{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MEHRGMVPQBX4GJIX3SN6SDAK46","short_pith_number":"pith:MEHRGMVP","schema_version":"1.0","canonical_sha256":"610f1332af806fc32517dc9be90c0ae7a4a9f762cabf19825adaaf6af7979147","source":{"kind":"arxiv","id":"1804.07607","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.07607","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-04-19T15:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"a5b0285f243d113dd88277c6b0276c39cac4c94893c7b94c0ec553fe385a16ca","abstract_canon_sha256":"9eb24ffa4be4067ee1c1609086e8529843aa883c81a87a57f4103ef12f26da75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:58.331537Z","signature_b64":"+gHbCwYLb3NZDb60EH/5CLeY0UIfAeBeDKlSaUBEBXycz407rpoGRtBtONrqk6vUDVeO3Id8wSZvWzjBXY2lAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"610f1332af806fc32517dc9be90c0ae7a4a9f762cabf19825adaaf6af7979147","last_reissued_at":"2026-05-18T00:17:58.331001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:58.331001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.07607","created_at":"2026-05-18T00:17:58.331073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.07607v1","created_at":"2026-05-18T00:17:58.331073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07607","created_at":"2026-05-18T00:17:58.331073+00:00"},{"alias_kind":"pith_short_12","alias_value":"MEHRGMVPQBX4","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MEHRGMVPQBX4GJIX","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MEHRGMVP","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46","json":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46.json","graph_json":"https://pith.science/api/pith-number/MEHRGMVPQBX4GJIX3SN6SDAK46/graph.json","events_json":"https://pith.science/api/pith-number/MEHRGMVPQBX4GJIX3SN6SDAK46/events.json","paper":"https://pith.science/paper/MEHRGMVP"},"agent_actions":{"view_html":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46","download_json":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46.json","view_paper":"https://pith.science/paper/MEHRGMVP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.07607&json=true","fetch_graph":"https://pith.science/api/pith-number/MEHRGMVPQBX4GJIX3SN6SDAK46/graph.json","fetch_events":"https://pith.science/api/pith-number/MEHRGMVPQBX4GJIX3SN6SDAK46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46/action/storage_attestation","attest_author":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46/action/author_attestation","sign_citation":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46/action/citation_signature","submit_replication":"https://pith.science/pith/MEHRGMVPQBX4GJIX3SN6SDAK46/action/replication_record"}},"created_at":"2026-05-18T00:17:58.331073+00:00","updated_at":"2026-05-18T00:17:58.331073+00:00"}