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Re: 5,31,7625597485003

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  • Mark Underwood
    ... Thank you David, how you find things like that is beyond me. It was a nice feeling while it lasted. :) As it stands, I have lost about all expectation that
    Message 1 of 5 , Jul 30, 2009
      --- In primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:
      >
      > --- In primenumbers@yahoogroups.com,
      > "Mark Underwood" <mark.underwood@> wrote:
      >
      > > 1^1^1^1^1 + 2^2^2^2^2
      > >
      > > If the above has been proven composite (don't know)
      > > then it will greatly lower my expectation that
      > > 2^2^2^2 + 3^3^3^3 is prime
      >
      > Not only is the former number composite, but
      > we also know two of its prime factors:
      >
      > 825753601
      > found by Selfridge in 1953
      >
      > 188981757975021318420037633
      > found by Crandall and Dilcher in 1996
      >
      > http://www.jstor.org/pss/2585029
      >
      > David
      >

      Thank you David, how you find things like that is beyond me. It was a nice feeling while it lasted. :) As it stands, I have lost about all expectation that 2^2^2^2 + 3^3^3^3 is prime. One reason: what you just posted. Another reason: I just got through some fiddling and see that even small prime factors intrude into the mix at higher powerings (if I have calculated correctly).

      For instance if 2^2^2^2 + 3^3^3^3 is considered the fourth powering, then at the 26th powering the factor of 283 is introduced.

      This same factor of 283 then reappears every 21st power after that: at the 47,68,89,110,131,etc. powering. (I think.)

      Mark
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