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 2009-08-04, 22:51 #628 lycorn     Sep 2002 Oeiras, Portugal 140010 Posts pi_rho is the forum nickname for Michael Schafer, of Michigan State University. His computer discovered the 40th known mersenne prime on the 17th of November 2003. (and only now are we getting close to proving it is indeed M40!...)
2009-08-04, 22:55   #629
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17×251 Posts

Quote:
 Originally Posted by Dougal Who is pi_rho,and what prime did he dicover?i cant the results of the prime he found,but it says he found one!
I got excited, but then I found he was the discoverer of M20996011 (which might be M40). Apparently all past primes were entered into the v5 system as successes (e.g. curtisc has two successes).

Last fiddled with by Mini-Geek on 2009-08-04 at 22:56

2009-10-07, 03:56   #630
Damian

May 2005
Argentina

18610 Posts

Quote:
 Originally Posted by Primeinator Ah, okay. It did not look like there was an error code with the LL, though. Perhaps some other bug in the Prime95 caused it to beep? Perhaps it was something else on the computer? It would not beep prior to a test being completed...
It seems there Was an error on that LL. Someone has double-checked and triple-checked it now:

Code:
Verified test results
Exponent	User name	Computer name	Residue	Date found
28222361	ScottBardwick	SDB-Tosh-Lappy	82EA4572240B785E	2009-08-22 19:07
28222361	ScottBardwick	Q6600	82EA4572240B785E	2009-09-08 09:05

Exponent	User name	Computer name	Residue	Error code	Date found
28222361	S349120	CF9A4026F	1B7A5F9E15E942E4	00000000

2010-05-25, 18:43   #631
davieddy

"Lucan"
Dec 2006
England

145128 Posts
Wagstaff refined

Quote:
 Originally Posted by CRGreathouse Doing the calculation slightly differently (prime-by-prime, splitting by value mod 4) I get an average of 2.411 Mersenne primes in that range. (20M - 48M)
Quote:
 Originally Posted by R. Gerbicz I think it is better to do simulation, using http://primes.utm.edu/notes/faq/NextMersenne.html conjecture for the probability that Mp is prime. 2000 simulations for the [2,5*10^7] interval, gives: I've also counted the number of Mersenne primes in the runs. Note that using the conjecture the expected number of primes is about 48.9 (I've included p=2 in every cases).
Quote:
 Originally Posted by davieddy Glad (as always) to provoke mirth But unless Gauss' 1/log k law is better expressed as (1 + (log2 + log6)/(2log k))/log k, then the numbers bandied about (1.78 mersenne primes between exponents x and 2x, gradient of the log exponent graph etc) are out by about 10% for the range tested to date. I thought this was worth pointing out. David
http://primes.utm.edu/mersenne/heuristic.html

I have been bothered for a long time about neglecting
log a (a=2 or 6) in the formula for the probability of
a random exponent yielding a Mersenne Prime.
Both Greathouse and Gerbicz used the third part of
the conjecture on each prime exponent, and their results
confirm my suspicion. Furthermore, the approximation is
unnecessary:

(egamma/log2)(1/k + (log2+log6)/2/klogk)

Integrate to get the expected number of Mersennes up to k:

(egamma/log2)(logk + log(logk)(log2+log6)/2)

Between 20M and 48M we expect:

log(48/20)/log1.47576 + 1.242log(log48M/log20M)/log1.47576

= 2.2496 + 0.1621
= 2.4117

The second term adds 7.2% -- hardly neglible!

_____________________
The small k to k=50M case is more problematic, but note that
log(50M/2)/log1.47576 is only 43.7

David

Last fiddled with by davieddy on 2010-05-25 at 19:14

 2010-05-26, 10:33 #632 davieddy     "Lucan" Dec 2006 England 2·3·13·83 Posts The expected number of Mersenne primes with exponents between x and x^2 is: (logx/log1.47576) + 2.2129 So between 7000 and 49000000 we expect 22.75 + 2.2129 Or 25 +/- 5 between 83 and 7000 we expect 11.375 + 2.2129 between 9 and 83 we expect 5.69 + 2.2129 ... Last fiddled with by davieddy on 2010-05-26 at 11:18

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