20180801, 20:10  #56 
"Robert Gerbicz"
Oct 2005
Hungary
1,531 Posts 
Not going into this deep numerology staff, but we have already a lot of results, if I understand correctly the search for Wagstaff prime is complete up to p=15e6, the Mersenne prime search also reached this. We have 43 Wagtsaff prime, and **only** 39 Mersenne prime up to p=15e6, so what would you search? My 2 cents: probably the density is the same (a similar heuristic what used for Mersenne could work here), ofcourse the big drawback for Wagstaff that we have no (known) fast primality test.

20180801, 20:15  #57  
Sep 2006
The Netherlands
30E_{16} Posts 
Quote:
Distance between each wagstaff and the next one simply is factor 3 nearly. 

20180801, 20:23  #58 
"Robert Gerbicz"
Oct 2005
Hungary
1,531 Posts 

20180801, 20:26  #59 
Sep 2006
The Netherlands
2·17·23 Posts 
You ignore what i wrote.
To find the NEXT one, even if 3 prp's lurk nearby, you want to know the DISTANCE you need to search to find 'em. 3 x 13M = 40M 
20180802, 01:04  #60  
Sep 2003
5×11×47 Posts 
Quote:
For Mersennes, the highest ratios are: Code:
521 / 127 = 4.10 756839 / 216091 = 3.50 For Wagstaffs, the highest ratios are: Code:
1709 / 701 = 2.44 42737 / 14479 = 2.95 986191 / 374321 = 2.63 4031399 / 986191 = 4.09 13347311 / 4031399 = 3.31 Those three very high ratios in a row do seem anomalous. But can we be certain they are real? Maybe I'm mistaken, but I think the large rangers were tested with programs that assumed the VrbaReix conjecture is correct. If there are counterexamples to this conjecture, then maybe some Wagstaff primes were missed? Quote:
Today mprime can do PRP testing with Gerbicz error checking, and it does not depend on VrbaReix being true. And we have faster CPUs with more cores, and faster GPUs that can find more factors. I am seriously considering throwing some resources into Wagstaff testing old ranges using mprime. I don't know how far it would go, but the goal would be to publish the PRP residues and a consolidated list of new factors and old factors from multiple available sources, as a permanent verifiable record. Sadly, there don't seem to be too many published results from the 2013 efforts, other than the primes that were found. Some lists of factors were published, but others are harder to track down and might even be lost. Ideally, the PRP residues should be recorded with a lot more than 64 bits. If the only goal is doublecheck verifiability, then 64 bits is plenty; however, larger residues might let us do quick PRPcofactor checking for newly discovered factors. (I presume the analysis at the linked page for Mersennes applies similarly for Wagstaffs, or is "inv" different?) So, at least 512 bits, or with an eye to future decades, who knows, maybe even 2048. Storage is very cheap. I'm not aware of any undoc.txt setting for mprime that would output residues larger than 64 bits, but hopefully it would be straightforward to add. 

20180802, 10:10  #61 
Sep 2006
The Netherlands
2×17×23 Posts 
Yeah you are mistaken.
Things at million bit size really works different than at a handful of bits. If you want to search in the dozens of millions bit range and then basing your expectation to find something upon a handful of bits for that, makes no sense at all. Last fiddled with by diep on 20180802 at 10:19 
20180802, 11:22  #62  
Banned
"Luigi"
Aug 2002
Team Italia
2×41×59 Posts 
Quote:
If a Law works in math, the number of involved bits does not matter. 

20180802, 11:57  #63 
Sep 2006
The Netherlands
1100001110_{2} Posts 
it's about the short term expectation how much of a computational work you need to throw in to find the next gem.
Whether you find 1 or a million doesn't matter  you first have to do that huge computational effort to find at least 1. So the way how the PRP's have been spread also matter quite a lot. Last fiddled with by diep on 20180802 at 12:01 
20180802, 14:00  #64 
Sep 2002
Database er0rr
3^{2}·443 Posts 
If one was searching for Wagstaff cofactors then they can be PRP'ed over 2^p+1 before a final modular reduction. I guess Prime95 does this.
Last fiddled with by paulunderwood on 20180802 at 14:05 
20180802, 14:33  #65 
Aug 2006
3·1,993 Posts 
So in summary:
diep: We should ignore everything but the big numbers, numbers at millions of bits aren't like numbers with just a few bits. The big Wagstaff exponents are spread very thin. GP2: You're throwing out most of the data, if you look at the broader picture you see the Wagstaff exponents aren't that thin. Also, the higher ranges might have missed some primes because searches relied on a conjecture. 
20180802, 15:05  #66 
Sep 2006
The Netherlands
2×17×23 Posts 
You mean missed above 10M until 13M?
Possible. Until 10M you won't find anything new. A 3PRP will find anything of course there for both mersenne and wagstaff. Doing a 27PRP test which the conjecture uses is pretty obvious the same thing like doing a 3PRP at least. So it won't miss anything. Whether it is a method to prove them prime  that i leave up to the theoretists with enough time :) 
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