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Old 2021-04-28, 04:07   #10
Mar 2021

4410 Posts

Originally Posted by charybdis View Post
Feitsma's data suggests a rough 4.5-times increase in the number of 2-PSPs for each additional 5 powers of 2. So the file for 2^79 would be ~90 times the size of the file for 2^64: very large for a download but not hard to store. 2^128 would of course be totally impractical. The proportion of 2-PSPs below 2^64 that are strong pseudoprimes is about 27%, and this appears to increase as the numbers get bigger, so it's not a whole load easier to only store the SPSPs.

The larger problem would be finding all these PSPs. The search up to 2^64 took tens of CPU-years. Granted, that was in 2009, and GPUs would likely be useful as it appears that the most difficult part of the search involved doing a lot of trial-factoring of Mersenne numbers. Going up to 2^79 ought to be ~2^15 times harder than 2^64 (as we just have to trial-divide 15 bits higher, right?). Even if using modern GPUs gives a speedup of factor 2^15 relative to CPUs from 2009 - others can enlighten me on what a realistic number would be - this would still suggest tens of GPU-years for a search to 2^79.

And that's before we get on to this part, where the algorithm that Feitsma used would require over a terabyte of memory, so a slower method would likely be required.
Charybdis, this is awesome to me, i'm looking for these SPRP's, is there really no place to download them at? Obcoisouly i'm hoping for sizes larger than 64 but it really seems like if i want to do this that i'm going to have to buy the hardware and make them myself

Last fiddled with by LarsNet on 2021-04-28 at 04:10
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