Q-Hot Cache: A High-Throughput Method for Empirical Verification of the Even Goldbach Conjecture

We present the Q-Hot cache method, a novel algorithm for high-throughput verification of the even Goldbach conjecture. The method exploits temporal locality in Goldbach pairs — consecutive even numbers tend to share large prime components — by maintaining a ring buffer of recently proven primes. Over 99.98% of even numbers resolve from the cache alone, reducing verification to a subtraction and a table lookup. Key results: - 939 million verifications per second on a single 12-OCPU AMD EPYC VM (Oracle Cloud)- Currently verifying [4×10¹⁸, 4.001×10¹⁸] — extending the world record set by Oliveira e Silva et al. (2014)- Zero failures across trillions of even numbers verified- Total compute cost: under $48 The repository includes the full paper, C++ source code with checkpointing support, and an independent verification script using SymPy.