Generating large prime numbers via The Goldbach Conjecture and The Symmetry of Prime Pairs around any integer

This paper presents a new approach, supported by two new algorithms for efficient prime
number generation based on The Goldbach Conjecture and its relation to arithmetic symmetry.
The algorithms use the assumption, derived from the conjecture, that around every number there
exists at least one symmetric pair of prime numbers, which significantly reduces the number of
candidates for testing. Even without a full proof of the conjecture, its partial validity (e.g., 90%
or 50%) is sufficient for a simplified and accelerated generation process. We demonstrate the
effectiveness of the method by generating 30 prime numbers with 200–300 digits in minutes
using a fast search procedure.