Arturo´s criterion for additive prime blocks: A necessary condition based on local density for finite Goldbach closure

Key Points

• This research aims to establish a condition for odd primes to generate even numbers up to a limit through sums.
• Proving that the closure of additive blocks occurs when n is the largest of a prime quadruple.
• Analyzing the implications of local density in relation to the closure property for finite sets of primes.
• The closure property holds true only when n ≡ 9 (mod 10).
• The largest known prime M = 2^136279841 - 1 does not satisfy this closure, indicating limits for Goldbach Conjecture.