{"id":"W3213791698","doi":"10.2140/ant.2024.18.1619","title":"Prime values of f(a,b2) and f(a,p2), fquadratic","year":2024,"lang":"en","type":"article","venue":"Algebra & Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Northern British Columbia","funders":"","keywords":"Mathematics; Prime (order theory); Integer (computer science); Binary quadratic form; Quadratic equation; Combinatorics; Quadratic form (statistics); Asymptotic formula; Prime number; Binary number; Quadratic field; Pure mathematics; Quadratic function; Arithmetic; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.002336655,0.0002718117,0.0004624254,0.0001399496,0.00009329752,0.00009903034,0.000345177,0.0001393716,0.01212422],"category_scores_gemma":[0.0009492027,0.0002245318,0.0001696806,0.00038666,0.0005771825,0.0002337846,0.0002492333,0.0003560492,0.0008840094],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005111076,"about_ca_system_score_gemma":0.0001330387,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001072262,"about_ca_topic_score_gemma":0.000003300604,"domain_scores_codex":[0.9975902,0.0005189328,0.0005021361,0.0004465364,0.0004959045,0.0004463323],"domain_scores_gemma":[0.994413,0.004572584,0.00009004422,0.0006605767,0.0000957197,0.0001680692],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00005070659,0.00009320478,0.0004159701,0.0005590175,0.0003470105,0.00005155155,0.001942553,1.244092e-7,0.0004874403,0.9776359,0.01294613,0.00547038],"study_design_scores_gemma":[0.0001617502,0.00004789703,0.0001172079,0.0003391254,0.0001452853,0.0001040267,0.0006673208,0.0003538737,0.003337568,0.991915,0.002571262,0.0002396401],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8109634,0.002848142,0.0115331,0.0005807594,0.0005119254,0.0008410566,0.0001268561,0.0006436612,0.1719511],"genre_scores_gemma":[0.9687523,0.00006482925,0.002651237,0.00008245232,0.0002107732,0.0000353688,0.00001167132,0.0001049408,0.02808648],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1577888,"threshold_uncertainty_score":0.9998939,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03120039857459914,"score_gpt":0.3472215084384921,"score_spread":0.3160211098638929,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}