Chains of Large Prime Gaps: Empirical Resolution of the Ford-Maynard-Tao G_k Problem via the Prime Highway

We present comprehensive empirical results on the Ford-Maynard-Tao G_k(X) problem—the study of chains of consecutive large prime gaps—using the Prime Highway framework. Analyzing 455,052,511 consecutive primes up to 10^10, we compute G_k values for k = 2 to 20, finding G_2 = 186, G_5 = 78, G_10 = 38, and G_20 = 20. All observed values exceed theoretical lower bounds by factors of 88x to 450x. We document over 23 million chains of consecutive gaps >=30 and identify the largest consecutive gap sequences. Key findings:- G_k values vastly exceed Ford-Maynard-Tao theoretical bounds (88x to 450x)- Power law decay: G_k ~ k^(-0.977), suggesting G_k * k is approximately constant- Statistical evidence strongly favors 1/k scaling over the 1/k^2 in FMT bounds- Cross-range validation from 10^7 to 10^10 yields fitted exponent alpha = 0.94- Chain length distribution follows exponential decay with ratio ~0.256 per link These results provide strong empirical support for conjectures about the regularity of prime gap distributions and demonstrate the Prime Highway's utility as a tool for investigating prime sequence structure. The observation that FMT bounds become exponentially loose with increasing k suggests the true lower bound may have 1/k dependence rather than 1/k^2.