20090928, 13:00  #1 
"Lucan"
Dec 2006
England
14512_{8} 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 20090928 at 13:06 
20090928, 14:06  #2 
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

20090928, 14:33  #3 
"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 20090928 at 14:36 
20090928, 14:47  #4  
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Quote:
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? 

20090928, 15:02  #5 
Cranksta Rap Ayatollah
Jul 2003
641_{10} Posts 
Hmm, thinking on it for more than 15 seconds, I might have to retract my statement.

20090928, 15:09  #6 
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 log_{2}(2^{n})*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes) Last fiddled with by Orgasmic Troll on 20090928 at 15:11 
20090928, 15:33  #7 
"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 20090928 at 15:36 
20090928, 15:39  #8 
"Lucan"
Dec 2006
England
14512_{8} Posts 
I assume you meant e.g. and not i.e.

20090928, 15:51  #9 
Cranksta Rap Ayatollah
Jul 2003
281_{16} Posts 

20090929, 05:07  #10  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Quote:
Does n=r? More to come. David 

20090929, 05:38  #11 
"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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