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 2009-09-28, 13:00 #1 davieddy     "Lucan" Dec 2006 England 145128 Posts Call me lazy but... ASSUMING we can expect 1.78 Mersenne primes between exponents x and 2x, what ratio r of exponents gives us the "half life" (0.5 probabiliiy of no primes between x and rx)? I miss Mally's prolific old chestnuts. David Last fiddled with by davieddy on 2009-09-28 at 13:06
 2009-09-28, 14:06 #2 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts I think there are large assumptions (on top of the ones you've already made) that are necessary before this is solvable. I'm pretty sure that once those assumptions are made, the result will have nothing to do with Mersenne primes
 2009-09-28, 14:33 #3 davieddy     "Lucan" Dec 2006 England 2·3·13·83 Posts OK forget the sodding Mersenne primes, but I'm pretty sure there are some people here (Blipp being one) who can interpret/rigorize the question and supply an answer. PS I remember your proclaimed disdain for "Applied Math" David Last fiddled with by davieddy on 2009-09-28 at 14:36
2009-09-28, 14:47   #4
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

641 Posts

Quote:
 Originally Posted by davieddy OK forget the sodding Mersenne primes, but I'm pretty sure there are some people here (Blipp being one) who can interpret/rigorize the question and supply an answer. PS I remember your proclaimed disdain for "Applied Math" David
There's no need to get pissy. You just need to figure out what you're asking.

Expected values don't tell us anything about the distribution, so we need to assume a distribution before we can even attempt the problem.

It's possible that assuming the expected value is 1.78 across all intervals forces a single distribution, but I think you'd need to assume your distribution was continuous.

And what the hell does applied math have to do with this?

 2009-09-28, 15:02 #5 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 64110 Posts Hmm, thinking on it for more than 15 seconds, I might have to retract my statement.
 2009-09-28, 15:09 #6 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts I think r = 1.21495... is what you're looking for. This is assuming that the expected number of mersenne primes in the interval (x,rx) is log2(2n)*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes) Last fiddled with by Orgasmic Troll on 2009-09-28 at 15:11
 2009-09-28, 15:33 #7 davieddy     "Lucan" Dec 2006 England 2·3·13·83 Posts OK I'll check it out in the morning when I'm sober. (and you will still be ugly... (Churchill)) Meantime I'm searching for Flouran's description of me as "great". I wanted to say "Some are born great, some achieve greatness, and others have it thrusted upon them" Last fiddled with by davieddy on 2009-09-28 at 15:36
2009-09-28, 15:39   #8
davieddy

"Lucan"
Dec 2006
England

145128 Posts

Quote:
 Originally Posted by Orgasmic Troll I think r = 1.21495... is what you're looking for. This is assuming that the expected number of mersenne primes in the interval (x,rx) is log2(2n)*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes)
I assume you meant e.g. and not i.e.

2009-09-28, 15:51   #9
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

28116 Posts

Quote:
 Originally Posted by davieddy I assume you meant e.g. and not i.e.
no, I think "that is" fits in there just as well.

2009-09-29, 05:07   #10
davieddy

"Lucan"
Dec 2006
England

145128 Posts

Quote:
 Originally Posted by Orgasmic Troll I think r = 1.21495... is what you're looking for. This is assuming that the expected number of mersenne primes in the interval (x,rx) is log2(2n)*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes)
We are extracting more mileage out of this thread than I anticipated.
Does n=r?

More to come.

David

 2009-09-29, 05:38 #11 davieddy     "Lucan" Dec 2006 England 2×3×13×83 Posts Fawlty Towers Sybil is wizard on "Mastermind" - speciality topic: The Bleedin' Obvious. Can you get that pigeon out of the water tank please. The hotel inspectors will be round in a minute. Manuel: "Que?" This isn't a proposition from Wittgenstein

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