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Old 2004-09-01, 17:20   #4
wblipp
 
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"William"
May 2003
New Haven

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Quote:
Originally Posted by Bob Silverman
You can't just compute the probability that (say) the largestis less than x^k and the probability that the second largest is less than x^j and conclude that the probability that the largest is less than x^k
AND that the second largest is less than x^j is the product of the two...
Of course you can't.

And I didn't.

What I said is that we have two descriptions for the same set.

The Rho Description - This is the set of numbers whose largest prime factor is less than x2/3.

The Mu Description - This is the set of numbers that satisfy both
1. The largest prime factor is less than x2/3

AND

2. The second largest prime factor is less than x1/2.


Note we are talking about joint distributions, not joint densities, so we cannot make infereneces based on assuming the largest factor is near x2/3.

I claim these two sets are identical, and hence their probabilities should be the same. If you think I've made an error, please demonstrate a number that belongs to one set and not the other.

William
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