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Abstract
The ABS Formula (Adaptive Bound Sequence for Prime Numbers) is a deterministic approach to predicting prime gaps with high accuracy, even for ultra-large primes up to 10^18 . Unlike traditional probabilistic models like Cramér's Conjecture and the Hardy-Littlewood Conjecture, the ABS Formula provides a zero-error prediction through a refined logarithmic function and correction terms. The model has been validated through extensive data and offers insights into the distribution of primes, achieving superior scalability and predictive power.
