## Re: [PrimeNumbers] Re: Take any even number! A prime puzzle

Expand Messages
• ... It s 30, but you ll never prove it. :) Proving that it s 30 would seem to be roughly as difficult as proving the Goldbach conjecture. The numbers which
Message 1 of 3 , Mar 31, 2006
jbrennen <jb@...> wrote: --- Bob Gilson wrote:
> Question: What is the highest even number that will resolve to zero?

It's 30, but you'll never prove it. :)

Proving that it's 30 would seem to be roughly as difficult as proving
the Goldbach conjecture.

The numbers which resolve to 0 are 4, 6, 10, 16, 22, and 30.

You could create other related conjectures. One might be:

Assume that you can choose ANY pair for a number, rather than
always having to choose the largest pair. Which even numbers
cannot resolve to 0? It appears that only 2, 8, and 12 cannot
resolve to 0. Again, proving it is the tough part. You need
to show that every even number > 12 can be expressed as a sum
of primes p+q where abs(p-q) is not 2, 8, or 12, which is
basically Goldbach plus a twist.

And there was I, drinking a Brandy & Coke, watching the moon rising over the Waterfront in Cape Town, suddenly having this really amazing truly original thought, only to find (as usual), that someone's thought about it before. Ah well, hey ho, BUT one day.....

Thanks for the enlightenment, anyway.

Bob

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
The Prime Pages : http://www.primepages.org/

---------------------------------

To unsubscribe from this group, send an email to: