I figure I'll drop a couple of more points on this since nobody else seems to have twigged to them.... Goldbach's original conjecture is crap. There is NO way that 3 odd numbers will ever equal an even number. Odd + Odd is Even. Even + Odd is Odd. Fermat was a hell of a lot more charitable to the original assertion than I would have been. Goldbach's existing conjecture can be worded another way: Any even number may be represented by the sum of 3 even numbers provided two of the numbers are 1 less than a prime and we add 2. It's obvious that an even number can always be the sum of other even numbers, it's axiomatic. The question actualy is: Is the set of even numbers whose members are one less than the corresponding member of the primes sufficient, when added to 2, to sum to all the even numbers. As far as I can find nobody has written a lot on patterns of even numbers 1 less than the odds. There's not even a name for the set that I can find. As to somebodies assertion that an odd number can be represented by the sum of two odds, better study your math a tad better. Odd + Odd is *always* Even, never Odd. Happy Thanksgiving! ____________________________________________________________________ Technology cannot make us other than what we are. James P. Hogan The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------