142857 and the Blue Corpse Prime
by Jason Earls, author of Cocoon of Terror & How to Become a Guitar Player from Hell http://becomeguitaristfromhell.blogspot.com/ http://www.youtube.com/user/zevi35711
The most well-known example of a cyclic number is probably 142857. A cyclic number is one that forms cyclic permutations of its digits when it is multiplied by different numbers. For example, watch what happens when you multiply 142857 by 2: 142857 x 2 = 285714 The new number contains the same digits as the original, but with the first two moved to the end. Neat, isn’t it? Now if we continue the multiplication process with other consecutive numbers we get: 142857 x 3 = 428571 142857 x 4 = 571428 142857 x 5 = 714285 142857 x 6 = 857142 142857 x 7 = 999999 Notice the new numbers have their digits in the same order except they begin at different points. That’s the cyclic part, which is why 142857 is known as a cyclic number. Unfortunately, whenever we multiply 142857 by 7, the pattern stops working since 7 is the number’s ‘generating prime.’ (When any cyclic number is multiplied by its generating prime, the result will be repeating 9s.) Next, you need to know about ‘concrete mathematics.’ Concrete mathematics are unusual mathematical entities I invented one night when I couldn’t sleep and my brain went into hyperoverdrive and I had a psychotic delusion and almost died (just kidding about those last two parts). Concrete math involves certain classes of numbers (such as squares, harshads, primes, triangulars, etc.) but with words, figures, or symbols apparent in the decimal expansions to add a striking visual component to the number. Classes of numbers that possess a certain optical component when the digits are arranged in a specific way is a concept closely related (in my opinion) to “concrete poetry” – (poems in which the typographical arrangement of symbols or words plays a direct role in conveying the “meaning” of the poem); hence I have dubbed numbers like the prime you’ll soon see below, “concrete mathematics.” One other thing before we get to the main concrete math object in this article. Blue Corpse is an album by the outsider musician Jandek. He is a reclusive guitar player and singer based in Houston, Texas who recently came out of hiding and began performing in public. Jandek has released 43 albums since 1978 through his own record label, Corwood Industries, and his music is a good example of what I occasionally like in some forms of art (but not exclusively): primitive, almost atonal music, filled with emotion and without too much technique or craft interfering with the basic message. Most people don’t like it. Some don’t even consider Jandek’s albums to be music. But Blue Corpse is my favorite album by the unique, reclusive, outsider musician known only as Jandek.
Here is a prime that includes 142857 as a math curiosity, along with the phrase Blue Corpse, the title of one of Jandek’s numerous albums. It is my little tribute to him and the number 142857 because in my opinion it is ‘outsider mathematics’ at its best, as well as a conglomeration of blood and usurpation drifting from the thick eyebrows of a ghoul in the soft moonlight, or a stab in the apocalyptic elbow of the mystical beyond, if you will.
Blue Corpse Prime
7777777777777777777777777777777777777777777777777777777777777777 7000000000000000000000000000000000000000000000000000000000000007 7000000000000444444400044000000004400004400444444440000000000007 7000000000000440000440044000000004400004400440000000000000000007 7000000000000440000440044000000004400004400440000000000000000007 7000000000000444444000044000000004400004400444444400000000000007 7000000000000440004400044000000004400004400440000000000000000007 7000000000000440000440044000000004400004400440000000000000000007 7000000000000440004400044000000000440044000440000000000000000007 7000000000000444444000044444444000044440000444444440000000000007 7000000000000000000000000000000000000000000000000000000000000007 7000000000000000000000000000000000000000000000000000000000000007 7000000000000000000000000000000000000000000000000000000000000007 7000000000000000000000000000142857000000000000000000000000000007 7000000000000000000000000000285714000000000000000000000000000007 7000000000000000000000000000428571000000000000000000000000000007 7000000000000000000000000000571428000000000000000000000000000007 7000000000000000000000000000714285000000000000000000000000000007 7000000000000000000000000000857142000000000000000000000000000007 