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Math Help - help with Pepin's primatlity test

  1. #1
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    help with Pepin's primatlity test

    In class today, the prof explained Pepin's test, but I got lost midway. This is what I have so far:
    Let F_{n}=2^{2^n}+1, then \frac{F_{n}-1}{2}=2^{2^n-1} Call this number q.
    If 3^q \equiv -1 (mod F_{n}) (1), then 3^{2q} \equiv 1(mod F_{n}). Because of (1), 2q is the order. What I don't understand is how this shows that F_{n} is prime. I also don't get how F_{n} \equiv 2(mod 3).
    Any help is much appreciated.
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  2. #2
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    Read this:
    Pépin's test - Wikipedia, the free encyclopedia

    Wikipedia for the win!

    (I feel too tired right now to do anything useful)
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