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Old 2010-05-25, 19:45   #1
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Default Sieve depth vs. prime probability

A 300,000 digit number has no factors below 1 billion (10^9). What's the probability that this number is prime?
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Old 2010-05-25, 20:23   #2
R.D. Silverman
 
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Quote:
Originally Posted by Unregistered View Post
A 300,000 digit number has no factors below 1 billion (10^9). What's the probability that this number is prime?
I get approx 5.3 x 10^-5.. It is simple conditional probability: P(A|B) =
P(A)/P(B). User Mertens' Thm.
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Old 2010-05-25, 20:51   #3
Mini-Geek
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"Tim Sorbera"
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Quote:
Originally Posted by R.D. Silverman View Post
I get approx 5.3 x 10^-5.. It is simple conditional probability: P(A|B) =
P(A)/P(B). User Mertens' Thm.
Yep, that's it. I get:
5.3430028E-05 (out of 1), which is
1 in 18,716.07
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