The Largest Known Primes website claims that the number 232582657-1 is the largest known prime number. How can this number be the largest known prime number? Is the next prime number after 232582657-1 not a prime? Is it not a number? Is it not known? Can’t it be calculated? I can write a simple algorithm that will print the first n prime numbers for every n. Are there not enough prime numbers? Are they not infinite? Is the term “the largest known prime number” well defined? Is it a number? Is it real? Does it have a factorial? Can’t its factorial be substracted by one? Can’t the result be factorized into prime factors? And if it can, is the largest prime factor not larger than “the largest known prime number”? Is it not known?
The answer to the question “is 232582657-1 the largest known prime number?” depends on who’s asking and who’s answering the question. If you’re asking me, 232582657-1 is definitely not the largest known prime. If it is a prime, and I’m not sure it is, then a larger prime can also be calculated. Therefore, it is already known. Or at least, it is not unknown. Maybe it’s just another example of an unknown unknown. In any case, the answer to this question is not deterministic.
It appears to me that any language, whether human language, mathematical language or computer language, contains ambiguities, paradoxes and vague definitions. No language is both deterministic and fully consistent. If a language is inconsistent, then in what sense can it be deterministic? Which leads me to the conclusion that determinism doesn’t exist even in theory. With any given number, there is some uncertainty whether it is or is not a prime.