[mathemadigal]

I think we’ll need to wait for an answer to if there is a prime number generating function.

At that time we can determine if 1 is prime.

If it’s found that Eratosthenes’ sieve is the only prime generating function then we have our answer.

[dullcrisp]

We'd have our answer in what way?

[mathemadigal]

I apologize for the ambiguity, it’s apparent when you’ve read the article as it addresses this specific point.

Namely, if the sieve is the only generating function for all of the primes then 1 would need to be omitted as prime as removing its factors would remove every number, thus failing to generate the list of primes.

[fhars]

If you treat one as prime number when running the sieve algorithm, one is the only prime number that remains after you have removes all its multiples from the list of candidate numbers.