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Re : Quadratic Prime Chains: irreducible polynomials are prime producing

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  • Kermit Rose
    1a. Quadratic Prime Chains Posted by: aldrich617 aldrich617@yahoo.com aldrich617 Date: Sun May 25, 2008 6:28 am ((PDT)) Can anyone factor X4 - 97X3 + 3294X2
    Message 1 of 1 , May 25, 2008
      1a. Quadratic Prime Chains
      Posted by: "aldrich617" aldrich617@... aldrich617
      Date: Sun May 25, 2008 6:28 am ((PDT))



      Can anyone factor

      X4 - 97X3 + 3294X2 -45458X + 213589
      (49 consecutive primes)

      into quadratics?




      A basic theorem of algebra implies that
      a quartic polynomial that takes on more than eight prime values is
      irreducible.


      The basic reason is that if
      X4 - 97X3 + 3294X2 -45458X + 213589


      could be factored into quadratics then whenever the product is prime,

      one of the factors must be plus or minus that prime,
      and the other factor must be plus or minus one.
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