{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T07:52:49Z","timestamp":1772265169021,"version":"3.50.1"},"posted":{"date-parts":[[2018,11,29]]},"group-title":"PeerJ Preprints","reference-count":0,"publisher":"PeerJ","license":[{"start":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T00:00:00Z","timestamp":1543449600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We develop an efficient software package to test for the primality of p2^n+1, p prime and p&gt;2^n. This aids in the determination of large, non-Sierpinski numbers p, for prime p, and in cryptography. It furthermore uniquely allows for the computation of the smallest n such that p2^n+1 is prime when p is large. We compute primes of this form for the first one million primes p and find four primes of the form above 1000 digits. The software may also be used to test whether p2^n+1 divides a generalized fermat number base 3.<\/jats:p>","DOI":"10.7287\/peerj.preprints.27396v1","type":"posted-content","created":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T15:13:35Z","timestamp":1543504415000},"source":"Crossref","is-referenced-by-count":0,"title":["An open source software package for primality testing of numbers of the form p2^n+1, with no constraints on the relative sizes of p and 2^n"],"prefix":"10.7287","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9682-0940","authenticated-orcid":true,"given":"Tejas R.","family":"Rao","sequence":"first","affiliation":[{"name":"Santa Clara University, Campbell, United States"}]}],"member":"4443","container-title":[],"original-title":[],"link":[{"URL":"https:\/\/peerj.com\/preprints\/27396v1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/peerj.com\/preprints\/27396v1.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/peerj.com\/preprints\/27396v1.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/peerj.com\/preprints\/27396v1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T20:06:45Z","timestamp":1577131605000},"score":1,"resource":{"primary":{"URL":"https:\/\/peerj.com\/preprints\/27396v1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,29]]},"references-count":0,"aliases":["10.7287\/peerj.preprints.27396"],"URL":"https:\/\/doi.org\/10.7287\/peerj.preprints.27396v1","relation":{"references":[{"id-type":"doi","id":"10.7287\/peerj.preprints.27396v1\/supp-1","asserted-by":"subject"},{"id-type":"doi","id":"10.7287\/peerj.preprints.27396v1\/supp-1","asserted-by":"object"}]},"subject":[],"published":{"date-parts":[[2018,11,29]]},"subtype":"preprint"}}