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6. The 1st Diagonal that runs parallel to either side of the main Prime Diagonal (PD, not of PRIME numbers, but primary), is composed of the ODD WINs: 1,3,5,…infinity.


7. If we add +1 to each value, that 1st Diagonal now becomes a sequence of ALL the EVEN WINs (≥4): 4, 6, 8,…infinity.


8. Select ANY EVEN WIN and plot a line straight back to its Axis WIN — that Axis WIN = EVEN/2 = core Axis #.


9. Upon that same Axis, PRIME Pair sets (PPsets) — whose sum (∑) equals the EVEN WIN (on the 1st Diagonal) — will be found that form the base of 90° R-angled isosceles triangle(s) whose apex lie(s) on that straight line between the EVEN and its 1/2 Axis WINs. PPsets with identical PRIMES = 1/2 Axis value.


10. The proof that every EVEN WIN has ≥1 PPsets can be seen in the
Periodic Table Of PRIMES (PTOP) that stealthily informs the BIM of how each and every EVEN WIN is geometrically related to one or more PPsets.


11. These PPsets are NOT randomly contributing their ∑s to equal the EVEN WINs, rather they come about as the consequence of a strict
NPS: the sequential — combining, linking, concatenation — addition of the PRIMES Sequence (PS) — 3,5,7,11,13,17,19,…—to a base PS — 3,5,7,11,13,17,19,….

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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!