This is my first post, so apologies if I unwitingly fail to observe forum etiquette.
My question has to do with the number theory, but it also incorporates elements of phiosophy of mathematics, so please forgive if it seems odd. In a nutshell, I'm currently doing research on human cognitive limitations -- this is, I'm investigating if there are any areas that human beings, but virtue of their cognitive structure, are incapable of grasping. To this end, I'm exploring the ramifications of a hypothetical mind for which the sequence of primes is as intuitively obvious as the sequence of intergers is for us.
This brings me to my question: Would any practical value attach to having such a mind -- i.e. is there any task we'd like to be able to do but can't because we cannot construct an algorithm to generate the primes? (Note: I exclude solving cryptographic problems from this, as it trivially plays off our inability to discover in any easy way whether a number is prime or not).
Any thoughts very much appreciated.