{"id":1578,"date":"2018-07-21T22:28:53","date_gmt":"2018-07-21T22:28:53","guid":{"rendered":"http:\/\/bryceautomation.com\/?p=1578"},"modified":"2018-07-21T22:37:32","modified_gmt":"2018-07-21T22:37:32","slug":"marsenne-primes-2147483647","status":"publish","type":"post","link":"https:\/\/bryceautomation.com\/index.php\/2018\/07\/21\/marsenne-primes-2147483647\/","title":{"rendered":"Marsenne Primes &#8212; 2147483647"},"content":{"rendered":"<h2>Introduction to Marsenne Primes<\/h2>\n<p>Prime numbers are numbers that are only divisible by 1, and themselves of course.\u00a0 \u00a0Prime numbers (perfect numbers) are important for encryption, and very interesting to math enthusiasts who love to study their patterns.\u00a0 \u00a0 Obviously,\u00a0 with large numbers, prime numbers become more rare.<\/p><div id=\"bryce-3107527992\" class=\"bryce-afterfirst bryce-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-8316758073402323\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-8316758073402323\" \ndata-ad-slot=\"7728240895\" \ndata-ad-format=\"auto\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); \n<\/script>\n<\/div>\n<p>An understanding of Marsenne primes depends heavily on your understanding of the binary numbering system.\u00a0 \u00a0If you are unfamiliar with the binary numbering system, please check out my post on this <a href=\"https:\/\/bryceautomation.com\/index.php\/2017\/07\/10\/binary-numbering-system\/\">here<\/a>.<\/p>\n<h2>Understanding a Marsenne Prime<\/h2>\n<p>There are many posts on how Marsenne primes work.\u00a0 \u00a0 Most of them are very confusing and involve complex math.\u00a0 \u00a0I will explain this to you in a way that I understand it.\u00a0 \u00a0I&#8217;m a simple man, so I hope I can explain it in a way that you can understand this too as long as you understand how binary works.<\/p>\n<p>Simply put, a Marsenne prime is a prime number that is one less than any number to the power of 2.<\/p>\n<p>Any number in binary that is one less than the power of 2 has a certain number of bits that are set (1) in a row.<\/p>\n<p>We will start with 4.\u00a0 One less than that is 3.\u00a0 \u00a0This is a prime number, and 2 bits in a row (11) makes it a Marsenne prime.<\/p>\n<h2>Double Marsenne Primes<\/h2>\n<p>A double Marsenne prime is simple.\u00a0 \u00a0In the example above, we know that 3 is one less than 2 to the power of 2.\u00a0 That gave us the value of 3.\u00a0 \u00a0In binary that is 11.<\/p>\n<p>Let&#8217;s carry that one step further.\u00a0 \u00a0We know that 3 is a Marsenne prime.\u00a0 A double Marsenne prime means that we take the value of a Marsenne (or other) prime number, and put that many bits in a row.\u00a0 If the resulting number is a prime, we call that a double Marseene prime.<\/p>\n<p>In this case, 3 is a prime number, so we put 3 bits in a row&#8230;\u00a0 \u00a0111 in binary, which is 7 in decimal.\u00a0 \u00a0Since 7 is a prime number, we call this a double Marsenne prime.<\/p>\n<h2>32 bit signed integer<\/h2>\n<p>In the ControlLogix processor (and other 32 bit processors) The number 2147483647 is very important to us.\u00a0 \u00a0That is the maximum value that we can have for a timer or counter, or any other double integer.<\/p>\n<p>Here is the reason that 2147483647 is a double prime:\u00a0 If we take the number 5, which is a prime number, and put 5 bits in a row, we have 31.\u00a0 \u00a0Then if we put 31 bits in a row, we have 2147483647.<\/p>\n<p>I do not recommend setting the preset of a timer to this number though.\u00a0 Depending on your scan time, the timer could overrun causing a processor fault!<\/p>\n<p>Special thanks to a student in class, Casey who searched this number.\u00a0 He mentioned that this was a perfect number, and then I started researching this.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-1581 lazyload\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2018\/07\/unsignedinteger.png\" alt=\"Unsigned Integer\" width=\"490\" height=\"197\" data-srcset=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2018\/07\/unsignedinteger.png 490w, https:\/\/bryceautomation.com\/wp-content\/uploads\/2018\/07\/unsignedinteger-300x121.png 300w\" data-sizes=\"(max-width: 490px) 100vw, 490px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 490px; --smush-placeholder-aspect-ratio: 490\/197;\" \/><\/p>\n<p>For more information on ControlLogix, check out the <a href=\"https:\/\/bryceautomation.com\/index.php\/category\/controllogix\/\">ControlLogix<\/a> category!<\/p>\n<p>&nbsp;<\/p>\n<p>&#8211;Ricky Bryce<\/p>\n<p>&nbsp;<\/p>\n<div id=\"bryce-1447552180\" class=\"bryce-after-content bryce-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-8316758073402323\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-8316758073402323\" \ndata-ad-slot=\"4667596182\" \ndata-ad-format=\"auto\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); \n<\/script>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Introduction to Marsenne Primes Prime numbers are numbers that are only divisible by 1, and themselves of course.\u00a0 \u00a0Prime numbers (perfect numbers) are important for encryption, and very interesting to math enthusiasts who love to study their patterns.\u00a0 \u00a0 Obviously,\u00a0 with large numbers, prime numbers become more rare. An understanding of Marsenne primes depends heavily <a class=\"moretag btn btn-primary\" href=\"https:\/\/bryceautomation.com\/index.php\/2018\/07\/21\/marsenne-primes-2147483647\/\">Read More \u00bb<\/a><\/p>\n","protected":false},"author":1,"featured_media":1143,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,4,3],"tags":[113,112],"class_list":{"0":"post-1578","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-beginner","8":"category-controllogix","9":"category-information-technology","10":"tag-marsenne","11":"tag-prime-numbers","12":"czr-hentry"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Marsenne Primes and how it relates to the ControlLogix Processor<\/title>\n<meta name=\"description\" content=\"How Marsenne Primes work and the importance of these numbers in the ControlLogix processor. 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