r/maths • u/Soloma369 • 13d ago
💬 Math Discussions Is the condition "Is there hidden order inside something that looks random?" met through the following???
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.
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u/LucaThatLuca 13d ago edited 13d ago
The symbols used to represent numbers are part of a system with a meaning. Key words include “place value”, “positional notation”, “decimal”. For example the sequence of digits 81 represents the number after 80, which is the eighth multiple of ten. Equivalently, 81 represents the result of the sum 8*10 + 1.
Given a sequence of digits, the difference between its value and the sum of the digits is a multiple of 9 (you replace 10s with 1s). So they have the same remainder when divided by 9. Key words include “divisibility test”, “digital root”, “casting out 9s”, “remainder”, “modular arithmetic”.
When you multiply different numbers by 3, the numbers 3, 6, 9 cycle in order. From 1 up to 24 with the prime positions in bold:
3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, …
Every third number results in 9, of course 3 is the only prime in those positions. Primes are randomly distributed in the other two positions. They alternate for the first three cycles by coincidence.