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

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