Parity problem (sieve theory)

In the context of sieve theory, the "parity problem" generally refers to questions about the distribution of prime numbers. More specifically, sieve theory involves methods that can help determine how many integers in a given set meet certain criteria, often in relation to being prime or composite. The parity problem in sieve theory can typically involve exploring the even and odd behavior of prime numbers or their residues modulo some integer. One classic observation related to parity and primes is that all prime numbers except for 2 are odd.