This seems like... maybe "crankery" isn't the right word, but certainly something overblown in that ballpark. The claim is made "We obtain for the first time a

This seems like... maybe "crankery" isn't the right word, but certainly something overblown in that ballpark. The claim is made "We obtain for the first time an explicit relation for generating the full set P of prime numbers smaller than n or equal to n", but the rule ultimately boils down to just "A number is non-prime if it is either divisible by 2, or divisible by 3, or the product of two numbers which are neither divisible by 2 nor divisible by 3", which is completely trivial. (Also, the author was apparently attempting to patent this insight, as noted at the bottom of the first page. You know what? I've changed my mind. I'm going to happily call this "crankery". Well-LaTeXed crankery, but crankery nonetheless...)