20181213, 03:08  #34 
Jun 2003
2^{2}·5^{2}·47 Posts 

20181213, 04:20  #35  
Einyen
Dec 2003
Denmark
2^{7}×23 Posts 
Quote:
Quote:
http://www.ams.org/journals/mcom/198...54X/home.html 

20181213, 09:40  #36 
Dec 2012
The Netherlands
2642_{8} Posts 

20181213, 10:57  #37  
"Robert Gerbicz"
Oct 2005
Hungary
2570_{8} Posts 
Quote:
It would be much fair to test other ranges also, not only one fixed, where we see a crowd of Mersenne primes. So see if there is a T, where [T,8.5T] (for T<10e6) contains at least 13 Mersenne prime exponents or not. Modifying your code and doing 10000 iterations: (spec=0 means only that in the previous run there was no crowd, otherwise it gives the last prime in the first crowd) crowd: 2372, spec=0. 51 or more: 4848. 13 or more over 10M: 58 of 10000(27,2)(28,1)(29,1)(30,4)(31,4)(32,14)(33,12)(34,25)(35,42)(36,49)(37,76)(38,76)(39,140)(40,169)(41,216)(42,277)(43,371)(44,372)(45,484)(46,513)(47,538)(48,563)(49,588)(50,615)(51,617)(52,601)(53,518)(54,528)(55,422)(56,391)(57,366)(58,284)(59,254)(60,194)(61,165)(62,137)(63,99)(64,87)(65,61)(66,34)(67,28)(68,26)(69,11)(70,10)(71,6)(72,4)(73,2)(74,1)(76,1)(78,1) So we have roughly 24 percentage to see at least one crowd, nothing that very especial. Interestingly in the test the mode was at 51, ofcourse there is no full test up to 85e6, so "our" real count could be even higher. To see a typical (crowded) run: Simulated Mp: 2, 3, 5, 7, 11, 13, 17, 19, 31, 157, 251, 317, 397, 443, 457, 1193, 1789, 3623, 4201, 4603, 10061, 10477, 18919, 31573, 32363, 32887, 43451, 77029, 90821, 119173, 138427, 155377, 186551, 206051, 285071, 294313, 346139, 364213, 569251, 684889, 706337, 776453, 838091, 1312769, 1975511, 2507917, 4955761, 10955579, 15812651, 21375961, 39944243, 40921501, 52886513, 81814867. Total: 54 and here there is a crowd ending with p=706337, even ending with p=838091 there is a crowd with 14 primes, but nothing that very interesting in the (10m,85m) range: there are "only" 7 primes. Last fiddled with by R. Gerbicz on 20181213 at 10:58 Reason: typo 

20181213, 14:26  #38  
Feb 2017
Nowhere
110110100111_{2} Posts 
Quote:
Oh, Computer, could you please ask PariGP? ? exp(Euler)*log(85000000*log(2))/log(2) %1 = 45.973385236161997342391226401795683851 OK, looks good. I vote for "haven't reached `asymptotically' yet." The exponents haven't even reached 10^{8}. My analytic number theory prof once said, "Analytic number theory begins at 10^{40}." What's my guess for the new exponent? I don't have one. I reckon, I'll know soon enough... 

20181213, 16:43  #39  
"Mike"
Aug 2002
7710_{10} Posts 
Quote:


20181213, 21:44  #40  
∂^{2}ω=0
Sep 2002
República de California
11518_{10} Posts 
Quote:
Quote:
Last fiddled with by ewmayer on 20181213 at 22:00 

20181213, 21:52  #41 
If I May
"Chris Halsall"
Sep 2002
Barbados
9314_{10} Posts 

20181213, 22:04  #42 
∂^{2}ω=0
Sep 2002
República de California
11518_{10} Posts 

20181213, 22:15  #43  
If I May
"Chris Halsall"
Sep 2002
Barbados
2·4,657 Posts 
Quote:
Just asking... Have you been ever been body searched (at gunpoint) after demonstrating that a major telecoms provider might not wish to leave the default passwords on their deployed legacy Unix kit (which I paid for)? I have (true story). 

20181214, 01:11  #44 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9127_{10} Posts 
I've seen clumpy runs. Nothing special.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
500€ Reward for a proof for the Wagstaff primality test conjecture  Tony Reix  Wagstaff PRP Search  7  20131010 01:23 
Torture and Benchmarking test of Prome95.Doubts in implementation  paramveer  Information & Answers  32  20120115 06:05 
Wagstaff Conjecture  davieddy  Miscellaneous Math  209  20110123 23:50 
Algorithmic breakthroughs  davieddy  PrimeNet  17  20100721 00:07 
Conspiracy theories  jasong  Soap Box  11  20100705 12:23 