n-th prime and Goldbach
Name: Minimal integers m such that m=p(n)+q=sum of 2 primes, where
p(n)<=q is the n-th prime and there is no prime r<p(n) such that
m-r is prime.
Comments: Related to Goldbach conjecture, of course.
Example: a(4)=30=7+23 because p(4)=7,q=23 is prime and there is no prime
r<p(4)=7 such that a(4)-r is prime.
Author(s): Robin Garcia Feb 12 2005
I believe (conjecture is a too strong word), that every prime can be defined with these minimal m even integers.
According to Tomas Oliveira e Silva the largest p in a minimal Goldbach partition up to m=2*10^7 is p(1056)=8443 for m near 1.2*10^17
Would it be useful to look for patterns of successive maximal m/p(n) where m is minimal for every p(n) ?
Of course, this is not related at all with searching big primes.
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