{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:43:38Z","timestamp":1776789818565,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,8,1]],"date-time":"2009-08-01T00:00:00Z","timestamp":1249084800000},"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                    We exhibit ten new primitive trinomials over GF(2) of record degrees\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"24 036 583\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>24<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>036<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>583<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">24\\,036\\,583<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"25 964 951\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>25<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>964<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>951<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">25\\,964\\,951<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"30 402 457\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>30<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>402<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>457<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">30\\,402\\,457<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"32 582 657\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>32<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>582<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>657<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">32\\,582\\,657<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . This completes the search for the currently known Mersenne prime exponents.\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02170-4","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1197-1199","source":"Crossref","is-referenced-by-count":5,"title":["Ten new primitive binary trinomials"],"prefix":"10.1090","volume":"78","author":[{"given":"Richard","family":"Brent","sequence":"first","affiliation":[]},{"given":"Paul","family":"Zimmermann","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,8,1]]},"reference":[{"key":"1","unstructured":"Richard P. 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Also available as arXiv:0710.4410."},{"key":"7","unstructured":"The Great Internet Mersenne Prime Search, \\url{http:\/\/mersenne.org\/}."},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1142\/S0129183192000361","article-title":"New primitive trinomials of Mersenne-exponent degrees for random-number generation","volume":"3","author":"Heringa, J. R.","year":"1992","journal-title":"Internat. J. Modern Phys. C","ISSN":"https:\/\/id.crossref.org\/issn\/0129-1831","issn-type":"print"},{"issue":"230","key":"9","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1090\/S0025-5718-99-01168-0","article-title":"New primitive \ud835\udc61-nomials (\ud835\udc61=3,5) over \ud835\udc3a\ud835\udc39(2) whose degree is a Mersenne exponent","volume":"69","author":"Kumada, Toshihiro","year":"2000","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"194","key":"10","doi-asserted-by":"publisher","first-page":"817","DOI":"10.2307\/2008411","article-title":"Primitive \ud835\udc61-nomials (\ud835\udc61=3,5) over \ud835\udc3a\ud835\udc39(2) whose degree is a Mersenne exponent \u226444497","volume":"56","author":"Kurita, Yoshiharu","year":"1991","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"11","unstructured":"Victor Shoup, NTL: A library for doing number theory, \\url{http:\/\/www.shoup.net\/ntl\/}, 2007."},{"key":"12","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.2140\/pjm.1962.12.1099","article-title":"Factorization of polynomials over finite fields","volume":"12","author":"Swan, Richard G.","year":"1962","journal-title":"Pacific J. 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