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Math Help - find all primes

  1. #1
    Member
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    Angry find all primes

    find all primes of the form (2^2^n) + 5 where n is a nonnegative integer
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  2. #2
    Super Member PaulRS's Avatar
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    It is always divisbile by 3 for n>0 (and 2^{2^n}+5\neq{3} for all nonnegative integers n)

    Just note that: 2^{2^n}+5\equiv{(-1)^{2^n}+2}(\bmod.3)

    If n>0 we have that 2^n is even and therefore (-1)^{2^n}=1 thus: 2^{2^n}+5\equiv{3}\equiv{0}(\bmod.3)

    If n=0 we have: 2^{1}+5=7 that is prime

    Therefore the only prime in that sequence is 7
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