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Forum: Probability & Probabilistic Number Theory 2014-08-13, 18:46
Replies: 15
Views: 12,789
Posted By CRGreathouse
The only one I know is Diaconis who is a...

The only one I know is Diaconis who is a probabilist.
Forum: Probability & Probabilistic Number Theory 2014-08-12, 15:12
Replies: 15
Views: 12,789
Posted By CRGreathouse
Look what I found: Persi Diaconis, Frederick...

Look what I found:

Persi Diaconis, Frederick Mosteller, Hironari Onishi, Second-order terms for the variances and covariances of the number of prime factors—Including the square free case, Journal...
Forum: Probability & Probabilistic Number Theory 2014-08-05, 14:10
Replies: 15
Views: 12,789
Posted By CRGreathouse
I read it over last night -- Granville is a great...

I read it over last night -- Granville is a great expositor (in addition to being a first-rate mathematician). It doesn't look like their method easily extends to a correction term, since they're not...
Forum: Probability & Probabilistic Number Theory 2014-08-05, 00:05
Replies: 15
Views: 12,789
Posted By CRGreathouse
Interesting. I haven't worked through the...

Interesting.

I haven't worked through the proof yet. Do you recommend the original or a modern version (Granville-Soundarajan, etc.)?
Forum: Probability & Probabilistic Number Theory 2014-08-04, 18:33
Replies: 15
Views: 12,789
Posted By CRGreathouse
Me either -- but it's hard to factor big enough...

Me either -- but it's hard to factor big enough numbers to get useful information. Even if I used 100-digit numbers, at significantly greater effort, that would only increase the log log by about...
Forum: Probability & Probabilistic Number Theory 2014-08-04, 14:54
Replies: 15
Views: 12,789
Posted By CRGreathouse
Using \omega(n) (to avoid the extra variability...

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

1 distinct prime factor: 4290
2 distinct prime factors:...
Forum: Probability & Probabilistic Number Theory 2014-08-03, 06:12
Replies: 15
Views: 12,789
Posted By CRGreathouse
Sure, let's see. MM127 is an obvious candidate...

Sure, let's see. MM127 is an obvious candidate for a big number. For small... well, say 200^199 + 199^200 (http://factordb.com/index.php?id=1000000000044818224) in Paul's honour.

I think the...
Forum: Probability & Probabilistic Number Theory 2014-08-03, 05:42
Replies: 15
Views: 12,789
Posted By CRGreathouse
Hmm. I think I could do this, but it would be a...

Hmm. I think I could do this, but it would be a real bear to compute. I wrote code to compute, or at least closely estimate, that function a few years back and it wasn't easy. It seems like this...
Forum: Probability & Probabilistic Number Theory 2014-08-01, 19:09
Replies: 15
Views: 12,789
Posted By CRGreathouse
Estimating the number of primes in a partially-factored number

I'm interested in using information about a number to estimate the likelihood of it having a certain number of prime factors.

If we had no information about the number except its size, there are...
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