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Re: 40 prime polynomials

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  • Patrick Capelle
    ... Big false statement. But sometimes some errors are interesting. When i wrote this false conjecture, i had in front of me the prime-generating polynomials
    Message 1 of 4 , Mar 25, 2006
      --- In primenumbers@yahoogroups.com, "Patrick Capelle"
      <patrick.capelle@...> wrote:

      > A conjecture for the end :
      > All the prime-generating polynomials of degree n > 2 (without absolute
      > value) give less than 40 positive and distinct prime numbers.

      -------------------------------------------------------------
      Big false statement.
      But sometimes some errors are interesting.
      When i wrote this false conjecture, i had in front of me the
      prime-generating polynomials of the Carlos Rivera web site
      (see http://www.primepuzzles.net/puzzles/puzz_232.htm ).
      I was in fact astonished by the fact that all the cubic polynomials of
      this page were including negative values and that no example was given
      with only positive and distinct prime numbers.
      I saw that for the positive primes of each set given by the cubic
      polynomials, their number was always smaller than 40.
      Why 40 ? Because nearly all this day i was thinking to the quadratic
      polynomials, the Euler's quadratic polynomial and the lucky numbers of
      Euler.
      Starting with this observation, i don't know why i did suddendly this
      shift for higher degree.
      It would have been better that i stay with my first impression.
      Simply.
      So my question is this one :
      Do all the prime-generating polynomials of degree 3 (without absolute
      value) give less than 40 positive and distinct prime numbers ?

      Patrick Capelle.
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