Sunny King
Primecoin Mining Research
http://www.peercointalk.org/index.php?topic=813I am not sure if the Primecoin forum is very active, therefore I am posting my response to the posting above here also.
@Sunny
I am new to Primecoin but by no means new to Number Theory. I briefly looked at the source code of the latest version of mikaelh2's enhancements and I did not see much room for improvement. Using GMP for the modular exponentiation seems to be the biggest improvement. You can use the mod 60 wheel (sieve of Atkin) for the sieving step but I do not see that improving the overall run-time by any significant amount. The bottle neck is with the modular exponentiation of large numbers and Montgomery multiplication can be used to reduce multiplication time. But off course, Montgomery multiplication has its drawbacks, you are working with many different residue classes.
So now, there are two possible directions for the research of finding longer chains faster. The first direction is to continue making incremental improvements to the sieving and modular exponentiation arithmetic (brute force). And the second direction (which I prefer) is to analyze all of the data collected so far and come up with better arithmetic for finding longer chains. I assume that this was the reason that made Primecoin unique, otherwise it is no different from Bitcoin mining.
Unfortunately, carrying out the research to analyze collected data will require funding. I have been running "Primecoin version v0.1.2.0xpm-hp11-unk-beta" for 4 days now on a 32/64 core/thread server and I have only mined a block (primemeter 43807850 prime/h 663367364 test/h 180 7-chains/h 8.075400 chain/d). I just cannot see how anyone, other that people who have access to botnets, can be profitable at mining Primecoin.
Also, I am currently working on a GPU (Nvidia CUDA/PTX) off-load engine for the modular exponentiation (Montgomery) for the Primecoin miner. A GTX 580 should have the same throughput as all 32 cores/64 threads combined when performing Montgomery modular exponentiation. The sieve (of Atkin) will remain on the CPU to maximize performance.
@All
You can donate to the address below if you will like to see this research progress.
ALAxNNtF2hBPUpXFdN8Xexp1HbKwh4JeEK (Primecoin)
1MCqoWLA3eyqovRXKCydoDSfNN8C28y3k2 (Bitcoin)