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)

[url]http://primes.utm.edu/notes/faq/NextMersenne.html[/url]

"on average"

nuff said!

[QUOTE=garo]"on average"

nuff said![/QUOTE]

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
:razz:

"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

[QUOTE=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[/QUOTE]

yeah, I agree with you. I just wondering M44 may belong to the next cluster of Mersenne primes, not in the M40-43 one.

[QUOTE=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.[/QUOTE]

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).

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...

[QUOTE=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...[/QUOTE]Aaargh! Run away! Run away!


Paul

[QUOTE=xilman]Aaargh! Run away! Run away!


Paul[/QUOTE]
*checkingThatThisIsNotTheMathForum*

Could you describe your opinion a little more explicit?

[QUOTE=Mystwalker]*checkingThatThisIsNotTheMathForum*

Could you describe your opinion a little more explicit?[/QUOTE]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

I have seen it, but I'm afraid it's too long ago.
I remember the killer rabbit, though. :smile: