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Introduction


While the (strong) Goldbach Conjecture has been verified up to 4x10**18, it remains unproven.


A number of attempts have demonstrated substantial, provocative and often beautiful patterns and graphics, none have proven the conjecture.


Proof of the conjecture must not rely solely on the notion that extension of a pattern to infinity will automatically remain valid.


No, instead, a proof must, in its very nature, reveal something new about the distribution and behavior of PRIMES that it is absolutely inevitable that such pattern extension will automatically remain valid. The proof is in the pudding!


Proof offered herein is just such a proof. It offers very new insights, graphical tables and algebraic geometry visualizations into the distribution and behavior of PRIMES.


In doing so, the Proof of the Euler Strong form of the Goldbach Conjecture becomes a natural outcome of revealing the stealthy hidden
Number Pattern Sequence (NPS) of the PRIMES.

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PTOP & Goldbach Conjecture

By RBrooks

While “hidden” on the BIM (BBS-ISL Matrix), the PRIMES form PPsets — pairs — whose members lie in equal, symmetrical steps on either side of the EVENS number that has been divided by 2. This geometric, embedded pattern on the BIM can be presented as the PTOP: Periodic Table Of PRIMES. Here, these PPsets form the EVENS. The PPsets become “Trails” of PPsets, that increasingly overlap such that more than one PPset is present to compose a given EVEN. In doing so, they satisfy and prove the Goldbach Conjecture!