7000000000000000000000000000999999000000000000000000000000000007 7000000000000000000000000000000000000000000000000000000000000007 7000000000000000000000000000000000000000000000000000000000000007 7000000000000000000000000000000000000000000000000000000000000007 7000444444000004444000044444400004444440000044444440044444444007 7004400004400044004400044000444004400044400440000000044000000007 7004400000000440000440044000444004400044400440000000044000000007 7004400000000440000440044004400004400444000004440000044444440007 7004400000000440000440044444000004444400000000044400044000000007 7004400000000440000440044004400004400000000000000440044000000007 7004400004400044004400044000440004400000000000004400044000000007 7000444444000004444000044000044004400000000444444400044444444007 7000000000000000000000000000000000000000000000000000000000000007 7777777777777777777777777777777777777777777777777777777777777777 1111111111111111111111111111111111111111111111111111111111111111 4444444444444444444444444444444444444444444444444444444444444444 2222222222222222222222222222222222222222222222222222222222222222 8888888888888888888888888888888888888888888888888888888888888888 5555555555555555555555555555555555555555555555555555555555555555 7777777777777777777777777777777777777777777777777777777777777776 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999
Surely you can see how ‘BLUE CORPSE’ is spelled out in the bolded digits above using 4s? Also notice the 142857 cyclic permutation in the center of the prime. I hope a major magazine like Time or Newsweek soon discovers this prime and prints it on the cover of their next issue with some striking visual effects surrounding it. The Blue Corpse Prime’s full decimal expansion contains 3,105 digits and was found with the freely available program, WinPFGW. It’s a concrete prime, meaning it is an integer with no divisors other than itself and one; while the visual component is of course the phrase BLUE CORPSE and the number 142857, which are apparent because of the digits being arranged in a certain way. (This Blue Corpse prime originally appeared in my novel, Cocoon of Terror, published by Afterbirth Books. Help me out
by purchasing a copy today!) One more thing. I also decided (against my better judgment) to make a polynomial with 142857 involved and to test it for primes. Let f(n) = 142857 * 10n + 1. It’s prime when n = 1, 8, 10, 11, 16, 25, 29, 65, 77, 88, 107, 222, 664, and 1338, with no more found up to 3000. The last prime in the list, f(1338) is a titanic prime since it has more than 1000 digits. Here’s what one of the primes looks like: f(10) = 1428570000000001. It’s just the cyclic number curiosity at the beginning with many zeros and a 1 added to the end. Multiplying an interesting integer by 10n and adding 1 and testing for primality is a little (bad) habit of mine. Similar to lions leaping high with nerves hanging from their tan muscular legs and their stomachs popping the dry desert terrain like bright fireworks exploding in the lugubrious night sky; or a businessperson moving their gelatinous lips silently to the exact phrases spoken by a butcher mouthing calm words of persuasion over his nurturing shoulder, and things of that nature. -end(Thanks for reading. If you have any comments or know of any magazines that would like to publish this article, please contact the author: zevi_35711@yahoo.com. Also you would be helping out the author greatly if you purchased one of his books from Amazon.com or another online book store of your choice. Thanks again.) http://www.youtube.com/user/zevi35711 http://becomeguitaristfromhell.blogspot.com/ http://zombiesofthereddescent.blogspot.com/ Bio: Jason Earls is the author of Cocoon of Terror (Afterbirth Books), How to Become a Guitar Player from Hell, Heartless Bastard In Ecstasy, Zombies of the Red Descent, If(Sid_Vicious == TRUE && Alan_Turing == TRUE) {ERROR_Cyberpunk(); }, Red Zen, and 0.136101521283655... all available at Amazon.com and other online book stores. His fiction and mathematical work have been published in Red Scream, Yankee Pot Roast, M-Brane SF, MathWorld.com, three of Clifford Pickover’s books, Scientia Magna, AlienSkin, Recreational and Educational Computing, Escaping Elsewhere, Neometropolis, Thirteen, Dogmatika, Prime Curios, the Online Encyclopedia of Integer Sequences, OG’s Speculative Fiction, Nocturnal Ooze, Bust Down the Door and Eat All the Chickens and other publications. He currently resides in Oklahoma with his wife, Christine.