mersenneforum.org Are M41,42,43 too close to each other?
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 2005-12-22, 21:53 #1 nngs     Jun 2004 22·3·5 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_(n-1) http://primes.utm.edu/notes/faq/NextMersenne.html
 2005-12-22, 22:23 #2 garo     Aug 2002 Termonfeckin, IE 24·173 Posts "on average" nuff said!
2005-12-22, 22:38   #3
nngs

Jun 2004

3C16 Posts

Quote:
 Originally Posted by garo "on average" nuff said!
sorry my poor English. what does "nuff" mean?

I checked all Mesenne primes (1-42, and a guessed 43), it seems Pn/Pn-1~1.5 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 2005-12-22 at 22:41

 2005-12-22, 22:43 #4 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts "nuff" means "enough". The point is that the estimate of Pn/P{n-1}~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
2005-12-22, 22:49   #5
nngs

Jun 2004

22·3·5 Posts

Quote:
 Originally Posted by akruppa "nuff" means "enough". The point is that the estimate of Pn/P{n-1}~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
yeah, I agree with you. I just wondering M44 may belong to the next cluster of Mersenne primes, not in the M40-43 one.

2005-12-23, 00:26   #6
jinydu

Dec 2003
Hopefully Near M48

33368 Posts

Quote:
 Originally Posted by nngs yeah, I agree with you. I just wondering M44 may belong to the next cluster of Mersenne primes, not in the M40-43 one.
I don't know about that; I would think that one Mersenne number being prime would not affect the probability of another Mersenne number being prime. Then again, the notion of the "probability" of a number being prime isn't really that correct after all, since any particular number is either prime (so the probability of it being prime is 1) or composite (so the probability of it being prime is 0).

 2005-12-23, 10:25 #7 Mystwalker     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 50-50 chance. Changing the structure of the coin modifies the probability...
2005-12-23, 10:48   #8
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

264768 Posts

Quote:
 Originally Posted by Mystwalker 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 50-50 chance. Changing the structure of the coin modifies the probability...
Aaargh! Run away! Run away!

Paul

2005-12-24, 00:50   #9
Mystwalker

Jul 2004
Potsdam, Germany

3·277 Posts

Quote:
 Originally Posted by xilman Aaargh! Run away! Run away! Paul
*checkingThatThisIsNotTheMathForum*

Could you describe your opinion a little more explicit?

2005-12-24, 10:38   #10
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

264768 Posts

Quote:
 Originally Posted by Mystwalker *checkingThatThisIsNotTheMathForum* Could you describe your opinion a little more explicit?
Have you seen the movie "Monty Python and the Holy Grail"?

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 2005-12-24 at 10:38

 2005-12-24, 11:59 #11 Mystwalker     Jul 2004 Potsdam, Germany 14778 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 2005-12-24 at 12:00

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