20210906, 14:46  #276 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
13×769 Posts 
The long drought is long and the area cleared is large.

20210906, 16:16  #277  
Einyen
Dec 2003
Denmark
5^{2}×127 Posts 
Quote:
https://www.timeanddate.com/countdow...3&font=cursive So far this is the 3rd longest GIMPS gap. On Nov 19th 2021 it will be the 2nd longest at 1078 days, and on July 31st 2022 it will be the longest gap at 1332 days. Lets hope we do not beat that record: Code:
M(1398269) Nov 13 1996 M(2976221) Aug 24 1997 +284 days M(3021377) Jan 27 1998 +156 days M(6972593) Jun 1 1999 +490 days M(13466917) Nov 14 2001 +897 days M(20996011) Nov 17 2003 +733 days M(24036583) May 15 2004 +180 days M(25964951) Feb 18 2005 +279 days M(30402457) Dec 15 2005 +300 days M(32582657) Sep 4 2006 +263 days M(43112609) Aug 23 2008 +719 days M(37156667) Sep 6 2008 +14 days M(42643801) Jun 4 2009 +271 days M(57885161) Jan 25 2013 +1331 days M(74207281) Jan 7 2016 +1077 days M(77232917) Dec 26 2017 +719 days M(82589933) Dec 7 2018 +346 days  +8059 days (=503.7 days average) 

20210906, 22:19  #278 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
13×769 Posts 

20210906, 23:46  #279 
"6800 descendent"
Feb 2005
Colorado
2^{3}·5·17 Posts 
I say "Yay!" I mean, this is why we're all here, isn't it? If we hit a new record without a new Mersenne prime, I say we party!

20210928, 23:27  #280 
"Tucker Kao"
Jan 2020
Head Base M168202123
5·97 Posts 
Just to make sure the rule, so is it correct that I'll be able to guess again starting Oct 1, 2021?

20210929, 01:11  #281  
If I May
"Chris Halsall"
Sep 2002
Barbados
26D7_{16} Posts 
Quote:
Others with some understand are playing a bit of a game. No need for your noise. You will please note I have not ever guessed. 

20210929, 02:09  #282  
"Tucker Kao"
Jan 2020
Head Base M168202123
111100101_{2} Posts 
Quote:
Solidly at least the #2 longest gap confirmed at the moment. Last fiddled with by tuckerkao on 20210929 at 02:37 

20210929, 11:06  #283 
Sep 2002
Database er0rr
17·227 Posts 
How about 104 years between M31 (Euler) and M127 (Lucas)? Or 184 years between M19 (Cataldi) and M31.
Last fiddled with by paulunderwood on 20210929 at 11:11 
20210929, 12:02  #284  
Feb 2017
Nowhere
3^{2}×7×79 Posts 
Quote:
M127 is the largest Mersenne number proved to be prime (1876) without the aid of a computer, and is likely to remain so. The next Mersenne prime, M521, is the first to be proved prime (1952) with the aid of a computer. To my mind consecutive exponents differing by a factor of over 4 is more noteworthy than the time gap. I find it somewhat amusing that the recent discoveries of Mersenne primes led to speculation that maybe the heuristic formula for how often M_{p} is prime was wrong, because "too may" exponents yielding Mersenne primes were showing up. If instead you assume that the estimate for the number of p <= X for which M_{p} is prime holds good "in the long run," and figure how big X has to be in order that the estimate hold with the exponents for which M_{p} is prime already in hand, the present drought might not seem surprising. 

20210929, 12:58  #285  
Apr 2020
1ED_{16} Posts 
Quote:
The resulting value is an expectation of 50.3 Mersenne primes up to the (presumed) 51st Mersenne prime. The glut of primes in the GIMPS era is more of a reversion to the mean after lower ranges contained fewer primes than expected. Last fiddled with by charybdis on 20210929 at 12:59 

20210929, 14:01  #286  
Feb 2017
Nowhere
11561_{8} Posts 
Quote:
According to your interpretation, when does the expected number of Mersenne primes actually hit 52? 

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