Pascal's OPN roadblock files

[ryanp]

Originally Posted by Pascal Ochem

There is already a file t2200 of first-encountered composites replacing t2100.
There will be a last update of mwrb2100 in a week or two, only to see the impact of your nearly 300 factors.
There will be a file mwrb2200 in 2 or 3 months if nothing goes wrong, which will imply OPN > \(10^{2200}\).

I assume you have a FactorDB scraper, but I also posted the full list of factors found so far (276 right now) to https://cs.stanford.edu/~rpropper/mwrb2100_factors.txt. I'll update periodically.

[lavalamp]

If no-one has any objection I will run some ECM on the t2200 file at the 35 digit level, B1=1E6. I already ran 128 composites at the beginning of the file and found a few factors, but I've decided to switch to a bottom up approach now.

Sadly, ECM-GPU seems restricted to composites less than 2^1018 in size, which limits me to the first sixth or so of the file.

The last number I can run is:

33100272759546513743540025392907714658971195397577775668521338093978667943386009924363532641^5-1

I will start here and work back up to the start. I expect this to take at least a month on a single RTX 2070, so if I'm lucky it might complete by Christmas.

If anyone knows where I might get a more up-to-date binary for Windows for ECM-GPU I'd appreciate it, pretty sure the version I'm using was compiled before the 20 series cards were even released, so perhaps there's some speedup to be gained.

[lavalamp]

Follow up question, I just took a 41 digit bite out of this number.

Should I keep going on it and run the rest of my curves? How much is factored enough?

At the moment I've set ECM to quit a number and move on if it finds a factor without finishing the block of 1152 stage 1 curves that were done on the GPU, but should I finish them off in case another factor pops out?

[Pascal Ochem]

mwrb2100 will be updated soon, but I can already tell that the weight of sigma(6115909044841454629^16) drops from 65263134 to 60351951.

Originally Posted by mathwiz

What is the "most important" thing to contribute to now? t2200 or mwrb2100?

Both! However, ECM on mwrb2100 will not be very fruitful: even with Ryan's computing power, you will only get a few ECM misses.

Originally Posted by lavalamp

Should I keep going on it and run the rest of my curves? How much is factored enough?

Indeed, prime cofactors are better to get a lower bound on N, so running curves on the cofactor makes sense.
For a lower bound on \(\Omega(N)\), we prefer to get a composite cofactor, since it means more prime factors.
And if we are confident that the composite cofactor has only 2 prime factors, than factoring it is not necessary since
it wouldn't change the factor count nor the smallest available prime that we branch on.

By the way, a run for proving \(\Omega(N)\ge 111\) has recently finished without trouble.
So an odd perfect number has at least 111 (not necessarily distinct) prime factors. This improves the bound \(\Omega(N)\ge 101\) from 2012.

[ryanp]

Originally Posted by Pascal Ochem

mwrb2100 will be updated soon, but I can already tell that the weight of sigma(6115909044841454629^16) drops from 65263134 to 60351951.

I'm still poking at the current mwrb2100 a bit. I guess when new mwrb2100/mwrb2200 are ready, you will make an announcement here?

[lavalamp]

Originally Posted by lavalamp

I will run some ECM on the t2200 file at the 35 digit level, B1=1E6

Due to the slow rate but large size of the factors that have been popping out for me so far, I've decided to restart this at the 40 digit level, B1=3E6. It will clearly not be done by Christmas now, it will take at least 3 months. Though to really complete the search I should run a second pass for a total of 6 months, we shall see.

Despite what I just said, I'm also running a "low-hanging-fruit" pass over the remainder of the 58185 of 71669 composites in the t2200 file that are too big for GPU stage 1. Just 8 curves each at the 25 digit level which should only take a couple of days. I don't expect to find much, but the machine was idle so why not.

[henryzz]

Originally Posted by lavalamp

Due to the slow rate but large size of the factors that have been popping out for me so far, I've decided to restart this at the 40 digit level, B1=3E6. It will clearly not be done by Christmas now, it will take at least 3 months. Though to really complete the search I should run a second pass for a total of 6 months, we shall see.

Despite what I just said, I'm also running a "low-hanging-fruit" pass over the remainder of the 58185 of 71669 composites in the t2200 file that are too big for GPU stage 1. Just 8 curves each at the 25 digit level which should only take a couple of days. I don't expect to find much, but the machine was idle so why not.

Whatever you do I would suggest not doing the full ecm for each level. Doing half a level gives 39.3% chance of finding a factor at the level(and more for smaller). The full level is 63.2% so the second half is only around half as efficient at covering the remaining factors at the level and a little below the level even worse. Better would be running something like half of each level or something like t40 made up of half the curves at 3e6 and half at 11e6. This will be a little slower but will have a greater probability of finding a factor overall as a larger chunk of t45(the higher probability bit) will have been done.
It will depend on your system, the size of the number and what software you use but 11e6 might not be slower for t40 than 3e6. They run about the same speed in the tests I just ran. I would suggest looking at AVX-ECM for stage 2(assuming it accepts the curve type that GPU-ECM uses).

[lavalamp]

Originally Posted by henryzz

It will depend on your system, the size of the number and what software you use but 11e6 might not be slower for t40 than 3e6. They run about the same speed in the tests I just ran. I would suggest looking at AVX-ECM for stage 2(assuming it accepts the curve type that GPU-ECM uses).

I will definitely look into AVX-ECM, hopefully there are some EXEs for Ryzen/Windows to be had.

The way I am running these curves at the moment is I have a RTX 2070 GPU running stage 1 (with a VERY old binary ) and 1152 curves in parallel, then I have a 3900X CPU that very approximately tries to keep pace with the GPU by setting the B2 bound appropriately.

I was a bit greedy and set B2=14e9 so the CPU is running somewhat slower than the GPU at the moment, but it should speed up when it gets to the smaller composites.

Since the run time of stage 1 on the GPU is essentially linear w.r.t. B1 that essentially means that B1=11M will take 3.67 times as long as B1=3M. A full pass of that would basically take a year to run about a quarter of the required curves to complete that level.

Edit: Looks like AVX-ECM requires AVX512 support, which is only available on a select few Intel platforms thus far.

[henryzz]

I was under the impression that there was codepaths for lesser CPUs.

[Pascal Ochem]

Originally Posted by ryanp

I guess when new mwrb2100/mwrb2200 are ready, you will make an announcement here?

The old and new mwrb2100 are here:
http://www.lirmm.fr/~ochem/opn/old_mwrb2100.txt
http://www.lirmm.fr/~ochem/opn/mwrb2100.txt

The run for 10^2200 started 17 days ago and is about halfway through. No problem so far.

[henryzz]

Originally Posted by Pascal Ochem

The old and new mwrb2100 are here:
http://www.lirmm.fr/~ochem/opn/old_mwrb2100.txt
http://www.lirmm.fr/~ochem/opn/mwrb2100.txt

The run for 10^2200 started 17 days ago and is about halfway through. No problem so far.

Can some parts of the proof be easily pushed further than others. Is the majority of the runtime excluding one or two of the primes?
Obviously, the later parts assume the earlier parts.