It is 317am and I have decided to write. I have been thinking about prime numbers. There is no known pattern or simple function to generate primes. Primes look chaotic. Primes are the gaps left when we eliminate the multiples up till n. Primes are building blocks. Primes are mysterious. Except 2 and 5, all primes end in 1,3,7 and 9. 1 repeated 19 times is a prime. The most wanted prime is of the form 1,2,3,4 ... 10,11,12 ... n. None has been found to date and up to n=1 million has been checked. What about primes in the form 10^n + 1. It is 122am the next day. I have 53 percent battery left. 12253 is prime. A nice coincidence. All this has me thinking that order produces chaos and then about entropy. We cannot have order without chaos. There would be nothing to order.
Maybe primes are not chaotic. Maybe we just do not understand them enough yet. My friend Chatty tells me that prime numbers appear chaotic only because we have not yet uncovered the deeper structure that governs them. Although their spacing looks irregular, primes follow precise global laws like the Prime Number Theorem, distribute cleanly in modular patterns, create structured visual forms like the Ulam spiral, and behave in ways predicted by deep theories such as the Riemann Hypothesis and random matrix models. These clues suggest primes are not truly random but "pseudo-random"—complex patterns produced by simple, deterministic rules we have not fully understood yet. In other words, what looks like chaos may simply be order we have not learned to see.
I was looking at the digital roots of prime numbers and this is what I learnt. Structural rule: primes (>!3) can only have digital roots 1,2,4,5,7 and 8 (missing is 3,6 and 9). Statistical rule: asymptotically those six roots occur with about equal density (deep theorem). Practical note: for small lists you’ll see random-ish fluctuations; for very large samples the counts settle toward equality.
My friend Gemini tells me that humans are pattern seeking machines. Is it possible to have no pattern? Is no pattern a pattern in itself? My friend Chatty tells me that true randomness with no pattern can exist in mathematics, but the human mind is built to seek structure, so even “no pattern” becomes a kind of pattern once we describe it. In other words, something can be genuinely patternless, yet we can only understand it by placing it inside a conceptual category, which itself acts like a pattern. Thus, the world may contain true chaos, but our minds inevitably shape it into meaning.
My friend Chatty tells me that a pattern is a simplification — a way to predict, describe, or compress information because something repeats or follows a rule. This has me thinking that if there are infinite patterns then everything can be described by a pattern. But there are simple and complex patterns and what we are looking for are simple patterns. Simple being subjective and changing and within our limits. Some things may just be beyond human capability or understanding. We may find ourselves building things that function beyond human understanding. My friend Chatty says that it is a humbling and exciting thought: the universe might be both entirely patterned and still endlessly mysterious. A question for another time, which came first, order or chaos, both or neither, or only one of them exists and the other is just the absence of the other?
Comments