{"id":"W2008496693","doi":"10.1090/s0025-5718-02-01418-7","title":"New quadratic polynomials with high densities of prime values","year":2002,"lang":"en","type":"article","venue":"Mathematics of Computation","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary; University of Manitoba","funders":"University of Waterloo","keywords":"Discriminant; Mathematics; Riemann hypothesis; Combinatorics; Polynomial; Quadratic equation; Prime (order theory); Order (exchange); Class number; Delta; Discrete mathematics; Pure mathematics; Mathematical analysis; Geometry; Physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002010361,0.0007754246,0.001019187,0.003185768,0.001923321,0.003197408,0.001405726,0.001154697,0.01477504],"category_scores_gemma":[0.02302483,0.001125562,0.001009291,0.001765412,0.004735016,0.006251971,0.003545799,0.004158287,0.002262574],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002320663,"about_ca_system_score_gemma":0.0009573395,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001422631,"about_ca_topic_score_gemma":0.001304312,"domain_scores_codex":[0.9978587,0.0005647009,0.00005720806,0.000425674,0.0007114456,0.0003822056],"domain_scores_gemma":[0.9903795,0.005643797,0.0007258319,0.000765696,0.001198894,0.001286248],"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":[0.0001250043,0.00003746765,0.001344405,0.00008056602,0.00001101682,0.0002301776,0.0003623936,0.001925201,0.0009503614,0.9778203,0.005222075,0.01189101],"study_design_scores_gemma":[0.00004402675,0.0000442493,0.001170534,0.00002832444,0.00001159487,0.0004944387,0.000119486,0.01886669,0.0008950533,0.973254,0.005037614,0.00003396123],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5760915,0.002395961,0.2565806,0.0085471,0.001365855,0.00009294474,0.0008818457,0.00137242,0.1526717],"genre_scores_gemma":[0.941833,0.0006240792,0.02183815,0.0007691312,0.001685107,0.0001055672,0.0004633022,0.0003322579,0.03234942],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01477504,"threshold_uncertainty_score":0.04942745,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05804371422392374,"score_gpt":0.317600054715775,"score_spread":0.2595563404918512,"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."}}