20180103, 15:17  #34  
Einyen
Dec 2003
Denmark
3^{4}·5·7 Posts 
Quote:
https://www.mersenne.org/report_expo...ll=1&ecmhist=1 

20180103, 15:20  #35  
Jul 2003
535_{16} Posts 
Quote:


20180103, 15:48  #36  
Sep 2003
2·1,289 Posts 
Quote:
However, it would be truly astounding if the curve does anything other than cluster around a straight line over the long term. There is no proof, but persuasive heuristic arguments: https://primes.utm.edu/notes/faq/NextMersenne.html 

20180103, 16:25  #37 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
2^{2}·37·61 Posts 
In many similar series, there is the same gammabound slope, as well as a lot of misleading noise. Human eye is 'trained by nature' to see patterns even where there are none.
http://mersenneforum.org/showthread....478#post470478 
20180103, 21:31  #38  
∂^{2}ω=0
Sep 2002
República de California
2·5,581 Posts 
Quote:


20180104, 08:31  #39  
Dec 2017
2×5^{2} Posts 
Quote:


20180104, 08:33  #40  
Dec 2017
32_{16} Posts 
Quote:


20180104, 08:37  #41  
Dec 2017
2×5^{2} Posts 
Quote:
Last fiddled with by George M on 20180104 at 08:38 

20180814, 19:47  #42  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{2}·3·11·29 Posts 
Quote:
And, note that M1626 while not as remarkably low or seemingly uniform a slope as the M4050 run, is equal in run length, and M1213, M2628, M3132, M3740 are noticeably higher slope than the overall trend. We may be in for a drought. And that all of that has precious little predictive value. Adding another order of magnitude at the top of the chart appears to be the work of about a GIMPScentury. It would be interesting to see what a discrete Fourier analysis of the sequence would say. I think Chris Caldwell's pages say it's consistent with what one statistically expects. 

20180814, 20:32  #43  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{2}·3·11·29 Posts 
Quote:
The list of known Mersenne primes is available at https://www.mersenne.org/primes/ and many other locations, only a reasonably effective web search away; M50 ~77.2M. There's also periodic press coverage when a new one is found, in which the new world record exponent is typically given Current routine assignments for primality testing are around exponent 81 million, more than a factor of 12 lower than a billion. It takes of order a year with a fast gpu (~GTX1080) and best available software to primality test a single gigabit Mersenne. Preparatory optimizedduration TF and P1 factoring attempts can take weeks or months per exponent on lesser hardware (midstream gpus, or multiplecpucore workers). The latest prime95 readme states the maximum exponent that can be primality tested is 596 million. As I recall, the highest known completed primality test was part of a group of exponents around 604 million. A quick scan of the work distribution map at https://www.mersenne.org/primenet/ confirms that, and shows that except for a clump of hundreds for exponents around a third of a billion, primality tests above exponents of a hundred million are rather rare. I've put considerable effort into documenting what the capabilities and limitations are of the most popular Mersenne prime hunting software, and other reference material for gpu computing mostly, and posting links to the tabulation. Nothing implements primality testing beyond a 64M fft length (~1.14 billion), because the run times are too unacceptably long. The reliability of the code in the higher reaches is doubtful, both because it sees little use, and there are documented issues from very limited purposeful brief testing. It takes an estimated century at our current rate to advance the GIMPS wavefront to near a billion for a primality test. There were numerous available indications that guessing the next Mersenne prime to be found is in the multiple billions and proposing to test such large exponents was off the mark, in multiple ways, including other posters' reactions to your posts. Somehow all those got missed, ignored, dismissed, or misinterpreted, while the fixed misconception of known prime exponent ~ a billion remained not sufficiently questioned. It could be useful to look at that process and learn from it. 

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