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Old 2018-12-03, 02:37   #1
goldbug
 
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Dec 2018

1616 Posts
Cool 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


2n-p1=2197=p2^3
2n-p2=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.
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