20090804, 22:51  #628 
Sep 2002
Oeiras, Portugal
1400_{10} 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!...) 
20090804, 22:55  #629  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Quote:
Last fiddled with by MiniGeek on 20090804 at 22:56 

20091007, 03:56  #630  
May 2005
Argentina
186_{10} Posts 
Quote:
Code:
Verified test results Exponent User name Computer name Residue Date found 28222361 ScottBardwick SDBToshLappy 82EA4572240B785E 20090822 19:07 28222361 ScottBardwick Q6600 82EA4572240B785E 20090908 09:05 Bad test results Exponent User name Computer name Residue Error code Date found 28222361 S349120 CF9A4026F 1B7A5F9E15E942E4 00000000 

20100525, 18:43  #631  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Wagstaff refined
Quote:
Quote:
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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: (e^{gamma}/log2)(1/k + (log2+log6)/2/klogk) Integrate to get the expected number of Mersennes up to k: (e^{gamma}/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 20100525 at 19:14 

20100526, 10:33  #632 
"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 20100526 at 11:18 
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