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Re: [PrimeNumbers] CONTEST!

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  • Jacques Tramu
    You have to read , Alan. (Furious activity is not substitue from carefully reading). The prime test is on A, not x . (I checked Aldrich conjecture for large
    Message 1 of 3 , Dec 25, 2007
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      You have to read , Alan. (Furious activity is not substitue from carefully reading).

      The prime test is on A, not x .

      (I checked Aldrich conjecture for large values of x, and found no counter example)

      Regards,
      JT

      ------------------------------------------------------
      http://www.echolalie.com
      http://www.echolalie.org/wiki

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      ----- Original Message -----
      From: Alan Eliasen
      To: aldrich617
      Cc: primenumbers@yahoogroups.com
      Sent: Friday, December 21, 2007 12:23 AM
      Subject: Re: [PrimeNumbers] CONTEST!


      aldrich617 wrote:

      > I offer a $50 prize to the first person who can submit
      > a verifiable counterexample or proof by New Year's day
      > for the following primality conjecture:
      >
      > (x,A,B,c,k,f : integers)
      > Let A = 20x^2 + 10x + 1;
      > Let B = 10x^2 + 4x + 1;
      > Let c = trunc(A/sqrt(5)) - 1;
      >
      > For any x > 0, apply the issquare test to each k
      > in the interval c <= k < B. If there is no value
      > of k that satisfies the conditions of the test,
      > then A is Prime.
      > (issquare test: 0 < 5*(2*k -1)^2 - 4*A^2 = f^2)

      Wasn't much of a challenge. Is it a homework problem? The first
      counterexample is at x=5 (which we can all agree is prime.)

      Here, A=551 B=271 c=245

      In this case, when k=247, the value of the expression
      5*(2*k -1)^2 - 4*A^2

      is 841, which equals 29^2. Thus, your algorithm would declare 5 not
      prime, which is incorrect.

      I can provide other examples where it fails in the opposite way, that
      is, declaring a composite number to be prime. The first occurs at x=8
      (which we can all agree is composite.)

      In this case, A=1361 B=673 c=607

      In this case, none of the positive values for 5*(2*k -1)^2 - 4*A^2
      from 607 to 672 produce a square.

      Aldrich Stevens, please transfer the money to my PayPal account by
      clicking the "donate" button here:

      http://futureboy.us/frinkdocs/donate.html

      --
      Alan Eliasen | "Furious activity is no substitute
      eliasen@... | for understanding."
      http://futureboy.us/ | --H.H. Williams




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