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

2535Re: Wieferich primes

Expand Messages
  • torasso.flavio@enel.it
    Sep 5, 2001
      --- In primenumbers@y..., John McNamara <mistermac39@y...> wrote:
      > (1) Let f(x,y) = x^2 - y^2 -2xy.
      > f(3511,1093) = 7294949 and is prime P.
      >
      > (2) 7294950 = 2*3*3*5*5*13*29*43 which made it easy to
      > factorise into its 8 factors, of which 5 are less than
      > (P+1)^(1/8) and all less than (P+1)^(1/4). This fact
      > seem to me to make 7294950 fairly interesting as only
      > 6435 previous composites have the property of having 8
      > prime factors, one in more than a thousand.

      Notice that (1) should be read f(x,y) = x^2 - y^2 -xy
      to get f(3511,1093) = 7294949.

      Assuming this, other prime pairs (x,y) exist that
      satisfy f(x,y) = P (prime) and P+1 have the property
      of having 8 prime factors.
      As an example, the prime pair (47,2) gives
      P=f(47,2)=2111 prime and P+1=2*2*2*2*2*2*3*11.

      Regards
      Flavio Torasso
    • Show all 5 messages in this topic