20190820, 03:02  #1 
"Sam"
Nov 2016
2·163 Posts 
Probability N has a prime factor > sqrt(N)
For some integer N chosen at random, what is the probability that N has a prime factor > sqrt(N)? This also includes when N is prime, therefore the probability is greater than 1/ln(N).
Furthermore, what's the probability that N has a prime factor > N^(1/k) ? Thanks for any new leads. 
20190821, 10:16  #3 
(loop (#_fork))
Feb 2006
Cambridge, England
7·911 Posts 
It takes a long time to reach an asymptote ...
Code:
c=0;for(t=10^12,10^12+10^6,F=factor(t);lp=F[matsize(F)[1],1];if(lp*lp<=t,c=1+c)); c Code:
1e6 270639 1e8 276912 1e10 282202 1e12 286014 1e14 288791 1e16 291417 1e18 293196 1e20 294238 Last fiddled with by fivemack on 20190821 at 10:21 
20190821, 10:29  #4  
"Robert Gerbicz"
Oct 2005
Hungary
2^{2}×3×7×17 Posts 
Quote:


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