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

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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.

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