's post that I quoted - this is important, you tell me why! hehe]

The method you describe is EXTREMELY inefficient. Letting apart the fact that inventing your own notation scores high on the crankometer. There is a dedicated notation for all this stuff. For a first step, think about the fact that any possible factor of a mersenne number with an odd exponent can only be 1 or 7 (mod 8). As p is a prime (an odd prime), it can only be 1 or 3 (mod 4). Now, if k is 2 (mod 4), you get q=2*k*p+1, compute this (mod 8), for both cases when p=1 or 3 (mod 4). You will get q=2*2*(either 1 or 3)+1=(either 5 or 13) (mod 8) which is always q=5 (mod 8).

So, k=2, 6, 10, 14, 18, 22, etc can NEVER occur in a q which is a factor of a mersenne number m=2^p-1, for a prime p.

By excluding k=2 (mod 4), which is one case in 4, your factoring program can be 25% FASTER. (now it is 33% slower, think about it! Like in forex trading, if you have $100 and lose $20, then you are 20% less, but now you have $80 and you will need to gain 25%, i.e. $20, to break even, percentages are odd )

Now again, you can continue splitting, if p=1 (mod 4), and k=1 (mod 4), you get q=2*1*1+1=3 (mod 8), another unacceptable case.
If p=3 (mod 4), and k=3 (mod 4), you get q=2*3*3+1=19=3 (mod 8), another unacceptable case.

So, you can DOUBLE the output of your factoring program by testing the modularity of p to 4 (which is extremely easy, just read the last two bits of the memory representation of your number) and if p=1 (mod 4), only test for k=3, 4, 7, 8, 11, 12, etc, i.e. k=0 or 3 (mod 4) - eliminating 50% of the cases, and if p=3 (mod 4), only test k=1, 4, 5, 8, 9, 12, etc, i.e. k=0 or 1 (mod 4), eliminating 50% of the cases also, from the start.

Here you are, what George said that you can DOUBLE the output of your software, he was right, even if you didn't believe him.

Try playing a bit with mfaktX on your GPUs. That program(s) in discussion take the "splitting" mentioned above and sieving to much higher levels, doing modularity not to 4 or 8, but to 420, or 4620 (why? can you tell what the reason for these numbers?), this way eliminating more than 95% of the "k" candidates. This way, they are already 20 TIMES FASTER than your factoring program even if they would run on the same hardware and even if they would not have another million optimizations.

So, how can you compete? How can you convince us to use your program?
Also (now playing the "credit whore" card!), everybody knows I am here for the credit and for the money, the first I get from GIMPS and the second - if I am lucky - I will get from George yarrrr...
What do you offer to convince me to run your program, beside of a much slower progress and much higher electricity bill for me?
(no, it is not rhetoric!)

[Uncwilly]

Originally Posted by Madpoo

How efficient it is on a CPU, I don't know. I got the assignment to factor 2^3,321,928,381-1 which tells me there are over 2.7 billion "k-factors". I got up to 100 or so by the time I exited the app.

It's not too efficient with CPU. On a 4-core system it was using 25%, so it's not multithreading at any rate, and it's not affined to a single CPU. The active core jumped around quite a bit.

So just for the fun of it, I fired up Luigi's old Factor5 program on my 2.4Ghz Core2Duo laptop and gave it 1 core to use (while letting Prime95 have 1 core and surfing the web). I fed it 3,321,928,381, setting it to take it to 64 bits from 1 bit (I know, but I just used that as a test.) It took it 7 minutes 40 seconds.

D:\prime\factor5-win32-win64-src>factor5 3321928381 1 64 1

Factor5 v. 5.01 - December 27th, 2007 - Pentium4/Win32 compile - GMP 4.2.1_MPIR_1.0.0

Current date Wed Sep 16 22:49:32 2015

Factoring M3321928381 from 2^1 to 2^64   0.993% completed.
Factoring M3321928381 from 2^1 to 2^64   7.537% completed.
Factoring M3321928381 from 2^1 to 2^64  13.824% completed.
Factoring M3321928381 from 2^1 to 2^64  20.221% completed.
Factoring M3321928381 from 2^1 to 2^64  26.802% completed.
Factoring M3321928381 from 2^1 to 2^64  33.309% completed.
Factoring M3321928381 from 2^1 to 2^64  39.670% completed.
Factoring M3321928381 from 2^1 to 2^64  46.287% completed.
Factoring M3321928381 from 2^1 to 2^64  52.868% completed.
Factoring M3321928381 from 2^1 to 2^64  59.486% completed.
Factoring M3321928381 from 2^1 to 2^64  66.067% completed.
Factoring M3321928381 from 2^1 to 2^64  72.611% completed.
Factoring M3321928381 from 2^1 to 2^64  79.155% completed.
Factoring M3321928381 from 2^1 to 2^64  85.736% completed.
Factoring M3321928381 from 2^1 to 2^64  92.354% completed.
Factoring M3321928381 from 2^1 to 2^64  98.935% completed.
No factor found

Performed    110261547 powmod operations since last restart.
Used 110839 primes, max. prime = 1452991
Current date Wed Sep 16 22:57:12 2015

D:\prime\factor5-win32-win64-src>

BTW, if someone wanted to check the status of that number (it has been tested to 83 bits), they could go to the Operation Billion Digits page here. The OBD forum would also be a good place to check for factors. I submitted a large number of factors to Will Edgington a while back. I guess our friend already knew that because:

I've already incorporated all of the published (on the internet) known factors for both types of primes into the CEMPLLA database, and will continue to do so as they are published. Some are actually larger than CEMPLLA is even capable of finding, because CEMPLLA is limited to 64-bit modulus arithmetic. But they're in there nonetheless, appropriately marked as "too large" (i.e. "too large to display", but there was no room in the text box to fit all that in)..

[Uncwilly]

Originally Posted by CEMPLLA Author

MPCG has factored another 100 million decimal digit prime candidate since my last post

Originally Posted by Uncwilly

Give us a rough range for that number, the bit size of the factor, and how much time it took the program to run that exponent from the which bit level until it found the factor. I could set a Core2Duo off finding factors at a rather steep rate, if I chose to.

So I decided to play with this. I set Prime95 to factor the first 500 potential numbers, in the 100M digit range, from 1 (actual it is 29) to 50 bits. One a single core, it took under 2 minutes (it may be closer to 1 minute flat). I found lots of already known factors.

How does your program stack up to that?

BTW, the stats for my machine are posted above.