You were guessing that an AI could increase efficiency, using numbers which show you know nothing about the topic.
Primes have lots of order and patterns, so references to chaos and "no such order exists" aren't really relevant.
As to "why" - this is recreational mathematics. It's because people find it fun or engaging. And it isn't special - recreational mathematics covers far more than just primes. There's a lot of people who love calculating digits of pi, as one clear example.
>> There's a lot of people who love calculating digits of pi, as one clear example.
Right... that's what I meant about irrational numbers. I'm not trying to rain on the parade of the hobby of it all, but if there were an actual pattern, primes would not be useful in cryptography. The hobby of trying to find "the pattern" is Sunday morning armchair alchemy. Nothing wrong with it, and maybe there's a pattern to be found one day. Great. Whether there is or isn't is only relevant given that we don't know what that pattern is yet. It doesn't, as some imagine, imply the existence of a higher order intelligence.
Note that none of these refer to a definite "the pattern."
Primes are useful in the RSA cryptosystem because modulo exponentiation is cheap while in general factoring the product of two large prime numbers is far less tractable - as far as we know.
Primes have lots of order and patterns, so references to chaos and "no such order exists" aren't really relevant.
As to "why" - this is recreational mathematics. It's because people find it fun or engaging. And it isn't special - recreational mathematics covers far more than just primes. There's a lot of people who love calculating digits of pi, as one clear example.