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On the primality of 2^p+3^q

  1. Sep 15, 2009 #1
    Let [tex]\mathbb{P}[/tex] the set of primes. Lets [tex]p,q \in \mathbb{P}[/tex] and [tex]p \le q.[/tex] Find the pairs [tex](p,q)[/tex] such that [tex]2^p+3^q[/tex] and [tex]2^q+3^p[/tex] are simultaneously primes.
  2. jcsd
  3. Sep 15, 2009 #2


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  4. Sep 15, 2009 #3
    Hi Borek,
    I do not have a solution for this problem...
    I found only four solutions: [tex](1,1), (1,2), (2,3), (2,6).[/tex]
  5. Sep 19, 2009 #4
    wait... 6 is not a prime...
  6. Sep 19, 2009 #5
    Neither is 1 so only one of the 4 pairs posted is acceptable. There is still another very obvious pair that was overlooked.
  7. Sep 19, 2009 #6
    Sorry... :blushing: I meant the sixth prime number.
    In summary, then, the only solutions [tex](p,q)[/tex] that I found are [tex](2,2),(2,3),(3,5), (3,13).[/tex]
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