20210427, 19:28  #1 
Mar 2021
2^{2}×11 Posts 
Where can i find huge lists of primes up to as close to 2^128 as possible of SPRP's
For example i can find 2SPRP2to64.zip at https://millerrabin.appspot.com/ Are there any other repos or places i can find large numbers like this. Wikipedia often mention tests at higher than 2^64 but fails to link to them, i'm wondering if anyone here knows of any places to find numbers like these to test against.
Also, if such lists don't exist publicly, if i wanted to make a 2SPRP2 list to say 2^79, what would be the minimum investment required to do something like this and what kind of equipment what be needed. Last fiddled with by LarsNet on 20210427 at 19:45 
20210427, 20:49  #2 
Sep 2002
Database er0rr
3,853 Posts 
I would imagine a list up to 2^65 would take twice as much disk space as the list up to 2^64. Thus such a file would be 2^64 times as big as the the list up to 2^64. That would be about 1,000,000,000,000,000,000,000 Gigabytes.
Last fiddled with by paulunderwood on 20210427 at 20:49 
20210427, 22:15  #3  
Mar 2021
2^{2}×11 Posts 
Quote:
Code:
$ ls al 2SPRP2to64.txt rwrwr 1 user user 663879564 Apr 19 2011 2SPRP2to64.txt 

20210427, 22:57  #4  
"Curtis"
Feb 2005
Riverside, CA
1001110000000_{2} Posts 
Quote:
I think you'd be better off generating such a list live and testing them as they're generated. I'd rather spend 100x running time than 100x disk space! Of course, I've no idea how fast they are to generate vs read from disk, nor how many times you'll want to use the list maybe you should find out before you buy 20TB of storage. Last fiddled with by VBCurtis on 20210427 at 22:57 

20210427, 22:57  #5 
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{2}×11^{2} Posts 
This website allows the input of up to 128 digits of the numbers to test for its primality, the format can be composed of a short formula as well 
https://www.numberempire.com/primenumbers.php Last fiddled with by tuckerkao on 20210427 at 23:00 
20210427, 23:00  #6 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2×19×263 Posts 

20210427, 23:00  #7 
Apr 2020
17·29 Posts 
Feitsma's data suggests a rough 4.5times increase in the number of 2PSPs 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 2PSPs 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 CPUyears. 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 trialfactoring of Mersenne numbers. Going up to 2^79 ought to be ~2^15 times harder than 2^64 (as we just have to trialdivide 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 GPUyears 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. 
20210427, 23:04  #8 
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{2}×11^{2} Posts 
I have a formula that can generate some 128 digits primes with each smaller prime, but I still haven't figured out a way to generate large amount of primes with very short period of time.
I only have around 200 of them. The examples use 103374113, I can always substitute that number with another prime of the similar size, then try to adjust the 2^m and 3^n. Last fiddled with by tuckerkao on 20210427 at 23:12 
20210427, 23:11  #9 
Sep 2002
Database er0rr
3,853 Posts 
The OP is interested in (strong) pseudoprimes not primes
Last fiddled with by paulunderwood on 20210427 at 23:28 
20210428, 04:07  #10  
Mar 2021
2^{2}·11 Posts 
Quote:
Last fiddled with by LarsNet on 20210428 at 04:10 

20210428, 04:20  #11 
Romulan Interpreter
Jun 2011
Thailand
2^{4}×13×47 Posts 
What's the purpose of such a list? You can check the primality of any such small N extremely fast, by doing few divisions (very low TF) and then 1, or 2, or few PRP tests. That is because somebody else already did all the work for you, and such tests at this size take microseconds on a modern computer. That would be much faster than reading from a manyGBsized file.

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