## n-th prime and Goldbach

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• http://www.research.att.com/projects/OEIS?Anum=A102043 Sequence: 4,6,18,30,124,122,418,98,220,346,308,1274,1144,962,556,2512,
Message 1 of 1 , Feb 13, 2005
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http://www.research.att.com/projects/OEIS?Anum=A102043
Sequence: 4,6,18,30,124,122,418,98,220,346,308,1274,1144,962,556,2512,
4582,1382,4618,992,3818,7432,12778,5978,26098,2642,23266,
10268,19696,14198,34192,22606,5372,37768,13562,9596,22832,
59914,7426,88786,50312,97768,48002
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.
Keywords: nonn,new
Offset: 1
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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