Computational certification of OEIS A395171(11) and bounds for A395171(18)

This archive contains a technical note, C++ source code, raw computation logs, a curated interval manifest, and SHA-256 checksums for a computational certification of OEIS A395171(11). The main result is the certification that OEIS A395171(11) = 357913941. The computation verifies gcd(Phi_31(m), m! - 1) = 1 for every integer 2 <= m <= 357913940, and the final production run finds gcd(Phi_31(357913941), 357913941! - 1) = 715827883. The archive also reports computations for OEIS A395171(18), corresponding to p = 61. The m-first computation proves A395171(18) > 100000000. Together with the standard construction from the prime (2^61 + 1)/3, this gives 100000000 < A395171(18) <= 768614336404564649. A q-first search found no witness prime q <= 999999963 for 100000000 < m < 768614336404564649. The raw logs are included as generated and may contain interrupted or partially buffered terminal output. The curated file manifest.csv records the certified intervals used for the proof.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-13
DOI
https://doi.org/10.5281/zenodo.20682049
Primary Topic
Cryptography and Residue Arithmetic
Type
article
Field-Weighted Citation Impact
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article

Computational certification of OEIS A395171(11) and bounds for A395171(18)

Aldo Roberto Pessolano
Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
article

Computational certification of OEIS A395171(11) and bounds for A395171(18)

Aldo Roberto Pessolano
article en

Abstract

This archive contains a technical note, C++ source code, raw computation logs, a curated interval manifest, and SHA-256 checksums for a computational certification of OEIS A395171(11). The main result is the certification that OEIS A395171(11) = 357913941. The computation verifies gcd(Phi_31(m), m! - 1) = 1 for every integer 2 <= m <= 357913940, and the final production run finds gcd(Phi_31(357913941), 357913941! - 1) = 715827883. The archive also reports computations for OEIS A395171(18), corresponding to p = 61. The m-first computation proves A395171(18) > 100000000. Together with the standard construction from the prime (2^61 + 1)/3, this gives 100000000 < A395171(18) <= 768614336404564649. A q-first search found no witness prime q <= 999999963 for 100000000 < m < 768614336404564649. The raw logs are included as generated and may contain interrupted or partially buffered terminal output. The curated file manifest.csv records the certified intervals used for the proof.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 2%
Cryptography and Residue Arithmetic
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