{"id":"W4205654034","doi":"10.5539/jmr.v14n1p55","title":"Step Pyramid Distribution for Prime Numbers","year":2022,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Professional Engineers Ontario","funders":"","keywords":"Mathematics; Prime number; Prime (order theory); Prime k-tuple; Simple (philosophy); Pyramid (geometry); Combinatorics; Distribution (mathematics); Prime factor; Discrete mathematics; Arithmetic; Algorithm; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":[0.0002334909,0.0002848081,0.0003632544,0.001814959,0.0005628516,0.001389876,0.000402967,0.0002916819,0.01147013],"category_scores_gemma":[0.001727052,0.0001721961,0.0002468828,0.0009399161,0.0007153589,0.001720216,0.0007023076,0.000830906,0.002056229],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007708851,"about_ca_system_score_gemma":0.0004347215,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0015444,"about_ca_topic_score_gemma":0.0009994912,"domain_scores_codex":[0.9997658,0.00002729547,0.000007327717,0.00004633954,0.0001081017,0.00004517441],"domain_scores_gemma":[0.9994509,0.000142489,0.00005408627,0.00007837188,0.0002097514,0.0000644664],"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":[0.0003983041,0.00005583671,0.002883942,0.0001625309,0.00001759975,0.0004452453,0.0004399095,0.01805045,0.04680971,0.7794461,0.01085732,0.1404331],"study_design_scores_gemma":[0.00006245491,0.0001534095,0.005309571,0.00005190523,0.00002350665,0.0009661285,0.0004502877,0.3477264,0.04086589,0.5670182,0.03729786,0.00007443815],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2466394,0.0004485268,0.6875485,0.0006513344,0.000144921,0.0001028863,0.0006759765,0.003303298,0.06048523],"genre_scores_gemma":[0.8372298,0.0004651287,0.1423982,0.0001893843,0.0000816832,0.0001023945,0.0006376323,0.0005555006,0.01834023],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01147013,"threshold_uncertainty_score":0.03837144,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2373013219245879,"score_gpt":0.4912377813029475,"score_spread":0.2539364593783596,"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."}}