Loading ...
Sorry, an error occurred while loading the content.

Off the cuff speculation

Expand Messages
  • Kermit Rose
    Hello. Because of an alternative factoring algorithm I am working on, the following speculation occurred to me. I know that it is not wise to state a
    Message 1 of 1 , Oct 3, 2009
    • 0 Attachment
      Hello.

      Because of an alternative factoring algorithm I am working on,
      the following speculation occurred to me.

      I know that it is not wise to state a conjecture like this
      before I can test it out myself.

      Perhaps some of you might deem it a puzzle to see how
      quickly you can find counter examples.

      Speculation:

      If z1 is an odd positive integer,
      of the form p * 2**k + 1,
      where p is a prime,


      then

      For c = at least one of the two solutions to
      c**2 = z1 mod p**2, with 0 < c < p**2,

      if z2 = c**2 + (z1 - c**2)/p**2

      has factors z2 = x * y such that (y - x) = 2**k and x > 1,

      then z1 is prime.

      Kermit
    Your message has been successfully submitted and would be delivered to recipients shortly.