mersenneforum.org Sieve depth vs. prime probability
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 2010-05-25, 19:45 #1 Unregistered   23×3×13×17 Posts 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?
2010-05-25, 20:23   #2
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

2·3·31·41 Posts

Quote:
 Originally Posted by Unregistered 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.

2010-05-25, 20:51   #3
TimSorbet
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

11×389 Posts

Quote:
 Originally Posted by R.D. Silverman 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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