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Looking carefully, you have this very, very wrong. You've said:

    Today I found something called Wolstenholme’s
    theorem, which says: 

        A number n (> 3) is prime if the numerator
        of H(n-1) is a multiple of n², where
        H(n) =  1/1 + 1/2 + ... 1/n
No, no, no, no, no ...

The theorem says:

        For a prime p > 3, the numerator of H_{p-1}
        is divisible by p^2.
You have your "if" condition the wrong way round.

I've tried to comment on your blog, but it requires a login using any of several techniques, none of which I use, and none of which I'm willing to create just for this. So I didn't.

Thank you for taking out the time. I've updated my post now.

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