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This research aims to evaluate the directional bias in minimal prime offsets and quantify the independence gap.

June 20, 2026Open Access

Numerical Evaluation of the Stopping-Time Sign Bias in Minimal Prime Offsets and Quantification of the Independence Gap

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This research aims to evaluate the directional bias in minimal prime offsets and quantify the independence gap.
Extended empirical dataset to 455 million primes up to 10^10 utilizing optimized multiprocessing sieve.
Constructed a systematic truncated stopping-time sum and computed a weighted average over empirical distributions.
Assessed theoretical predictions against the empirical measurements under the Hardy–Littlewood k-tuple conjecture.
Identified a systematic bias of 0.5313 ± 0.0005 above 0.5, indicating substantial asymptotic drift.
Quantified an independence gap of approximately 2.0 percentage points based on empirical data.
Measured tie frequency at 1.12% of all primes, compared to a model prediction of 1.38%.

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Randomized trial quantifies bias in prime offsets, revealing independence gaps in numerical evaluation.

Kumar et al. (2026) studied this question.

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