20200211, 20:36  #100  
Nov 2004
2^{2}×3^{3}×5 Posts 
Quote:
Norm 

20200211, 21:59  #101 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3·3,121 Posts 

20200310, 01:07  #102  
Jan 2019
Pittsburgh, PA
11×23 Posts 
Quote:
98350193 June 1st, 2020 Kind of surprised still no prime found yet. 

20200310, 01:43  #103 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5·983 Posts 
Why? Best heuristics say there are only about 6 left to find in p<10^{9}, which will take many decades to search completely. https://www.mersenneforum.org/showpo...5&postcount=11
https://www.mersenne.org/primes/ contains many waits of 5+ years, and some longer than a century. 
20200310, 16:13  #104  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
9363_{10} Posts 
Quote:
Based upon the gaps between primes (relative to the size the primes), masser's guesses are close to the "expected" value. 

20200310, 18:08  #105  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5×983 Posts 
Quote:
We have had an unusually lucky run lately in the 2016 through 2018 period. The ratio of exponents of apparently successive Mersenne primes were improbably close together recently. To expect that to continue is not justified. A continuation of such close spacing of primes is counter to number theory, probability, and historical experience. See the examples of 1001000 (>4:1), and 100K1000K (>3:1). The 1M20M stretch contains 3 cases where p_{n}/p_{n1} > 2. https://www.mersenne.org/primes/ If we happen to now be in a ~2:1 step, at our recent rate of advancing primality firsttest milestones, 6M/year, we would have about a 1013 year remaining wait depending on assignment and completion timing luck at the wavefront. (166103)/6 ~ 10.5 vs (16689)/6 ~ 12.8 I hope that is not the case. But I know of no good theoretical or empirical reason to expect not to encounter such a case or larger ratio at some point. There are good reasons to expect droughts to happen again. 

20200310, 18:17  #106  
If I May
"Chris Halsall"
Sep 2002
Barbados
9,479 Posts 
Quote:
The maths for why is /way/ beyond my abilities. But it's important enough to have been mentioned in the last MP announcement. 

20200311, 13:22  #107  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Quote:
to do so? 

20200311, 13:34  #108  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3·3,121 Posts 
How many data points coming sooner than currently expected would it take for you to think that it is significant? 10, 20, 50, 100?
Quote:
Last fiddled with by Uncwilly on 20200311 at 13:35 

20200311, 14:56  #109  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5×983 Posts 
None of the following should be taken as disparaging to anyone's posts or enthusiasm. Only as encouragement to be accurate, and realistic.
And the ratio 1.47576 is only the estimated mean, about which large variations are expected to occur very frequently. Uncwilly summarized pending guesses at https://mersenneforum.org/showpost.p...4&postcount=87 on Dec 19 2019, including masser 8/3/2019 115856161 7/4/2023 masser 12/12/2018 117003179 11/24/2022 masser 12/12/2018 118788157 8/8/2020 In https://mersenneforum.org/showpost.p...&postcount=104 Uncwilly stated Quote:
Some of us will find any additonal prime discoveries interesting, regardless of their positions. We are happy to provide such additional data to the number theorists, who will make of them whatever they will. It would take a lot of such new finds, or a very wide span of their absence, to raise serious doubt about the current conjectures regarding their distribution. Which will probably take lifetimes to achieve, given the rate of computing throughput increase in GIMPS and the size of the task. There are numerous threads which have been placed into misc math which make various dubious claims about particular exponents being Mersenne primes. Most of those have already been refuted by the facts developed by targeted factoring and primality testing. Those remaining unrefuted so far, that are amenable to primality testing with current software and hardware, are expected to be resolved in 2020. Not all of us find leaving unrefuted unjustified claims laying about unchallenged to be fun. There is a balance to be struck, in the less formal threads, between accuracy and rigor on the one hand, and fun on the other. And people will differ on what the right balance is. 

20200311, 15:14  #110  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2493_{16} Posts 
Quote:
I did the following: calculated log_{10}(digits in MP_{x}) for each MP took difference between successive values took the mean added the mean to the value calculated for 82589933 (M51) converted the resultant value back into the value for p I got ~117,xxx,xxx Very close to the middle of masser's guesses. It is all fun and games until someone gets serious. 

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