2^p+3^q, p and q in P

Discussion in 'Math Research' started by Spertejo, Jul 7, 2009.

  1. Spertejo

    Spertejo Guest

    Let P the set of prime numbers in N. Let p, q in P and p<q.
    To find the pairs (p, q) such that 2^p +3^q and 2^q +3^p are primes
    simultaneously.
    The solutions are finite?
     
    Spertejo, Jul 7, 2009
    #1
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  2. There are at least 3 solutions, listed as pairs (p,q, the prime 2^p+3^q):
    2 3 31
    3 2 17

    3 5 251
    5 3 59

    3 13 1594331
    13 3 8219

    The primes 31, 17, 251, ... listed as the third numbers are necessarily a subset
    of sequences A004051 and A164074 of the OEIS at
    http://research.att.com/~njas/sequences .

    --
    Richard J. Mathar Tel (+31) (0) 71 527 8459
    Sterrewacht Universiteit Leiden Fax (+31) (0) 71 527 5819
    Postbus 9513
    2300RA Leiden
    The Netherlands URL http://www.strw.leidenuniv.nl/~mathar
    office: Niels Bohrweg 2, 2333 CA Leiden, H104
     
    Richard Mathar, Sep 18, 2009
    #2
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