{"id":336335,"date":"2016-12-14T07:43:03","date_gmt":"2016-12-14T15:43:03","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=336335"},"modified":"2025-07-31T10:18:44","modified_gmt":"2025-07-31T17:18:44","slug":"finding-large-prime-numbers-hardware-software-codesign-system","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/finding-large-prime-numbers-hardware-software-codesign-system\/","title":{"rendered":"Finding Large Prime Numbers: A Hardware-Software Codesign System"},"content":{"rendered":"<p>We describe a fast method to find primes of the form 2<em>p\u2014<\/em>1, by implementing special circuits to perform modulo 2<em>p\u2014<\/em>1 arithmetic, where <em>p<\/em> itself is an input to the circuit. We have followed a codesign approach. The primality verification is implemented in hardware. The software component supplies inputs to the randomized verification algorithm.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We describe a fast method to find primes of the form 2p\u20141, by implementing special circuits to perform modulo 2p\u20141 arithmetic, where p itself is an input to the circuit. We have followed a codesign approach. The primality verification is implemented in hardware. The software component supplies inputs to the randomized verification algorithm.<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":null,"msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2016-12-13","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":null,"footnotes":""},"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193724],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[246691],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-336335","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us","msr-field-of-study-computer-science"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2016-12-13","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"336338","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","viewUrl":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2016\/12\/primes.pdf","id":"336338","title":"primes","label_id":"243132","label":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Vaibhav 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