Tuesday, June 30, 2020

[oylzskqk] Unusual Goldbach

For even numbers of a given size, what is the probability distribution for the number of decompositions of the even number into a sum of two primes?  How does mean and variance grow as the even number grows?

The current Wikipedia article on Goldbach's Comet contains histograms of the distribution.  It is unsourced and seems to be original work.  The distribution appears to have many peaks.

What are some even numbers whose number of prime decompositions is unusually high or low?  Can they be explained?

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