Can you find another number like 2200?
Here is something I am having trouble with related to Goldbach Conjecture and maybe someone has some ideas on how to improve the search? I think these numbers will be exceedingly rare if they exist at all.
Can anyone find another even number and two primes like 2200,3, and 13?
2n=2200
p1=3
p2=13
2np1=2197=p2^3
2np2=2187=p1^7
2n minus each prime equals the other prime to a power. This is the only example I have found, but I haven't checked very far (100000). It gets combinatorically hard to search pretty quickly so I would rather search smarter.
It is fairly easy to show there are no single prime patterns like this and I would like to extend the search to 3,4, etc primes as well where each of the differences composed only of powers of the other primes.
