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19. Similar to how the grid cell values of the Axis, PD and IG of the Pythagorean Triples reveal additional, intimate connections within the BIM, so too do the PPsets: the 1st PRIME values of each set points to the # of STEPS from the PD that intersects the given EVEN WIN (Axis**2), on a straight line path back to its Axis, at the apex where its other PPset member intersects — this is no mere coincidence — and that apex is, of curse, the 90° R-angle isosceles triangle that results. For example: EVEN = 24, Axis = 12, PD = 144, # of STEPS from PD towards Axis = 5 and 19 for the 5+19 PPset and 7 and 17 for the 7+17 PPset, and 11 and 13 for the 11+13 PPset that each forms the EVEN 24.


20. As the bifurcation concatenation of the PS — 3,5,7,11,13,17,19,..— with the same base PS — 3,5,7,11,13,17,19,…— of those EVEN WIN — that when “3” is subtracted, the remainder is a next-in-the-sequence PRIME — remains one of a similar split with the Pythagorean Triples: for every “Primitive” parent PT, there are multiple “Non-Primitive” child PTs and it is the PPTs (Primitive Pythagorean Triples) that ultimately form the inter-connectedness of ALL PTs back to the original PPT — the 3-4-5. With the PRIMES, one raises the question: why are these “EVENS” preselected to be the “parent” EVENS forming the “beginning” or “start” of every PPset Trail with all other EVENS hitching on to that Trail further down the sequence?


21. Another set of STEPS (S) from the core Axis Value , directly on the Axis, identifies each symmetrical pair of a given PPset that forms that given EVEN. These STEPS may by Universally calculated from the EVENS, P1 and P2 values.

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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!