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RE: [PrimeNumbers] Primes ax^+bx+c

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  • Milton Brown
    Using the step function you can make a function, which produces as many primes as desired. Here is one which yields the primes 2, 3, 5, 7, 11, 17, 23, 29, ...
    Message 1 of 5 , Jul 24 11:31 PM
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      Using the step function you can make a function,
      which produces as many primes as desired.

      Here is one which yields the primes 2, 3, 5, 7, 11, 17, 23, 29, ...
      (it skips the second of the twin primes)

      (x+2) +((x-2)/abs(x-2) +1)
      +3((x-4)/abs(x-4) +1)
      +2((x-5)/abs(x-5) +1)
      +3((x-6)/abs(x-6) +1)
      +3((x-7)/abs(x-7) +1)
      +...

      Milton L. Brown

      > [Original Message]
      > From: Juan Ignacio Casaubon <jicasaubon@...>
      > To: Juan Pablo Cosentino <juanpablocosentino@...>; Jorge
      Escudero <jorge@...>; Prime Number
      <primenumbers@yahoogroups.com>
      > Date: 7/24/2005 9:13:43 AM
      > Subject: [PrimeNumbers] Primes ax^+bx+c
      >
      > Hi
      >
      > Euler (1772)
      >
      > x^2-x+41 is prime for x from 0 to 40
      >
      > Legendre (1798)
      >
      > x^2+x+41 is prime for x from 0 to 39
      >
      > Chaffey (2003)
      >
      > 2x^2-88x+997 is prime for x from 0 to 50
      >
      > Hartley (2003)
      >
      > 2t^2-112t+1597 is prime for x from 0 to 56 (same as
      >
      > Chafey using x = t - 6 )
      >
      > i.e. Chaffey for a few negative values of x
      >
      > The question: One can stablish a Theorem?
      >
      > a x^2 + b x + c is prime for x from 0 to N, taken a(N),
      >
      > b(N), c(N) functions.
      >
      > bye
      >
      > Ignacio
      >
      >
      >
      >
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