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Old 2014-08-04, 18:26   #8
R.D. Silverman
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"Bob Silverman"
Nov 2003
North of Boston

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Originally Posted by CRGreathouse View Post
Using \omega(n) (to avoid the extra variability from the small primes that \Omega brings) and searching an interval around 1020 I find

This supports the intuition that Landau is better for small numbers of prime factors and Erdős-Kac better for large. In this case the crossover is surprisingly large (8 prime factors) but neither estimate is particularly accurate.
I would not expect it to be for composites that are only 20 digits.
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