20060402, 18:15  #12  
"William"
May 2003
New Haven
3×787 Posts 
Quote:
In this message we have agreement that Brent's version of the 2parameter Dickman function is correct, along with an assurance that the error is cosmetic: http://www.mersenneforum.org/showpos...0&postcount=68 In this message we have a summary of the idea as using Baye's Theorem to update the Dickman function: http://www.mersenneforum.org/showpos...7&postcount=15 At first glance it appears that changing the Dickman function should change Equation 4.6, but I haven't yet taken the time to look into that issue. 

20060402, 18:40  #13  
Nov 2003
16444_{8} Posts 
Quote:
The probability that a large integer X has a factor between y and y^(1+e) is e/(e+1). So, for example, the probability that an integer (say) near 200 digits has a factor between 50 and 60 digits gives e = .2 and a probability of 1/6. This allows use to compute a density function for the probability that a factor exists in the range of interest. We then apply Bayes' Thm. using the ECM failures as a sample. 

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