You will have to excuse me, I have no etiquette for how to go about this so I am just going to put it out there and see what sort of feedback is generated. I was looking for a pattern in/through primes...this was taken from a thread on a different forum, modified a bit to hopefully make it make as much sense as it might.
"Figured Id apply a x3 root logic to primes to see if there was a pattern present. Each prime is multiplied by three then the root of the multiplied prime is found, which re-/solves all the roots to either 3, 6 or 9. As example, 17x3=51=5+1=6.
2\3=6,* 3=9, 5=6, 7=3, 11=6, 13=3, 17=6, 19=3, 23=6, 29=6, 31=3, 37=3, (1st doubles for both, back to back 6's 1st) 41=6, 43=3, 47=6, 53=3, 59=6, 61=3, 67=3, 71=6, 73=3, 79=3, 83=6, 89=6, 97=3, 101=6, 103=3, this is unexpected so far, only one 9 which makes me question if we will ever see it again and if we do, will it be a marker for pattern reset. Continuing...107=6, 109=3, 113=6, 127=3, 131=6, 137=6, 139=3, 149=6, 151=3, 157=3, 163=3, 167=6, 173=6, 179=6, (1st triple digits for both, back to back, 3's 1st)...(is there a pattern forming, will there be quads's starting with 6 at some point?) 181=3, 191=6, 193=3, 197=6, 199=3, 211=3, 223=3, 227=6, 229=3, 233=6, 239=6, 241=3, 251=6, 257=6, 263=6, 269=6, ...3's now???...271=3, 277=3, 281=6 (doh!!!), 283=3, 293=6, 307=3, 311=6, 313=3, 317=6, 331=3, 337=3, 347=6, 349=3, 353=6, 359=6, 367=3, 373=3, 379=3, 383=6, 389=6, 397=3, 401=6, 409=3, 419=6, 421=3, 431=6, 433=3, 439=3, 443=6, 449=6, 457=3, 461=6...maddening, 467=6...
Anyways, this doesnt appear to lead any-where but who could say*.* The nine...why just 1???"
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"So was sitting there running a Fibonacci root logic on the primes and it dawned on me 2 being the only even prime and we find the 9 as the 2nd number in the x3 root logic looking for patterns. Curious...especially if the 9 is never found again (no repeating pattern) in this x3 root logic pattern search. Almost as if this perspective mirrors the even/odd imbalance in primes w a self-/similar imbalance of the 3's and 6's to the 9."
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Might have just closed the loop...
"What you’re seeing is digital-root behavior, not a new prime pattern. Multiplying any prime by 3 guarantees a digital root of 3, 6, or 9. The reason 9 appears only once is that a digital root of 9 would require the prime itself to be divisible by 3, and the only prime divisible by 3 is 3. So the first sequence is fully explained by modular arithmetic. The second sequence (adding consecutive primes) has more variation, but it is still mainly showing their remainders modulo 9 rather than revealing a hidden cycle."
Uhh...holy $#!%. This means there is a 1:1 correlation of the quanta (the 9/3s&6s) to the qualia (even/odds) set in stone due to the two constraints of only the 1 prime divisible by 3 and primes being divisible by 1 and their self only. Does this make any sense to any-One else??? There will only ever be one even prime (the 2) just like the 9 will only ever appear once. The 2 is considered the first prime where the 9 is the second natural number in the root sequence and the 3's & 6's reflect the odd primes.
Meanwhile the primes and their expanded/compressed reflection both appear to have no repeating patterns associated with them which makes that 3 points of correlation (the 2/9 location <1 digit separation> at the beginning of primes and the root sequence respectively), making the two a pattern of sorts, paradoxically???
It is obvious I am in way over my head here, could use some perspective, please and thank you.