{"paper":{"title":"A study of divergence from randomness in the distribution of prime numbers within the arithmetic progressions 1+6n and 5+6n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Andrea Berdondini","submitted_at":"2018-04-19T15:12:01Z","abstract_excerpt":"In this article I present results from a statistical study of prime numbers that shows a behaviour that is not compatible with the thesis that they are distributed randomly. The analysis is based on studying two arithmetical progressions defined by the following polynomials: ($1+6n$, $5+6n$, $n\\in{N}$) whose respective numerical sequences have the characteristic of containing all the prime numbers except $3$ and $2$. If prime numbers were distributed randomly, we would expect the two polynomials to generate the same number of primes. Instead, as the reported findings show, we note that the pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07607","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}