Sieve depth vs. prime probability

2010-05-25, 19:45

A 300,000 digit number has no factors below 1 billion (10^9). What's the probability that this number is prime?

R.D. Silverman · 2010-05-25, 20:23

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.

TimSorbet · 2010-05-25, 20:51

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

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?

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