I am exploring the question of efficiently identifying two prime numbers that sum to a given large even number, particularly for even numbers exceeding 100 digits. While brute force and precomputed prime tables are common approaches, I am curious whether there exists a deterministic algorithm capable of solving this problem, given sufficient computational resources.

Specifically, I am interested in methods that:

    Avoid reliance on probabilistic techniques (e.g., random sampling of primes).
    Operate deterministically to find a valid prime pair for any even number within the given constraints.
    Scale efficiently as the size of the even number increases.

Are there any existing algorithms or advancements in this area that can achieve this deterministically? Alternatively, is there ongoing research into related methods for efficiently handling this problem?

I would appreciate any insights or pointers to theoretical or computational techniques that address this challenge. Thank you for your time and expertise.