TLDR: we have a “simple” formula that finds prime numbers but it’s not very efficient and becomes prohibitively expensive to compute for large numbers. Come up with a more efficient algorithm and you could claim the million dollar prize.

Does this mean this formula can calculate prime numbers without finding all smaller primes (as the Sieve of Erastothenes does)? Or is that somehow just implicitly done with all the factorials and sums and whatnot?