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24336Re: Primes again [really Mordell's equation]

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  • kevinacres
    Jul 31, 2012
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      --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
      [snip]
      >
      > http://oeis.org/A173795
      > shows the origin of my Prime Puzzle 36.
      >
      > > Second hint: Jens Kruse Andersen has already high-lighted
      > > Donovan Johnson's prime, in a closely related Prime Puzzle.
      >
      > http://www.primepuzzles.net/puzzles/puzz_563.htm
      > show a cognate Prime Puzzle, illuminated by Jens.
      >
      [snip]

      Results from a neat little algorithm devised by David Broadhurst has allowed extension of the above puzzle.

      In particular the prime number 107122676734733201 is a combination of positive cubes and squares in 14 different ways.

      David's investigations also unearthed a couple of primes (4417190430889897 and 84658174289284249), originally found in a search by Noam Elkies, that are combinations of positive cubes and squares in 11 and 12 different ways respectively.

      http://www.primepuzzles.net/puzzles/puzz_563.htm

      is now updated with these three new entries.

      Many thanks to David for both his algorithmic ingenuity and scholarly archeology.


      Kevin.
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