Modal Collapse and Sequential Dependence in LLM Random Number Generation: A Controlled 2×2×2 Study

This study evaluates LLM random number generation under a fully crossed 2×2×2 design: two models (claude-opus-4-6, gpt-5.4), two prompt styles (batch vs. sequential), and two number ranges (1–10, 0–255). Each of the eight conditionswas run 8 times with 125 numbers per run. Two findings are consistent across all conditions. First, batch mode produces a distributional-vs-sequential split: outputs pass KS uniformity tests while failing every independence test administered (ACFsignificant in all 8 runs for all batch conditions; no NIST SP 800-22 pass across both 0–255 batch conditions). Second, sequential mode produces prototype fixation: both models collapse to a single modal output (7 in the 1–10 range; 173 in the 0–255 range), with claude-opus-4-6 achieving complete fixation (std = 0) in the 1–10 condition. The cross-provider, cross-range convergence on specific prototype values distinguishes prototype fixation from generic distributional bias. No tested configuration produced output suitable for applications requiring both distributional uniformity and sequential independence.