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<html> <head><script type="text/javascript" src="/_static/js/bundle-playback.js?v=HxkREWBo" charset="utf-8"></script> <script type="text/javascript" src="/_static/js/wombat.js?v=txqj7nKC" charset="utf-8"></script> <script>window.RufflePlayer=window.RufflePlayer||{};window.RufflePlayer.config={"autoplay":"on","unmuteOverlay":"hidden"};</script> <script type="text/javascript" src="/_static/js/ruffle/ruffle.js"></script> <script type="text/javascript"> __wm.init("https://web.archive.org/web"); __wm.wombat("http://www.sgi.com:80/Headlines/1996/September/prime.html","19970606011821","https://web.archive.org/","web","/_static/", "865559901"); </script> <link rel="stylesheet" type="text/css" href="/_static/css/banner-styles.css?v=S1zqJCYt" /> <link rel="stylesheet" type="text/css" href="/_static/css/iconochive.css?v=3PDvdIFv" />  <link rev="made" href="mailto:webmaster@www.sgi.com"> <title>Largest known prime number discovered on cray research supercomputer</title> <meta http-equiv="Expires" content="Fri Sep 13 00:00:00 PDT 1997"> <meta http-equiv="Keywords" content="cray, prime number, supercomputer"> <meta http-equiv="Owner" content="erikaw@corp.sgi.com"> </head> <body bgcolor="#FFFFFF"> <img src="/web/19970606011821im_/http://www.sgi.com/Images/CorpID.gif" alt="SGI Logo" width="151" height="43"> <p> <h2>Largest Known Prime Number Discovered on Cray Research Supercomputer</h2> <p> <b> Cray Research and Silicon Graphics Responsible For All World's Largest Mersenne Prime Discoveries Over Past 25 Years </b> <p> EAGAN, Minn., September 3, 1996 -- Computer scientists at Cray Research have discovered the largest-known prime number while conducting routine tests on a CRAY T94 system, one of the company's latest supercomputers, at the company's engineering and manufacturing operation in Chippewa Falls, Wisconsin. <p> The new prime number is the 34th ever discovered and has 378,632 digits. Printed in newspaper-sized type, the number would fill approximately 12 newspaper pages. <p> The largest Mersenne prime previously known was discovered in January 1994, also at Cray Research's Wisconsin operation by the same computer scientists. That prime number has 258,716 digits. <p> Cray officials said seven of the last eight Mersenne prime discoveries occurred on Cray Research supercomputers, and the remaining number was discovered by Cray's parent firm, Silicon Graphics, Inc., Mountain View, Calif. All of world's largest Mersenne prime number discoveries over the past 25 years were made by Silicon Graphics or Cray employees. <p> <b>A Primer on Primes</b> <p> In mathematical notation, the new prime number is expressed as 2<font size="-1"><sup>1257787</sup></font>-1, which denotes two, multiplied by itself 1,257,787 times, minus one. Numbers expressed in this form are called "Mersenne" prime numbers after Father Marin Mersenne, a 17th century French monk who spent years searching for prime numbers of this type. <p> Prime numbers can be divided evenly only by themselves and one. Examples include 2, 3, 5, 7, 11 and so on. The Greek mathematician Euclid proved that there are an infinite number of prime numbers. But these numbers do not occur in a regular sequence and there is no formula for generating them. Therefore, the discovery of new primes requires randomly generating and testing millions of numbers. <p> "Finding these special numbers is a true 'needle-in-a-haystack' exercise, but we improve our odds by using tremendously fast computers and a clever program," said David Slowinski, a Cray Research computer scientist. Slowinski and fellow Cray Research computer scientist Paul Gage developed the program that found the new prime number. Mathematician Richard Crandall, Ph.D., independently verified the Cray team's prime number discovery. <p> <b>Practical Applications Of Prime Numbers</b> <p> Prime numbers have applications in cryptography and computer systems security. Huge prime numbers like those discovered most recently are principally mathematical curiosities, but the process of searching for prime numbers does have several practical benefits. <p> For instance, the "prime finder" program developed by Slowinski and Gage is used by Cray Research as a quality assurance test on supercomputer systems. A core element of this program is a routine that involves squaring a number repeatedly. As this process continues, it eventually involves multiplying immense numbers -- numbers of hundreds of thousands of digits -- by themselves. <p> "This acts as a real 'torture test' for a computer," said Slowinski. "The prime finder program rigorously tests all elements of a system -- from the logic of the processors, to the memory, the compiler and the operating and multitasking systems. For high performance systems with multiple processors, this is an excellent test of the system's ability to keep track of where all the data is." <p> Slowinski said the recent CRAY T94 system test in which the new prime number was discovered ran for over 6 hours on one central processing unit of the system. "If a machine can complete this exhaustive run-through, we can be confident everything is working as it should," said Slowinski. <p> In addition, Slowinski said, techniques used to speed up the performance of the prime finder can also be used to enhance the performance of programs customers use on real-world problems such as forecasting the weather or searching for oil. <p> "Through our work on the prime finder program, we learn new techniques for speeding up certain kinds of mathematical operations. These operations are often key elements of the most computation-intensive portions of software programs our customers run routinely on their Cray systems," said Slowinski. <p> <b>With Prime Comes Perfect</b> <p> Slowinski noted that with the discovery of the new prime number, a new "perfect" number, the 34th, can also be generated. A perfect number is equal to the sum of its factors. For example, 6 is perfect because its factors -- 1, 2 and 3 -- when added together, equal 6. Mathematicians don't know how many perfect numbers exist. They do know, however, that all known perfect numbers have a direct relationship to Mersenne primes. <p> Cray Research, a wholly owned subsidiary of Silicon Graphics, Inc., provides the leading supercomputing tools and services to help solve customers' most challenging problems. <p> <font size="2"> Silicon Graphics and the Silicon Graphics logo are registered trademarks of Silicon Graphics, Inc. </font> <hr size="6"> <a href="/web/19970606011821/http://www.sgi.com/"><img src="/web/19970606011821im_/http://www.sgi.com/Images/Icon/surf.gif"></a> <a href="/web/19970606011821/http://www.sgi.com/Headlines/"><img src="/web/19970606011821im_/http://www.sgi.com/Images/Icon/headlines_icon.gif"></a> <a href="/web/19970606011821/http://www.sgi.com/Overview/newsroom"><img src="/web/19970606011821im_/http://www.sgi.com/Overview/newsroom/images/news_room_btn.gif"></a> <br> <font size="-1">We welcome feedback and comments at <a href="/web/19970606011821/http://www.sgi.com/cgi-bin/form_feedback/webmaster@www.sgi.com">webmaster@www.sgi.com</a>. </font> <p> <a href="/web/19970606011821/http://www.sgi.com/Misc/sgi_info.html"><font size="-2">Copyright © 1996 Silicon Graphics, Inc.</font></a> <font size="-2">All Rights Reserved. <a href="/web/19970606011821/http://www.sgi.com/Misc/external.list.html">Trademark Information</a></font> </body> </html>