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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 $\\Omega_b$","authors_text":"Cathy Swaenepoel, C\\'ecile Dartyge, Jo\\\"el Rivat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21642","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f9f2f79ff845b6e5ab6be130d4369e0246799232a21d0120065f412e4137996","target":"record","created_at":"2026-07-05T11:34:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"617ef83f3461b53cebee0ea220a318835cc3b42fe247da8936ff8d4fbd204ec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-25T20:56:01Z","title_canon_sha256":"fa3ad1d1860119e564216376925c7ae985bd79c0b9792ce9e335636b9621e219"},"schema_version":"1.0","source":{"id":"2506.21642","kind":"arxiv","version":2}},"canonical_sha256":"0b06de5e0ab3e22ad1fbe45a77431d43dee777b08e9ccd9933409a2167549750","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b06de5e0ab3e22ad1fbe45a77431d43dee777b08e9ccd9933409a2167549750","first_computed_at":"2026-07-05T11:34:52.541167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:52.541167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbGOuIVpu/H7wCdeJMBf8RNlwjjrbGhin+OXjOyeiYreBqgf4vU+A/ojwuaC/aJAafrrl2TwyGuNwPl1dRloCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:52.541662Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.21642","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f9f2f79ff845b6e5ab6be130d4369e0246799232a21d0120065f412e4137996","sha256:72482d404aceb084ffbd799e474e64166673f76fdf35fc7fca191b26b2c12598"],"state_sha256":"da2c83de659c4834bd48829f96c3c486a0105c7ad542c120f55e29baf92b3728"}