20190403, 17:39  #12 
Xebeche
Apr 2019
πΊππΊ
1B6_{16} Posts 
One more interesting topic.
This is the plot that shows us the number of days (y axis) since 09 February 1997 (starting poin x=0, y=0) when all tests below chosen exponent (x axis) have been verified. https://ibb.co/2nbJs29 I took the data from here: https://www.mersenne.org/report_milestones I calculated the starting point 09 February 1997 (x=0, y=0) in such a way that the curve data approximation gave the smallest error. This mathematical function allows us to extrapolate the day (since 09 February 1997) for any exponent (x axis) when all tests below it will be verified. At the last 10 values, the error is quite small and does not exceed on average Β±45 days. Although of course the value can walk in the larger tube of error. I wrote about it here: https://www.mersenneforum.org/showpo...postcount=3072 We could estimate that all tests below M57885161 will be completed on 12 September 2021 Β±45 days. https://ibb.co/b11f3tt Assuming the validity of my hypothesis, it can be assumed that at least 3 new Mersenne Prime numbers will be open by this date. But there are no guarantees and of course not limited to this interval :) 
20190403, 17:54  #13 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
19·311 Posts 

20190403, 18:16  #14  
Xebeche
Apr 2019
πΊππΊ
2×3×73 Posts 
Quote:
But if we assume that there is only 1 new number, then it will look like this (orange line): https://ibb.co/X4pMdyx From my point of view it does not look very organic. But I will not argue, sure you could be right, time will tell. Last fiddled with by greenskull on 20190403 at 18:24 

20190403, 18:29  #15 
If I May
"Chris Halsall"
Sep 2002
Barbados
10,039 Posts 

20190403, 18:42  #16 
Xebeche
Apr 2019
πΊππΊ
1B6_{16} Posts 
50/50  it may or may not be correct :)
But seriously speaking, it all comes down to a smooth approximation of the Cumulative amount of Mersenne Primes on the interval M3021377..M43112609 and reliable extrapolation behind this interval. Everything else is not contradictive, you see all the explanations to the idea. 
20190403, 18:51  #17 
Jun 2015
Vallejo, CA/.
2×509 Posts 
The only case that I know of a Mersenne prime found out of order (and not by just 10 months like M_{42643801}) it is Mp_{110503} by Colquitt & Welsh on January 1988
We need to make note, however, that this was before GIMPS which started 8 years later in January 1996. Mp_{132049} and Mp_{216091} where discovered before M_{110503}, on Sept. '83 and Sept. '85 respectively. As far as I know when Colquitt and Welsh found 2^{110,503}1 to be prime, the search up to exponent 216,000 was _not_ exhaustive. So this was not the case (someone correct me if I'm wrong) of an exponent being check the first time and found composite by mistake and then discovered in a DC to be prime. 
20190403, 19:06  #18  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
19·311 Posts 
Quote:
There's no reason to think that sequence number versus p of the sorted Mp series should be a smooth function, and there are adjacent Mps that show it is not. Quote:
Last fiddled with by kriesel on 20190403 at 19:23 

20190403, 19:36  #19  
Xebeche
Apr 2019
πΊππΊ
2×3×73 Posts 
Quote:
I mean Cumulative amount of Mersenne Primes, not any others. I have no claim to absolute truth, I laid out some ideas, and described how I came to it. Time will show everything. Maybe I will make a couple more clarifications when I have new thoughts. 

20190404, 00:27  #20  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
19×311 Posts 
Quote:
As a former employer was fond of saying, the map is not the territory. We know the data has steps in it. It is a staircase with vertical increments of one. Graph # of known Mp below x, versus p, from M47. It's the same value, 47, from 43112609, all the way up to at least https://www.mersenne.ca/exponent/46769119, and probably to 57885143 or 57885160. 

20190404, 07:52  #21  
Xebeche
Apr 2019
πΊππΊ
2·3·73 Posts 
Quote:
Quote: ^ β As of March 29, 2019, 46,753,351 is the largest exponent below which all other prime exponents have been checked twice, so it is not verified whether any undiscovered Mersenne primes exist between the 47th (M43112609) and the 51st (M82589933) on this chart; the ranking is therefore provisional. Furthermore, 83,032,877 is the largest exponent below which all other prime exponents have been tested at least once, so all Mersenne numbers below the 51st (M82589933) have been tested. 

20190404, 08:27  #22  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6300_{10} Posts 
Quote:


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