{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:59Z","timestamp":1776728339325,"version":"3.51.2"},"reference-count":9,"publisher":"American Mathematical Society (AMS)","issue":"239","license":[{"start":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T00:00:00Z","timestamp":1042761600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We derive a conditional formula for the natural density\n \n \n \n \n E<\/mml:mi>\n (<\/mml:mo>\n q<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n E(q)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n of prime numbers\n \n \n \n p<\/mml:mi>\n p<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n having its least prime primitive root equal to\n \n \n \n q<\/mml:mi>\n q<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , and compare theoretical results with the numerical evidence.\n <\/p>","DOI":"10.1090\/s0025-5718-02-01370-4","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T15:46:54Z","timestamp":1032536814000},"page":"1307-1321","source":"Crossref","is-referenced-by-count":2,"title":["On the least prime primitive root modulo a prime"],"prefix":"10.1090","volume":"71","author":[{"given":"A.","family":"Paszkiewicz","sequence":"first","affiliation":[]},{"given":"A.","family":"Schinzel","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2002,1,17]]},"reference":[{"key":"1","first-page":"623","article-title":"Annihilator ideals and representation iteration for abstract rings","volume":"5","author":"Everett, C. J., Jr.","year":"1939","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"220","key":"2","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1090\/S0025-5718-97-00890-9","article-title":"Comments on search procedures for primitive roots","volume":"66","author":"Bach, Eric","year":"1997","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1006\/jnth.1998.2319","article-title":"On the \ud835\udc5f-rank Artin conjecture. II","volume":"75","author":"Cangelmi, Leonardo","year":"1999","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1112\/S0024610797005310","article-title":"On the average of the least primitive root modulo \ud835\udc5d","volume":"56","author":"Elliott, P. D. T. A.","year":"1997","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"113","DOI":"10.4064\/aa-29-2-113-146","article-title":"A generalisation of Artin\u2019s conjecture for primitive roots","volume":"29","author":"Matthews, K. R.","year":"1976","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"6","isbn-type":"print","volume-title":"Elementary and analytic theory of algebraic numbers","author":"Narkiewicz, W\u0142adys\u0142aw","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/3540512500","edition":"2"},{"issue":"4","key":"7","doi-asserted-by":"publisher","first-page":"465","DOI":"10.4153\/CMB-1995-068-4","article-title":"On minimal sets of generators for primitive roots","volume":"38","author":"Pappalardi, Francesco","year":"1995","journal-title":"Canad. Math. Bull.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-4395","issn-type":"print"},{"issue":"218","key":"8","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1090\/S0025-5718-97-00805-3","article-title":"On the \ud835\udc5f-rank Artin conjecture","volume":"66","author":"Pappalardi, Francesco","year":"1997","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"9","doi-asserted-by":"publisher","first-page":"396","DOI":"10.2307\/2003029","article-title":"Evaluation of Artin\u2019s constant and the twin-prime constant","volume":"15","author":"Wrench, John W., Jr.","year":"1961","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-239\/S0025-5718-02-01370-4\/S0025-5718-02-01370-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-239\/S0025-5718-02-01370-4\/S0025-5718-02-01370-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:00:54Z","timestamp":1776726054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-239\/S0025-5718-02-01370-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1,17]]},"references-count":9,"journal-issue":{"issue":"239","published-print":{"date-parts":[[2002,7]]}},"alternative-id":["S0025-5718-02-01370-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-02-01370-4","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2002,1,17]]}}}