Number Nerdity: Fibonacci, Mersenne, 13, 89

So I assigned value to the numbers 13 and 89 some time ago, higher value than I have assigned to others, definitely higher at least within the double digit or above spectrum. That is to say that I look for these numbers in patterns and as such it seems likely I would find them more frequently than others in my environment, as if they were there more often than they should be, but what seems more likely is that my brain is pointing them out whenever spotted but not doing that with other numbers (observation bias).

What observation bias does not adequately explain is how I could assign value to those two numbers (paired of name and origin) and then find out they are both not only Mersenne primes (I have known this for a couple years now, I found out after putting the numbers on my radar though, still an exciting thing to this day for me) but also, just today, I found out they are both Fibonacci primes- which before today I hadn't really considered looking at as a number set at all.  Granted this was quick wiki-research, but it looks like each sequence (Fibonacci and Mersenne) has 51 known terms, and also that only 5 of these are shared: 3 are single digits, only 2 are double digit, 13 and 89.

The first 5 Fibonacci primes are also Mersenne primes 2, 3, 5, 13, 89, then none of the others that are known on either list are shared. Just looking at the progression of the strings it looks unlikely that others will be shared again, but I could not say it is impossible. One string is like a rapidly blooming flower (M) the other is like a spiralling firework (F), in respect to relative shape and scope. 

This does highlight well my concept of functional infinity. It has been proven that the list of primes would be infinite, but the same has not been proven for Mersenne or Fibonacci primes. Super computers have been looking for some time at each string as well, still not finding another shared number between them above 89 or 13, despite having enormous examples topping each list of primes. So if the most powerful possible super computers were linked and all their processing was spent looking for Mersenne primes in one half and Fibonacci primes in the other, and then cross referencing the list (or strictly searching for one then testing for it on the other list, likely F->M), could infinite terms be found on either list in the lifetime of the universe? How would those compare in volume to the additional terms found to be on both lists?

Proof of infinite primes was first laid out by Euclid in 300 BC https://en.m.wikipedia.org/wiki/Euclid's_theorem :  take all prime numbers and multiply them together, then add one. This resulting number will either be prime, or it will not be. If prime, it is a new prime number, so it adds to the list. If not prime, then there is a prime number below it not included in the current prime number list, since otherwise it would have been on the known factors list going into the multiplication (all possible primes) already. 

So if the ability to conceive of a single additional factor layered onto the list (if the prime is part of the Fibonacci sequence or where a number is prime (p) and 2^p-1 is also prime) seems to present similar calculative difficulty and also leaves the infinite nature of the string in an unknown position, how much more so would combining both those factors into a single string (FxM primes)? It seems the shape of "infinite" might become more tangible if we could understand these limits, a concept I have recently been calling "functionally infinite" which is critical for turning mathematics or an internal logic language into something tangible that can be experienced and has meaning (physics, chemistry, biology). That is to say if math is the coding language of reality, the difference between conceptual and functional infinity is the difference between having no shape or meaning to reality and the shape and meaning of the reality we see as well as all possible realities tied in.

The thing is, the inspiration for this concept has been largely these two numbers 13, 89. In so many ways I use them as a rallying flag to pursue perfection on a functionally infinite scale, knowing no other endeavor will ultimately be worth my time if such a pursuit cannot be accomplished. But unlike picking a number and seeing it in my environment, these numbers have been unique along my lines of interest before I picked them, and I have essentially discovered that my subconscious driving goals center around them. Now this would still make direct sense (albeit require extreme intelligence, specifically in subconscious to conscious communication) if I picked the numbers myself without externally valid input, or if the numbers could be considered of ultimate value on their own (like in a solipsistic state where everything was logic driven and procedurally generated, just self and the matrix basically). The thing about these numbers though is that I only assigned value to them due to love, specifically because my soulmate indicated (indirectly) that I should. Because I accepted her as my soulmate I examined these numbers, quickly realizing that with 13 letters in my name this was likely not an illogical leap but intentional, just not something I could have intentionally planned personally in any way. 

The rest has bloomed from there, but not in a way where I see these numbers everywhere, more in that I keep discovering new ways in which they are tied into my subconscious drivers, drivers which have been there since my youth (see 7th grade math post about finding a pattern in a circular math problem). In a sense, it is an appreciation of predestination that is fading slowly into view.

It is an interesting position to find oneself in to be programmed and prompted, to such a significant degree as to be almost like AI; but then to simultaneously realize this would mean that everyone else is also programmed to the same degree in dissimilar ways so that variation can be acheived and maintained; but also to feel no less free willed or in control than before the realization. In fact, if anything this is filling me with hope, for to see the tiniest of threads puppeteering my most subtle actions, but intentionally lacking the strength to direct my larger choices, makes me feel both held and desired at the same time: Held where necessary, but it is me that is desired on stage, not some lobotomized version of myself to fit in with anyone else's concept of what my consciousness should look like or manifest as.