{"id":"W2408493172","doi":"10.1080/00029890.2008.11920529","title":"Prime Number Patterns","year":2008,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Queen (butterfly); Fermat's Last Theorem; Prime (order theory); Mathematics; Combinatorics; Prime number","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0004917359,0.0003029067,0.0007033894,0.00007434725,0.000178102,0.00002972364,0.0005235816,0.00006662765,0.00367449],"category_scores_gemma":[0.00116434,0.0002477191,0.0002295589,0.000402603,0.0008669765,0.0001245488,0.0001993165,0.0003522611,0.003756362],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009438515,"about_ca_system_score_gemma":0.00007449889,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008502793,"about_ca_topic_score_gemma":0.000007416954,"domain_scores_codex":[0.9972817,0.0001987676,0.0005635669,0.0004212112,0.0008272034,0.0007075676],"domain_scores_gemma":[0.996896,0.001495409,0.0002022909,0.0009261453,0.0001162589,0.000363953],"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":[0.0001067809,0.001659349,0.0340997,0.0002681738,0.0003823714,0.0006454601,0.003326427,0.000002322225,0.0001910204,0.9396549,0.01764204,0.002021404],"study_design_scores_gemma":[0.0004185031,0.0001244225,0.002935442,0.00007519203,0.00006070428,0.0002392783,0.000696288,0.001137931,0.0005734546,0.9923097,0.0009650285,0.0004640577],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5959292,0.000007899642,0.02996712,0.0005377742,0.00003742462,0.0004265814,0.00002213614,0.0003511911,0.3727207],"genre_scores_gemma":[0.9605556,0.000008466545,0.03139197,0.0002150482,0.0001239855,0.00006515322,0.0000040894,0.00009099553,0.007544683],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.365176,"threshold_uncertainty_score":0.9999975,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05161727341574661,"score_gpt":0.344875900589207,"score_spread":0.2932586271734604,"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."}}