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20523Re: Small prime divisors of very large numbers

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  • David Broadhurst
    Jun 30, 2009
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      --- In primenumbers@yahoogroups.com,
      "Jens Kruse Andersen" <jens.k.a@...> wrote:

      > David Broadhurst wrote:
      > > The first 7 primes that divide
      > > 137^(137^(137^(137^137))) + 73
      > > are 2, 3, 5, 29, 821, 23339, 67525153.
      > >
      > > Puzzle: Find the first 7 primes that divide
      > > 137^(137^(137^(137^(137^137)))) + 73
      >
      > The same.

      As might have been expected, Jens was the first
      to post what I believe to be the correct solution.

      Almost at the same time, Richard FitzHugh
      sent me, privately, the same answer:

      > I get the same first 7 primes to divide your larger number
      > (namely 2, 3, 5, 29, 821, 23339, 67525153). This seems very
      > strange indeed! It took about 6 minutes of actual processor
      > time, after about 20 minutes of trying to accurately place
      > all the brackets in the nested eulerphi calls!

      Like Richard, I find this result to be "strange indeed".

      Can anyone tell Richard and me why we should not be surprised?

      With thanks to all concerned

      David
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