20070813, 00:39  #1 
"Lucan"
Dec 2006
England
1100101001010_{2} Posts 
searching for Mersenne primes
You have two choices:
1) a program that takes 30 days with an x% chance of failing 2) a program that takes 40 days which is effectively reliable. At what x do you opt for 2 rather than 1 ? David Last fiddled with by davieddy on 20070813 at 00:41 
20070813, 01:07  #2 
Aug 2002
Ann Arbor, MI
1B1_{16} Posts 
With x% chance of failure each test run, the expected number of runs to get a correct result is 1/x. The break even point is when 30/x=40, or x=75%.
I'm fairly confident this still mostly works even with the application to GIMPS and the system of doublechecks in place. However, I have a feeling many people here would place additional value on having things done right the first time and not having to deal with unnecessary double checks due to errors. If this question happens to be related to OCing, I'd only push it far enough to still get consistently correct results. 
20070813, 01:29  #3  
"Lucan"
Dec 2006
England
6474_{10} Posts 
Quote:
David Last fiddled with by davieddy on 20070813 at 01:31 

20070813, 02:33  #4 
Feb 2006
Denmark
2·5·23 Posts 
No. With x% chance of failure, there is 1x% chance of a correct result. The expected number of runs to get a correct result is 1/(1x%). The break even point is when 30/(1x%)=40, or x=25.

20070813, 05:33  #5 
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
This is assuming that you only care about the expected value

20070813, 13:39  #6  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Bayesian statistics) is linear. This is also known in economics as a utility function. 

20070815, 13:25  #7 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
The (illdisguised) follow up question is:
What exponent size reduces the reliability of a 2048K FFT LLtest to 75% ? David 
20070821, 04:51  #8 
Aug 2002
Ann Arbor, MI
433 Posts 
Goddamnit, I'm screwed when school starts in two weeks if I can't even get that right .

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