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Code and data for: Gaps modulo 2q^2 between consecutive primes of a residue class modulo q: data for q = 3 up to 10^15, the singular-series model, and a blind test at q = 5

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Zenodo2026-10-31 更新2026-11-05 收录
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The deposit contains everything needed to regenerate every count, model value, table and figure of the paper. For the modulus 3 it provides the chunk-level counts of the three gap classes modulo 18 (and of pairs and runs of consecutive classes) between consecutive same-class primes, for 1.73 × 10⁹ gaps in nine windows from 10⁶ to 10¹⁵; the exact evaluation of the sieved Hardy–Littlewood model up to sieve level 29; the single-prime perturbations δ_q for 31 ≤ q ≤ 751 that define the perturbative estimate S_∞; and the two independent sieves (numpy and primesieve) whose outputs coincide. For the modulus 5 it provides the same for the five gap classes modulo 50, 1.99 × 10⁹ gaps in eight windows from 10⁸ to 10¹⁶, together with the model predictions that were computed from residue combinatorics alone and frozen — with their SHA-256 digests, included in PREDICTION_DIGESTS.txt — before any prime data for those windows were generated, so that the blind test of the paper can be audited. A root-level script (errors_v2.py) reproduces the revised error analysis with full covariance between classes; its output is included. All model values are exact finite sums over one period of admissible residues; no simulation is involved. The README gives, for each script, what it reads, what it writes and its running time, and the six-step sequence of the blind-test protocol. Dependencies: Python 3.10+ with numpy, scipy, matplotlib; a C compiler and primesieve ≥ 12 for the independent sieves. Code is released under the MIT licence, data files under CC BY 4.0. All counts in this deposit were independently reproduced by an external reviewer with his own implementation.

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Zenodo
创建时间:
2026-10-31
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