{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:12:46Z","timestamp":1776834766513,"version":"3.51.2"},"reference-count":4,"publisher":"American Mathematical Society (AMS)","issue":"240","license":[{"start":{"date-parts":[[2002,11,28]],"date-time":"2002-11-28T00:00:00Z","timestamp":1038441600000},"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":"<p>\n                    In this paper the densities\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper D left-parenthesis i right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>D<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>i<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">D(i)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of prime numbers\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    having the least primitive root\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"g left-parenthesis p right-parenthesis equals i\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>g<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>i<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">g(p)=i<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"i\">\n                        <mml:semantics>\n                          <mml:mi>i<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">i<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is equal to one of the initial positive integers less than 32, have been numerically calculated. The computations were carried out under the assumption of the Generalised Riemann Hypothesis. The results of these computations were compared with the results of numerical frequency estimations.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01382-5","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T14:12:48Z","timestamp":1032531168000},"page":"1781-1797","source":"Crossref","is-referenced-by-count":3,"title":["Numerical calculation of the density of prime numbers with a given least primitive root"],"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":[[2001,11,28]]},"reference":[{"issue":"220","key":"1","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"},{"key":"2","unstructured":"R. N. Buttsworth, A general theory of inclusion-exclusion with application to the least primitive root problem, and other density question, Ph.D. Thesis, University of Queensland, Queensland, 1983."},{"issue":"3","key":"3","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":"4","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"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-240\/S0025-5718-01-01382-5\/S0025-5718-01-01382-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-240\/S0025-5718-01-01382-5\/S0025-5718-01-01382-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:04:25Z","timestamp":1776726265000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-240\/S0025-5718-01-01382-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,28]]},"references-count":4,"journal-issue":{"issue":"240","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["S0025-5718-01-01382-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01382-5","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":[[2001,11,28]]}}}