20180725, 11:23  #34 
Sep 2006
The Netherlands
677 Posts 
I think another important thing to note is perspective from which you write things. If you work for government you probably have a lousy GPU and relative new CPU.
However, most users at home they have a fast GPU and old outdated CPU most of the cases and your computer works for more years than at the government. Especially the CAD i'm doing requires fast GPU's and whatever sort of CPU you got is total irrelevant. Kids that game want a fast GPU and the cpu really is less relevant and has less cores in general. So the amount of times the GPU is faster than the CPU is far greater than most uni professors over here. 
20180725, 11:46  #35  
Jun 2003
1001000111111_{2} Posts 
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20180725, 11:52  #36 
Sep 2006
The Netherlands
1010100101_{2} Posts 
>or same P wagstaff is 1.5 bits smaller than mersenn. Big deal! Makes no >difference. If anything, it makes wagstaff tiny bit likelier to be prime, but that's >neither here nor there.
You seem a few lightyears away from grasping Wagstaff. Can you compare odds for a prime wagstaff versus mersenne if we just look at the last few PRP's / primes found? It's like 1.2 for mersenne to the next one and factor 3 to 4 for wagstaff. that's not a 'tiny bit' of difference. Please do not just post cheap remarks. My time is more expensive than yours. 
20180725, 13:10  #37 
Jun 2003
123F_{16} Posts 

20180725, 17:36  #38 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·7·11·59 Posts 

20180726, 13:22  #39 
Aug 2006
16EF_{16} Posts 
You can do math that way, it's called experimental mathematics. But looking at just the last few doesn't give you enough statistical power to say anything meaningful, so I agree that would basically put you back in the realm of numerology.

20180727, 16:32  #40 
Sep 2003
2,579 Posts 
So far I have lists of factors from ATH, diep, lalera, bearnol... but not from some other major efforts that were active in 2013 and earlier. Perhaps those old factor lists were not conserved. Also FactorDB up to 1M.
ATH in particular "trialfactored: 10k<p<1M to 56bit, 1M<p<2M to 57bit, 2M<p<4M to 58bit, 4M<p<8M to 59bit, 8M<p<16M to 60bit, 16M<p<32M to 61bit, 32M<p<50M to 62bit." I think TJAOI's method "by k" could also be used to generate factors for Wagstaff numbers, because they have the same 2kp+1 form. And it would probably find a lot more first factors, since Wagstaffs have only been lightly factored compared to Mersennes. TJAOI's method was described by ATH in this post. I have no idea how many resources TJAOI is throwing at the problem, but here's the timetable of when he reached each bit level, and also he finished 65 bits on April 12 of this year. But assuming you only sieve the array up to, say, 50M instead of 1G, presumably it would go a lot faster? Edit: If I'm reading it correctly, the sieving stage seems to be independent of Mersennes, it would be applicable to anything that has factors of the form 2kp+1. So if the results of that sieving were available as a list of surviving k, perhaps you'd only need to retest those same k, but this time as candidate factors for Wagstaffs instead of Mersennes? Assuming TJAOI conserved that information, of course. How practical is this idea? And is it more suited to CPUs or GPUs? Last fiddled with by GP2 on 20180727 at 16:46 
20180727, 16:36  #41 
Sep 2003
2,579 Posts 
There is a wellknown heuristic for predicting the frequency of Mersenne numbers.
Do similar considerations apply for Wagstaff numbers? 
20180727, 16:55  #42  
Aug 2006
3·19·103 Posts 
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Last fiddled with by CRGreathouse on 20180727 at 16:56 

20180727, 17:12  #43  
Einyen
Dec 2003
Denmark
B4C_{16} Posts 
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20180727, 17:30  #44 
Sep 2003
2,579 Posts 

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