{"paper":{"title":"When the sieve works","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Andrew Granville, Dimitris Koukoulopoulos, Kaisa Matom\\\"aki","submitted_at":"2012-05-02T12:56:04Z","abstract_excerpt":"We are interested in classifying those sets of primes $\\mathcal{P}$ such that when we sieve out the integers up to $x$ by the primes in $\\mathcal{P}^c$ we are left with roughly the expected number of unsieved integers. In particular, we obtain the first general results for sieving an interval of length $x$ with primes including some in $(\\sqrt{x},x]$, using methods motivated by additive combinatorics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0413","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":""},"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"}