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Generating prime generating polynomials.

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  • Kermit Rose
    Define f_n(b) recursively by f0(b) = 0 f1(b) = 1 f_m(b) = b * f_(m-2) + f_(m-1) f0 = 0 f1 = 1 f2 = 1 f3 = b + 1 f4 = 2 b + 1 f5 = b**2 + 3b + 1 for b = 0 to
    Message 1 of 1 , May 6, 2008
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      Define f_n(b) recursively by

      f0(b) = 0
      f1(b) = 1
      f_m(b) = b * f_(m-2) + f_(m-1)


      f0 = 0
      f1 = 1
      f2 = 1
      f3 = b + 1
      f4 = 2 b + 1
      f5 = b**2 + 3b + 1

      for b = 0 to 1000,
      168 of f5 are prime.

      This is the same as the number of positive primes < 1000.

      f6 = 3 b**2 + 4 b + 1
      f7 = b**3 + 6 b**2 + 5b + 1

      For b = 0 to 1000,
      236 of f7 are prime.


      f8 = 4 b**3 + 10 b**2 + 6 b + 1
      f9 = b**4 + 10 b**3 + 15 b**2 + 7 b + 1
      f10 = 5 b**4 + 20 b**3 + 21 b**2 + 8 b + 1
      f11 = b**5 + 15 b**4 + 35 b**3 + 28 b**2 + 9 b + 1

      for b = 0 to 1000,
      165 of f11 are prime.
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