{"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"}