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Math Help - 2^p+3^q, p and q in P

  1. #1
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    2^p+3^q, p and q in P

    Let \mathbb{P} the set of prime numbers in \mathbb{N}. Lets p, q in \mathbb{P} and p<q.
    To find the pairs (p, q) such that 2^p +3^q and 2^q +3^p are primes simultaneously.
    Last edited by rrronny; September 5th 2009 at 03:10 AM.
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  2. #2
    Junior Member
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    Gothenburg, Sweden
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    Interesting question. It's easy for p \equiv q \pmod4 since 2^p+3^q \equiv 2^p + (-2)^q \equiv 0 \pmod5 iff p \equiv q \pmod4. When p \not\equiv q \pmod4 it seems to be a lot harder.
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