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Old 2021-09-06, 14:46   #276
Uncwilly
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The long drought is long and the area cleared is large.
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Old 2021-09-06, 16:16   #277
ATH
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Quote:
Originally Posted by Raydex View Post
Last week we passed the 1000 day mark without a new Mersenne prime discovery. Now at 1004 days, the progress exponent on the "Milestones page" for "tested and verified" is 104286673, which is 26.2% higher than 82589933.
Here is a "countup" timer:
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)
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Old 2021-09-06, 22:19   #278
Uncwilly
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Quote:
Originally Posted by ATH View Post
July 31st 2022 it will be the longest gap at 1332 days. Lets hope we do not beat that record:
Imagine were the tail end of the FTC's will be then. It will be a very large new prime and the biggest relative to the previous far and away.
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Old 2021-09-06, 23:46   #279
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Quote:
Originally Posted by Raydex View Post
Last week we passed the 1000 day mark without a new Mersenne prime discovery. Now at 1004 days, the progress exponent on the "Milestones page" for "tested and verified" is 104286673, which is 26.2% higher than 82589933.
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!
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Old 2021-09-28, 23:27   #280
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Quote:
Originally Posted by Uncwilly View Post
I just got back to the computer with my data. This guess does not count. Your previous guesses have not had 60 days elapse since the milestone passed them. See rule #6
Just to make sure the rule, so is it correct that I'll be able to guess again starting Oct 1, 2021?
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Old 2021-09-29, 01:11   #281
chalsall
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Quote:
Originally Posted by tuckerkao View Post
Just to make sure the rule, so is it correct that I'll be able to guess again starting Oct 1, 2021?
I would personally ask you not to guess.

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.
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Old 2021-09-29, 02:09   #282
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Quote:
Originally Posted by Uncwilly View Post
We have a loooong way to go to say it will be the longest gap.

2013-01-25 - 2009-04-12 = 1384 days
1996-09-03 - 1994-01-04 = 973 <- sort of counts.
2015-09-17 - 2013-01-25 = 965
2001-11-14 - 1999-06-01 = 897 days

As of now we are 882 days
As of 09/29/2021, we are at 1027 days, did you see how fast that catch up could go?

Solidly at least the #2 longest gap confirmed at the moment.

Last fiddled with by tuckerkao on 2021-09-29 at 02:37
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Old 2021-09-29, 11:06   #283
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How about 104 years between M31 (Euler) and M127 (Lucas)? Or 184 years between M19 (Cataldi) and M31.

Last fiddled with by paulunderwood on 2021-09-29 at 11:11
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Old 2021-09-29, 12:02   #284
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Quote:
Originally Posted by paulunderwood View Post
How about 104 years between M31 (Euler) and M127 (Lucas)? Or 184 years between M19 (Cataldi) and M31.
Har-de-har-har. I presume consideration is being restricted to times since GIMPS joined the hunt.

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 Mp 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 Mp 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 Mp is prime already in hand, the present drought might not seem surprising.
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Old 2021-09-29, 12:58   #285
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Quote:
Originally Posted by Dr Sardonicus View Post
I find it somewhat amusing that the recent discoveries of Mersenne primes led to speculation that maybe the heuristic formula for how often Mp 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 Mp 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 Mp is prime already in hand, the present drought might not seem surprising.
I think a lot of the speculation about the heuristic being wrong arose from people applying the linear approximation to the heuristic, in which the log(ap) factor in the probability that Mp is prime gets replaced with log(p) to make the integral easier. But we should really use the actual heuristic and calculate the expected number of primes numerically. The heuristic is invalid for p=2 and gives nonsensical probabilities greater than 1 for p=3 and p=5, so we start from p=7 and add 3 for the primes at p=2,3,5.

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 2021-09-29 at 12:59
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Old 2021-09-29, 14:01   #286
Dr Sardonicus
 
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Quote:
Originally Posted by charybdis View Post
<snip>
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.
The approach of disregarding 2, 3, and 7, then adding 3 for larger primes seems quite reasonable.

According to your interpretation, when does the expected number of Mersenne primes actually hit 52?
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