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Old 2019-08-21, 10:16   #3
(loop (#_fork))
fivemack's Avatar
Feb 2006
Cambridge, England

638210 Posts
Default It takes a long time to reach an asymptote ...

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
The normal suggestion is that it's about k^-k, so 1/4. But sampling ranges of 10^6 at different places suggests that the count (and so the implied probability) goes up perceptibly for larger N

1e6  270639
1e8  276912
1e10 282202
1e12 286014
1e14 288791
1e16 291417
1e18 293196
1e20 294238
Assuming that we're dealing with a Poisson process with a fixed probability at each sampling point, which I don't think is unfair, those observations are not consistent with the probability being the same at 1e6 as at 1e18.

Last fiddled with by fivemack on 2019-08-21 at 10:21
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