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20181209, 19:50  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10001111000100_{2} Posts 
Doubts, scientific breakthroughs and conspiracy theories about Wagstaff Conjecture (from Lucky13)
It is interesting that Pomerance, Lenstra and Wagstaff looked for heuristics when MP set was only known up to p<100,000. (ca. 1983)
Might there be some better summation techniques for the excluded factor probability corrections now? Those look pretty rough in the 1983 heuristic. E.g. the summation stops at 2k or 6k, but there are many more excluded divisors whose contributions to the correction alone are increasingly small but as a mass they can contribute significantly. 
20181210, 21:22  #2  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
4,703 Posts 
Quote:


20181210, 22:10  #3 
If I May
"Chris Halsall"
Sep 2002
Barbados
10010001101010_{2} Posts 

20181210, 23:15  #4 
Jun 2010
2^{2}·53 Posts 

20181211, 07:26  #5 
P90 years forever!
Aug 2002
Yeehaw, FL
2×3×1,193 Posts 

20181211, 13:09  #6 
Banned
"Luigi"
Aug 2002
Team Italia
13·367 Posts 
Question:
How (im)probable is to find such a cluster of Mersenne primes grouped together instead of laying on the linear regression line?

20181211, 13:23  #7  
Sep 2003
29×89 Posts 
Quote:
There is most likely only one prime in the 1 million to 10 million range, pending a verification run which has reached 6 million so far. 

20181211, 20:12  #8 
∂^{2}ω=0
Sep 2002
República de California
3·5^{2}·131 Posts 
I don't think "clustered" is the right word ... the last 12 simply appear to lie on a differentsloped regression line than the previous ones, which more or less followed the Wagstaffheuristic prediction. (I believe I can post this logplot w/o giving away too much re. the latest find ... but in any event we already have 1 independenthw/sw confirmation, so it's not a false positive).

20181211, 22:46  #9  
Sep 2003
29×89 Posts 
Quote:
We could do better than that of course. Simply identify the software that created the plot and start plotting points, varying the exponent value until you come up with a pixelbypixel reproduction of the plotted box pattern, including the pale shading and blur (sorry, I don't know the correct graphics terminology). Last fiddled with by GP2 on 20181211 at 23:15 Reason: final refinement of estimate 

20181211, 22:57  #10  
If I May
"Chris Halsall"
Sep 2002
Barbados
10010001101010_{2} Posts 
Quote:
Just to put on the table, I wish that people "in the know" would refrain from dropping hints. Many times in the past errors have been made (sometimes in combination with other hints) which narrowed down the possibilities to be far too fine for comfort.... 

20181211, 23:12  #11 
∂^{2}ω=0
Sep 2002
República de California
2661_{16} Posts 
I would be interested in some discussion of the statistical significance ascribable to the apparent trendline break of the last dozen Mprime exponents. Chris Caldwell's "this graph is amazingly linear" is getting more untenable with each new soonerthanexpected find.

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