20051222, 21:53  #1 
Jun 2004
74_{8} Posts 
Are M41,42,43 too close to each other?
around 24M, 26M, and 30M(?)
I read an article about prediction of the next Mersenne prime, which said, on average, P_(n) ~ 1.47576P_(n1) http://primes.utm.edu/notes/faq/NextMersenne.html 
20051222, 22:23  #2 
Aug 2002
Termonfeckin, IE
2·5·251 Posts 
"on average"
nuff said! 
20051222, 22:38  #3  
Jun 2004
3C_{16} Posts 
Quote:
I checked all Mesenne primes (142, and a guessed 43), it seems Pn/Pn1~1.5 is ok over the entire sequence, but some numbers (2or3) are clustered together. So, I think, M44 (very likely the 1st 10M digits number) probably is far away from M40, 41, 42, and 43 (forming a cluster), and makes a longer expectation of all GIMPSers Last fiddled with by nngs on 20051222 at 22:41 

20051222, 22:43  #4 
"Nancy"
Aug 2002
Alexandria
2^{5}×7×11 Posts 
"nuff" means "enough".
The point is that the estimate of Pn/P{n1}~1.5 holds on average  if you look at a very long sequence of Mersenne primes, the mean value of the ratios of exponents will be about 1.5. But this does not say anything at all about local behaviour of the sequence. It is perfectly possible that some Mersenne primes are close together, or that there is a long stretch with no Mersenne primes. Alex 
20051222, 22:49  #5  
Jun 2004
111100_{2} Posts 
Quote:


20051223, 00:26  #6  
Dec 2003
Hopefully Near M48
2·3·293 Posts 
Quote:


20051223, 10:25  #7 
Jul 2004
Potsdam, Germany
3×277 Posts 
That's basically correct  but IMHO, it's similar to "heads or tails". There, you also only have 2 extremes with nothing inbetween (assuming the coin doesn't fall on the thin side), but everyone talks about a 5050 chance. Changing the structure of the coin modifies the probability...

20051223, 10:48  #8  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
27CF_{16} Posts 
Quote:
Paul 

20051224, 00:50  #9  
Jul 2004
Potsdam, Germany
3×277 Posts 
Quote:
Could you describe your opinion a little more explicit? 

20051224, 10:38  #10  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3·43·79 Posts 
Quote:
I was afraid that the thread would degenerate into yet another discussion of the unsolvable three sided coin problem and was suggesting that we not go there. Paul Last fiddled with by xilman on 20051224 at 10:38 

20051224, 11:59  #11 
Jul 2004
Potsdam, Germany
3·277 Posts 
I have seen it, but I'm afraid it's too long ago.
I remember the killer rabbit, though. Last fiddled with by Mystwalker on 20051224 at 12:00 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Gaps to close  ET_  FermatSearch  59  20180727 17:05 
How close have you been to finding a Mersenne prime?  NBtarheel_33  Data  42  20130717 19:21 
Factors of Ms close to yummy M&Ms  aketilander  Operazione Doppi Mersennes  3  20121107 02:59 
How can I close my own threads?  petrw1  Information & Answers  1  20070925 21:02 
Getting close to checking all exponents below 13466917 once  eepiccolo  Lounge  7  20030825 09:12 