mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Lounge

Reply
 
Thread Tools
Old 2005-12-22, 21:53   #1
nngs
 
nngs's Avatar
 
Jun 2004

22·3·5 Posts
Default 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
nngs is offline   Reply With Quote
Old 2005-12-22, 22:23   #2
garo
 
garo's Avatar
 
Aug 2002
Termonfeckin, IE

24·173 Posts
Default

"on average"

nuff said!
garo is offline   Reply With Quote
Old 2005-12-22, 22:38   #3
nngs
 
nngs's Avatar
 
Jun 2004

3C16 Posts
Default

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
nngs is offline   Reply With Quote
Old 2005-12-22, 22:43   #4
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

2,467 Posts
Default

"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
akruppa is offline   Reply With Quote
Old 2005-12-22, 22:49   #5
nngs
 
nngs's Avatar
 
Jun 2004

22·3·5 Posts
Default

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.
nngs is offline   Reply With Quote
Old 2005-12-23, 00:26   #6
jinydu
 
jinydu's Avatar
 
Dec 2003
Hopefully Near M48

33368 Posts
Default

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).
jinydu is offline   Reply With Quote
Old 2005-12-23, 10:25   #7
Mystwalker
 
Mystwalker's Avatar
 
Jul 2004
Potsdam, Germany

3×277 Posts
Default

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...
Mystwalker is offline   Reply With Quote
Old 2005-12-23, 10:48   #8
xilman
Bamboozled!
 
xilman's Avatar
 
"๐’‰บ๐’ŒŒ๐’‡ท๐’†ท๐’€ญ"
May 2003
Down not across

264768 Posts
Default

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
xilman is online now   Reply With Quote
Old 2005-12-24, 00:50   #9
Mystwalker
 
Mystwalker's Avatar
 
Jul 2004
Potsdam, Germany

3·277 Posts
Default

Quote:
Originally Posted by xilman
Aaargh! Run away! Run away!


Paul
*checkingThatThisIsNotTheMathForum*

Could you describe your opinion a little more explicit?
Mystwalker is offline   Reply With Quote
Old 2005-12-24, 10:38   #10
xilman
Bamboozled!
 
xilman's Avatar
 
"๐’‰บ๐’ŒŒ๐’‡ท๐’†ท๐’€ญ"
May 2003
Down not across

264768 Posts
Default

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
xilman is online now   Reply With Quote
Old 2005-12-24, 11:59   #11
Mystwalker
 
Mystwalker's Avatar
 
Jul 2004
Potsdam, Germany

14778 Posts
Default

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
Mystwalker is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Gaps to close ET_ FermatSearch 59 2018-07-27 17:05
How close have you been to finding a Mersenne prime? NBtarheel_33 Data 42 2013-07-17 19:21
Factors of Ms close to yummy M&Ms aketilander Operazione Doppi Mersennes 3 2012-11-07 02:59
How can I close my own threads? petrw1 Information & Answers 1 2007-09-25 21:02
Getting close to checking all exponents below 13466917 once eepiccolo Lounge 7 2003-08-25 09:12

All times are UTC. The time now is 08:49.


Mon Dec 5 08:49:17 UTC 2022 up 109 days, 6:17, 0 users, load averages: 0.76, 0.99, 0.97

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

โ‰  ยฑ โˆ“ รท ร— ยท โˆ’ โˆš โ€ฐ โŠ— โŠ• โŠ– โŠ˜ โŠ™ โ‰ค โ‰ฅ โ‰ฆ โ‰ง โ‰จ โ‰ฉ โ‰บ โ‰ป โ‰ผ โ‰ฝ โŠ โŠ โŠ‘ โŠ’ ยฒ ยณ ยฐ
โˆ  โˆŸ ยฐ โ‰… ~ โ€– โŸ‚ โซ›
โ‰ก โ‰œ โ‰ˆ โˆ โˆž โ‰ช โ‰ซ โŒŠโŒ‹ โŒˆโŒ‰ โˆ˜ โˆ โˆ โˆ‘ โˆง โˆจ โˆฉ โˆช โจ€ โŠ• โŠ— ๐–• ๐–– ๐–— โŠฒ โŠณ
โˆ… โˆ– โˆ โ†ฆ โ†ฃ โˆฉ โˆช โŠ† โŠ‚ โŠ„ โŠŠ โŠ‡ โŠƒ โŠ… โŠ‹ โŠ– โˆˆ โˆ‰ โˆ‹ โˆŒ โ„• โ„ค โ„š โ„ โ„‚ โ„ต โ„ถ โ„ท โ„ธ ๐“Ÿ
ยฌ โˆจ โˆง โŠ• โ†’ โ† โ‡’ โ‡ โ‡” โˆ€ โˆƒ โˆ„ โˆด โˆต โŠค โŠฅ โŠข โŠจ โซค โŠฃ โ€ฆ โ‹ฏ โ‹ฎ โ‹ฐ โ‹ฑ
โˆซ โˆฌ โˆญ โˆฎ โˆฏ โˆฐ โˆ‡ โˆ† ฮด โˆ‚ โ„ฑ โ„’ โ„“
๐›ข๐›ผ ๐›ฃ๐›ฝ ๐›ค๐›พ ๐›ฅ๐›ฟ ๐›ฆ๐œ€๐œ– ๐›ง๐œ ๐›จ๐œ‚ ๐›ฉ๐œƒ๐œ— ๐›ช๐œ„ ๐›ซ๐œ… ๐›ฌ๐œ† ๐›ญ๐œ‡ ๐›ฎ๐œˆ ๐›ฏ๐œ‰ ๐›ฐ๐œŠ ๐›ฑ๐œ‹ ๐›ฒ๐œŒ ๐›ด๐œŽ๐œ ๐›ต๐œ ๐›ถ๐œ ๐›ท๐œ™๐œ‘ ๐›ธ๐œ’ ๐›น๐œ“ ๐›บ๐œ”