A randomly chosen number N satisfying $N ≡ 3(6)$ has zero probability of being prime.
I was thinking about the Prime Number Theorem but I'm not sure about how to do it.
2026-04-02 19:22:18.1775157738
How to make mathematical sense of the following statement?
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I'm guessing that "probability" here should be interpreted in the sense of asymptotic density. In that case the prime number theorem is not needed. Instead, note that $N=6k+3$ for some integer $k$. How often is such an $N$ prime?