mersenneforum.org Predict "M51" (discussion)
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2018-01-03, 15:17   #34
ATH
Einyen

Dec 2003
Denmark

2×13×109 Posts

Quote:
 Originally Posted by GP2 Edit: in case anyone is wondering what happened with M37,156,667, apparently it was churned several times and the eventual discoverer only ran his computer for 6 to 8 hours a day to save electricity:
Even more wierd that it has many factoring and P-1 attempts AFTER it was proven prime, even 3 times by CurtisC:
https://www.mersenne.org/report_expo...ll=1&ecmhist=1

2018-01-03, 15:20   #35
masser

Jul 2003

3·443 Posts

Quote:
 Originally Posted by ATH Even more wierd that it has many factoring and P-1 attempts AFTER it was proven prime, even 3 times by CurtisC: https://www.mersenne.org/report_expo...ll=1&ecmhist=1
Testing the factoring software?

2018-01-03, 15:48   #36
GP2

Sep 2003

2×1,289 Posts

Quote:
 Originally Posted by Uncwilly 521 and 127 are small numbers compared to what we are working on now. Who knows, maybe our new level of success is the norm. It could be that the curve bends lower....
I don't think it matters that those are relatively small numbers. In any case, there is also 756839/216091 = 3.50

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

 2018-01-03, 16:25 #37 Batalov     "Serge" Mar 2008 Phi(3,3^1118781+1)/3 100011001111012 Posts In many similar series, there is the same gamma-bound 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
2018-01-03, 21:31   #38
ewmayer
2ω=0

Sep 2002
República de California

3×5×743 Posts

Quote:
 Originally Posted by Batalov In many similar series, there is the same gamma-bound 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
Still, you gotta admit the run of 10+ which seem to conform to a significantly shallower log-line slope is rather remarkable.

2018-01-04, 08:31   #39
George M

Dec 2017

2×52 Posts

Quote:
 Originally Posted by George M First of all, I will try and pick a number that is greater than a billion so they are reasonable (perhaps I should put my previous guesses in the PREDICT M50 thread). I will have my final guess at the end of this post. Now, here are prime numbers $p$ that should not be picked if $p \ \in \ [74243591, \ 74243681]$ or $p \ \in \ [74294611, \ 74294861]$ Also, after looking at the 46th and 47th mersenne prime and the gap between both exponents, I consider my previous guess reasonable, but it doesn’t mean anything if M_n is factored, my previous guess being equal to n. So anyway, my final guess is..... Hmmm.... $1824261419$
I thought the current largest mersenne prime in the world $2^p - 1$ had $p$ close to a billion for some reason. This was why I was misunderstood.

2018-01-04, 08:33   #40
George M

Dec 2017

2×52 Posts

Quote:
 Originally Posted by George M 982451707 If anyone is struggling to come up with a prime (for any reason) then you can head below: http://www.primos.mat.br/2T_en.html :)
Oh, and this seems pretty dodgy. I downloaded two of the files to serve my curiosity, only to bring forward pages and pages of random-like code and letters and numbers..... uuhhh....

2018-01-04, 08:37   #41
George M

Dec 2017

628 Posts

Quote:
It doesnt take me a lot to see things. I only thought that the prime exponent in the largest prime in the world was close to a billion. That’s all. I looked back at it and realised I definitely misunderstood you. Sorry about that, and I am now aware of how my posts can be considered spam. I am also relatively new to the mersenne forum (of only three days), so I am not too familiar with the entire forum, but I still apologise. Consequently, I have launched my own thread on the subject of my most recent posts in this discussion.

Last fiddled with by George M on 2018-01-04 at 08:38

2018-08-14, 19:47   #42
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

2×1,907 Posts

Quote:
 Originally Posted by ewmayer Still, you gotta admit the run of 10+ which seem to conform to a significantly shallower log-line slope is rather remarkable.
Yes. But consider that the processing of the data helps create the remarkable seeming smoothness of the representation. First, it is an ordered list. Secondly, it's a log chart. Thirdly, what's being plotted in log coordinates is itself a log function (the exponent of the Mersenne prime, not the Mersenne prime number itself). So we are looking at log(log(sort(known Mersenne prime numbers))) in the vertical axis, vs sorted order position in the horizontal. I get something remarkably flat and smooth also, when doing log(log(sort(Wisconsin villages population counts))), which numbers are the results of millions of separate decisions about where to live. The three charts of ~400 data points are 3 different representations of the same population data.

And, note that M16-26 while not as remarkably low or seemingly uniform a slope as the M40-50 run, is equal in run length, and M12-13, M26-28, M31-32, M37-40 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 GIMPS-century. 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.
Attached Thumbnails

2018-08-14, 20:32   #43
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

381410 Posts

Quote:
 Originally Posted by George M I thought the current largest mersenne prime in the world $2^p - 1$ had $p$ close to a billion for some reason. This was why I was misunderstood.
It looks to me more a case of you misunderstanding. There's a surprising amount of learning curve in this arcane area. (How's the hill climb going?)

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 optimized-duration TF and P-1 factoring attempts can take weeks or months per exponent on lesser hardware (midstream gpus, or multiple-cpu-core 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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