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We establish a Bombieri-Vinogradov type theorem for the set of the reverses of the prime numbers. Combined with sieve methods, this permits us to prove that there exist $\\Omega_b\\in\\mathbb{N}$ and $c_b>0$ such that, for at least $c_b b^{\\lambda} \\lambda ^{-2}$ primes $p\\in \\left[b^{\\lambda-1}, b^{\\lambda}-1\\right]$, the reverse $R_\\lambda(p)$ has at most $\\Omega_b$"},"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":"2506.21642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-25T20:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"fa3ad1d1860119e564216376925c7ae985bd79c0b9792ce9e335636b9621e219","abstract_canon_sha256":"617ef83f3461b53cebee0ea220a318835cc3b42fe247da8936ff8d4fbd204ec9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:52.541662Z","signature_b64":"tbGOuIVpu/H7wCdeJMBf8RNlwjjrbGhin+OXjOyeiYreBqgf4vU+A/ojwuaC/aJAafrrl2TwyGuNwPl1dRloCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b06de5e0ab3e22ad1fbe45a77431d43dee777b08e9ccd9933409a2167549750","last_reissued_at":"2026-07-05T11:34:52.541167Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:52.541167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prime numbers with an almost prime reverse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cathy Swaenepoel, C\\'ecile Dartyge, Jo\\\"el Rivat","submitted_at":"2025-06-25T20:56:01Z","abstract_excerpt":"Let $b$ be an integer greater than or equal to $2$. For any integer $n\\in \\left[b^{\\lambda-1}, b^{\\lambda}-1\\right]$, we denote by $R_\\lambda (n)$ the reverse of $n$ in base $b$, obtained by reversing the order of the digits of $n$. We establish a Bombieri-Vinogradov type theorem for the set of the reverses of the prime numbers. Combined with sieve methods, this permits us to prove that there exist $\\Omega_b\\in\\mathbb{N}$ and $c_b>0$ such that, for at least $c_b b^{\\lambda} \\lambda ^{-2}$ primes $p\\in \\left[b^{\\lambda-1}, b^{\\lambda}-1\\right]$, the reverse $R_\\lambda(p)$ has at most $\\Omega_b$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21642","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.21642/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.21642","created_at":"2026-07-05T11:34:52.541217+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.21642v2","created_at":"2026-07-05T11:34:52.541217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21642","created_at":"2026-07-05T11:34:52.541217+00:00"},{"alias_kind":"pith_short_12","alias_value":"BMDN4XQKWPRC","created_at":"2026-07-05T11:34:52.541217+00:00"},{"alias_kind":"pith_short_16","alias_value":"BMDN4XQKWPRCVUP3","created_at":"2026-07-05T11:34:52.541217+00:00"},{"alias_kind":"pith_short_8","alias_value":"BMDN4XQK","created_at":"2026-07-05T11:34:52.541217+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.21876","citing_title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21876","citing_title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP","json":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP.json","graph_json":"https://pith.science/api/pith-number/BMDN4XQKWPRCVUP34RNHOQY5IP/graph.json","events_json":"https://pith.science/api/pith-number/BMDN4XQKWPRCVUP34RNHOQY5IP/events.json","paper":"https://pith.science/paper/BMDN4XQK"},"agent_actions":{"view_html":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP","download_json":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP.json","view_paper":"https://pith.science/paper/BMDN4XQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.21642&json=true","fetch_graph":"https://pith.science/api/pith-number/BMDN4XQKWPRCVUP34RNHOQY5IP/graph.json","fetch_events":"https://pith.science/api/pith-number/BMDN4XQKWPRCVUP34RNHOQY5IP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP/action/storage_attestation","attest_author":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP/action/author_attestation","sign_citation":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP/action/citation_signature","submit_replication":"https://pith.science/pith/BMDN4XQKWPRCVUP34RNHOQY5IP/action/replication_record"}},"created_at":"2026-07-05T11:34:52.541217+00:00","updated_at":"2026-07-05T11:34:52.541217+00:00"}