20140805, 00:55  #12 
Nov 2003
2^{2}×5×373 Posts 

20140805, 14:10  #13  
Aug 2006
2×29×103 Posts 
Quote:
But it struck me while reading the theorem that even more important than the correction term in variance is the correction term in mean, and it is purely elementary to improve the error term in the average order of from O(1) to M + O(1/log x), where the error term comes both from the fraction of numbers below x which are prime and from Mertens' theorem. I know this isn't the same as the normal order, and I doubt something so sharp could be proved at that level, but this should improve the practical performance. 

20140812, 15:12  #14  
Aug 2006
2·29·103 Posts 
Quote:
Persi Diaconis, Frederick Mosteller, Hironari Onishi, Secondorder terms for the variances and covariances of the number of prime factorsâ€”Including the square free case, Journal of Number Theory 9:2 (May 1977), pp. 187202. 

20140813, 13:05  #15  
Nov 2003
1D24_{16} Posts 
Quote:
The authors surprise me. None of them, AFAIK, is a number theorist. OTOH, I got to take statistics from Mosteller. He was a terrific lecturer. 

20140813, 18:46  #16 
Aug 2006
2·29·103 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Mersenne number factored (disbelievers are biting elbows)  alpertron  Data  549  20210224 20:17 
Largest Mersenne Number Fully Factored?  c10ck3r  Data  49  20171210 19:39 
Possibility of a FullyFactored Number  Trejack  FactorDB  7  20160514 05:38 
Estimating the number of prime factors a number has  henryzz  Math  7  20120523 01:13 
230 bits! M1237 (partially) factored  petrw1  Factoring  5  20101103 11:31 