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Re: RE 40 prime polynomials

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  • Mark Underwood
    ... Another example: Consider the (already known) prime poly 36x^2 - 810x + 2753 which produces 45 consecutive primes (including negatives) from x=0 to x=44.
    Message 1 of 12 , Apr 5, 2006
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      --- In primenumbers@yahoogroups.com, "Mark Underwood"
      <mark.underwood@...> wrote:
      >
      >
      > Anyways, the point I wanted to reiterate is that if one is searching
      > for prime polys of the form
      > ax^2 + bx + c
      > such that x roams in a certain range, one need only consider positive
      > b's from 0 to a. (Otherwise there is redundancy.)
      >

      Another example: Consider the (already known) prime poly
      36x^2 - 810x + 2753
      which produces 45 consecutive primes (including negatives) from x=0 to
      x=44.

      This poly can be reduced to
      36x^2 + 18x - 1801
      which is prime from x=-33 to x=11.
      Notice how b is positive and no more than a. Also notice how b contains
      all the prime factors of a. It must, or else the poly is forced to
      contain the prime factors of a which b doesn't have.

      Mark
    • Mark Underwood
      ... wrote: ... Correction: 9x^2 + 3x + 41 is prime from x=-13 to x=26 Mark (no alcohol required to goof up) Underwood
      Message 2 of 12 , Apr 5, 2006
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        --- In primenumbers@yahoogroups.com, "Mark Underwood"
        <mark.underwood@...> wrote:>
        > But these three can be simplified to
        > x^2 + x + 41 (prime from x=0 to x=39)
        > 4x^2 + 2x + 41 (prime from x=-20 to x=19)
        > 9x^2 + 3x + 41 (prime from x=-20 to x=19)
        >

        Correction: 9x^2 + 3x + 41 is prime from x=-13 to x=26

        Mark (no alcohol required to goof up) Underwood
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