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thomblake comments on "What Is Wrong With Our Thoughts" - Less Wrong
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I agree that I'm not sure how you're intending to use 'why' here, and I'm pretty sure there's a good answer for any particular meaning.
To answer the question in a possibly unsatisfactory way, 3 is prime because it is a natural number which has exactly two distinct natural number factors, whereas 4 is not prime because it has more than two distinct natural number factors.