{"id":202,"date":"2019-06-26T23:00:51","date_gmt":"2019-06-26T23:00:51","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=202"},"modified":"2019-12-03T19:28:01","modified_gmt":"2019-12-03T19:28:01","slug":"largest-known-primes","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/largest-known-primes\/","title":{"rendered":"Largest Known Primes"},"content":{"rendered":"\n<p>Since there are\u00a0infinitely many primes, what are the largest primes that we know of?The largest known primes are ones of the form (2<sup>m<\/sup>\u00a0&#8211; 1). The reason is that there exist efficient ways to test whether such numbers are prime. Primes of this type are called a\u00a0<em>Mersenne<\/em>\u00a0primes.As of Sept 2010, the largest known primes were\u00a0<\/p>\n\n\n\n<p>2<sup>43,112,609<\/sup>&nbsp;&#8211; 1&nbsp;<br>2<sup>42,643,801<\/sup>&nbsp;&#8211; 1&nbsp;<br>2<sup>37,156,667<\/sup>&nbsp;&#8211; 1&nbsp;<\/p>\n\n\n\n<p>The largest is over 2 million digits long! These primes were all discovered in the last 3 years; the search for large primes has accelerated with the help of several hundred people across the internet in a project called GIMPS [the Great Internet Mersenne Prime Search]. For more on this, see the URL in the reference.<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Ask students to guess how large those numbers are, before you tell them.<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>As it turns out, knowing large\u00a0primes\u00a0is very important in cryptography. Being able to factor large numbers is &#8220;equivalent&#8221; to being able to crack codes, and typical codes that are nearly impossible to break are ones which depend on knowing a large number that is almost prime.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong><br>Su, Francis E., et al. &#8220;Largest Known Primes.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.\n<\/p>\n\n\n\n<p><strong>References:<\/strong><br><a href=\"https:\/\/primes.utm.edu\/largest.html#largest\">Chris Caldwell&#8217;s prime pages<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Since there are\u00a0infinitely many primes, what are the largest primes that we know of?The largest known primes are ones of&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,10,49],"class_list":["post-202","page","type-page","status-publish","hentry","tag-easy","tag-numtheory","tag-prime"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/202","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=202"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/202\/revisions"}],"predecessor-version":[{"id":1508,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/202\/revisions\/1508"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=202"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}