Leyland Primes (x^y+y^x primes) - Page 5

rogue · 2014-07-07, 15:17

Quote:

Originally Posted by wombatman

Runs great on a GTX570, but I did encounter an error as documented below:

Code:

$ xyyxsievecl64.exe -x100 -X200 -y3000 -Y10000 -P2e6 -t2 -s3000 -S+ -oxyyx.pfgw

xyyxsievecl v1.0.0, a GPU program to find factors numbers of the form x^y+y^x
Sieve started: (cmdline) 0 <= p < 2000000 with 287349 terms
OpenCL Error: Out of resources
       in call to clEnqueueReadBuffer
       argument: counter

My GPU has ~1.2GB of RAM and usually about 1GB actually available.

I have seen that as well. I haven't figured it out yet. The program doesn't use that much global GPU memory so I suspect it is a problem with local GPU memory. I have a table of powers for each kernel. I'll reduce the size of that table as it has too many zeros in it. Hopefully that will help. One other issue is that the number of factors returned might be causing problems. It could be overflowing in the GPU. I'm not certain how to avoid that without losing useful information.

As for two "-f" options, I modified factorsinrate to use -F.

If anyone can provide some speed comparisons with MultiSieve that would be nice.

I'm also working on a change to pfgw so that the factors output from sieving programs can be easily verified. I though I had done something like that already, but maybe I never released that code.

rogue · 2014-07-07, 17:38

The "Out of resources" seems to have been caused by having too many small factors. I'll do two things to address that. First, I'll increase the buffer size so that more factors can be collected. (I've also added a check so the program can tell you if you missed factors due to too many being found.) Second, I've added a "small primes" check to eliminate all terms that are factored by p < 100 before I start the GPU sieve. That can eliminate 75% of the terms up front.

wombatman · 2014-07-07, 18:36

Excellent!

rogue · 2014-07-07, 19:55

Quote:

Originally Posted by wombatman

Excellent!

By "Excellent!", do you mean this:

rogue · 2014-07-07, 19:56

Quote:

Originally Posted by wombatman

Excellent!

or this?

wombatman · 2014-07-07, 20:12

Why not both?

rogue · 2014-07-07, 20:47

Attached is the latest code. Here is what the output looks like now. This is a rather extreme range to do. It still fails if the range gets larger. I know why, but fixing is a bigger challenge. It is probably better to take smaller ranges and paste together one file and restart from there, although I haven't test the ability to restart the sieve from the output file.

Code:

xyyxsievecl64.exe -x2 -X2500 -y3 -Y7500 -P1e6 -t2 -s2000 -S+ -oxyyx.pfgw
xyyxsievecl v1.0.1, a GPU program to find factors numbers of the form x^y+y^x
Quick elimination of terms info (in order of check):
    7807501 because the term is even
    1478788 because x and y have a common divisor
    4472597 because the term is divisible by a prime < 100
Sieve started: (cmdline) 0 <= p < 1000000 with 1857365 terms
Thread 2 has completed 1818380 of 1862363 iterations
CTRL-C accepted.  Please wait for threads to completed.s/factor, 0.15 CPU cores, 25.6% done. ETA 07 Jul 15:53

Thread 2 has completed 383059 of 390048 iterations
Sieve interrupted: 3 <= p < 1000000  26624 primes tested
Clock time: 539.27 seconds at at 49 p/sec.  Factors found: 1472315
Processor time: 92.09 sec. (8.53 init + 83.55 sieve).
Seconds spent in CPU and GPU: 65.70 (cpu), 1044.80 (gpu)
Percent of time spent in CPU vs. GPU: 5.92 (cpu), 94.08 (gpu)
CPU/GPU utilization: 0.17 (cores), 1.00 (devices)
Percent of GPU time waiting for GPU: 46.87
Started with 1857365 terms and sieved to 281719.  385050 remaining terms written to xyyx.pfgw

rogue · 2014-07-07, 20:56

I think I just found another "Out of resources" trigger. Working on it.

rogue · 2014-07-07, 22:05

I fixed that one, but I still have a problem elsewhere. It is only an issue when trying to do obscenely large search spaces. I tried to implement different logic to collect factors, but my video card does not support the OpenCL functcion atom_min.

wombatman · 2014-07-07, 23:44

No problem. Like you said, smaller ranges work fine. I just wanted to point it out in case it was a larger issue than that. Very impressive work!

rogue · 2014-07-08, 12:04

Thanks. This was a very difficult program to optimize. If the range of x is large you think of optimizing in one direction. If the range of y is large, then you think of optimizing in a different direction. If both are large, then you think of a way to get the best of both worlds. Unfortunately memory and latency quickly get in the way of most potential optimizations.

Due to the bug in MultiSieve, I'm going to sieve x^y+y^x for x and y < 10000. I will also update PRPNet to support an x^y+y^x search. I don't know if I'll be able to run every term (as there will probably be close to a million after sieving), but since all of them are small it might be doable.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Leyland Primes: ECPP proofs	Batalov	XYYXF Project	17	2021-07-12 20:05
Mersenne Primes p which are in a set of twin primes is finite?	carpetpool	Miscellaneous Math	3	2017-08-10 13:47
Distribution of Mersenne primes before and after couples of primes found	emily	Math	34	2017-07-16 18:44
On Leyland Primes	davar55	Puzzles	9	2016-03-15 20:55
possible primes (real primes & poss.prime products)	troels munkner	Miscellaneous Math	4	2006-06-02 08:35

2014-07-07, 17:38	#46
rogue "Mark" Apr 2003 Between here and the 11·577 Posts	The "Out of resources" seems to have been caused by having too many small factors. I'll do two things to address that. First, I'll increase the buffer size so that more factors can be collected. (I've also added a check so the program can tell you if you missed factors due to too many being found.) Second, I've added a "small primes" check to eliminate all terms that are factored by p < 100 before I start the GPU sieve. That can eliminate 75% of the terms up front.

2014-07-07, 18:36	#47
wombatman I moo ablest echo power! May 2013 6E9₁₆ Posts	Excellent!

2014-07-07, 20:12	#50
wombatman I moo ablest echo power! May 2013 11011101001₂ Posts	Why not both?

2014-07-07, 20:56	#52
rogue "Mark" Apr 2003 Between here and the 1100011001011₂ Posts	I think I just found another "Out of resources" trigger. Working on it.

2014-07-07, 22:05	#53
rogue "Mark" Apr 2003 Between here and the 1100011001011₂ Posts	I fixed that one, but I still have a problem elsewhere. It is only an issue when trying to do obscenely large search spaces. I tried to implement different logic to collect factors, but my video card does not support the OpenCL functcion atom_min.

2014-07-07, 23:44	#54
wombatman I moo ablest echo power! May 2013 29×61 Posts	No problem. Like you said, smaller ranges work fine. I just wanted to point it out in case it was a larger issue than that. Very impressive work!

2014-07-08, 12:04	#55
rogue "Mark" Apr 2003 Between here and the 11·577 Posts	Thanks. This was a very difficult program to optimize. If the range of x is large you think of optimizing in one direction. If the range of y is large, then you think of optimizing in a different direction. If both are large, then you think of a way to get the best of both worlds. Unfortunately memory and latency quickly get in the way of most potential optimizations. Due to the bug in MultiSieve, I'm going to sieve x^y+y^x for x and y < 10000. I will also update PRPNet to support an x^y+y^x search. I don't know if I'll be able to run every term (as there will probably be close to a million after sieving), but since all of them are small it might be doable.