[math-fun] Re: [PrimeNumbers] "Contact" primes
If one converts the prime: 1412007000395936567688325529242177821814480981887773276739818172174237144350800185420854858836262254435789289718814792571362186754193456509548811926587255022099203909145779862540980335509923043069239333581971669175500801 to binary, arranges the bits into a 27 x 27 matrix, and then replaces each 1 by * and each 0 by a blank one obtains the following pattern: * * * * * * * * * * * * * * * * * * * * * * * * * --Edwin
Can we have a smiley face, or the Mona Lisa or something? Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com -----Original Message----- From: Edwin Clark [mailto:eclark@math.usf.edu] Sent: 10 July 2003 14:15 To: primenumbers@yahoogroups.com Cc: math-fun@mailman.xmission.com Subject: Re: [PrimeNumbers] "Contact" primes If one converts the prime: 1412007000395936567688325529242177821814480981887773276739818172174237144350 8001854208548588362622544357892897188147925713621867541934565095488119265872 55022099203909145779862540980335509923043069239333581971669175500801 to binary, arranges the bits into a 27 x 27 matrix, and then replaces each 1 by * and each 0 by a blank one obtains the following pattern: * * * * * * * * * * * * * * * * * * * * * * * * * --Edwin ------------------------ Yahoo! Groups Sponsor ---------------------~--> Buy Coral Calcium for Greater Health. 1 month supply - $23.95 (1 bottle, 90 tablets, 400mg each with Magnesium & Vitamin D) http://www.challengerone.com/t/l.asp?cid=2805&lp=calcium2.asp http://us.click.yahoo.com/mcIe3D/v9VGAA/ySSFAA/8HYolB/TM ---------------------------------------------------------------------~-> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com The Prime Pages : http://www.primepages.org/ Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
Does the following work? Choose the bits of the 27 by 27 array to give the desired picture - whatever it may be. Jiggle the bits systematically so as not to change the picture too much and check the modified numbers for primality. Presumably log n changes will ordinarily yield a prime.
Thu, 10 Jul 2003 14:37:37 -0700 (PDT) John McCarthy <jmc@steam.Stanford.EDU> Does the following work? Choose the bits of the 27 by 27 array to give the desired picture - whatever it may be. Jiggle the bits systematically so as not to change the picture too much and check the modified numbers for primality. Presumably log n changes will ordinarily yield a prime. Hmm. I may be off the mark here, but from my naive perspective, this "ordinarily yield a prime" seems optimistic for such a sparse and structured picture. There are only 25 "dots" in the picture. If you let each jiggle by about 2 spaces in all directions that gives you around 25 possibilities for each dot. Presumably the density of primes is about 1 in 27^2; so it seems, if there are any primes with such a property, that there is on the order of only one that will look reasonably close to your desired picture. On the other hand, if you had more dots (or even better, a grey-scale photograph), or less structure (so you could move things around more), it seems much easier. I bet it would be easier to take a 15pixelx15pixel 4-bit grey-scale photograph (this is so small it would be an icon) and encode it as a prime number.
Perhaps the bible could be interpreted as a prime number p, with respect to a suitable radix. And then if p is the n-th prime, n as well as p would be of great significance. __________________________________ Do you Yahoo!? SBC Yahoo! DSL - Now only $29.95 per month! http://sbc.yahoo.com
Thu, 10 Jul 2003 18:17:16 EDT Michael B Greenwald <mbgreen@central.cis.upenn.edu> Thu, 10 Jul 2003 14:37:37 -0700 (PDT) John McCarthy <jmc@steam.Stanford.EDU> Does the following work? Choose the bits of the 27 by 27 array to give the desired picture - whatever it may be. Jiggle the bits systematically so as not to change the picture too much and check the modified numbers for primality. Presumably log n changes will ordinarily yield a prime. Hmm. I may be off the mark here, but from my naive perspective... Yes, someone pointed out to me in email that I was totally off the mark here, to put it mildly. I was wrong, not naive. Ignore my last note --- 25 dots gives you enough jiggle room to find loads of primes.
On Thu, 10 Jul 2003, John McCarthy wrote:
Does the following work?
Choose the bits of the 27 by 27 array to give the desired picture - whatever it may be. Jiggle the bits systematically so as not to change the picture too much and check the modified numbers for primality. Presumably log n changes will ordinarily yield a prime.
I think so. As more evidence consider the following prime (actually probabilistic prime) found by Renaud Lifchitz: p=3101805506546616280631635616871932001139678275905519848096343683700 1064413299689909982581233599912690445747213000469488219983668395902399 2112714513427534901236590365687502134385507575859451115751110533156859 6161851812364061151621609005081840974114067184997406430437877618405800 0031904561144039147499937678209426297296078944799076442958087621851150 6376879633780612363524021157887: Converting it to binary, replacing 1's by *'s and 0's by blanks and arranging in a 19x66 array we get the self-proclaiming prime pattern: ****************************************************************** * * * * * * * ** * * ** * * * * ***** ** *** ** *** *** * * ** **** * * ** ** *** ** *** ** ** ** * ** ** ** * * ** ** ** ** ** ** * ** ** ** * * ******* ** ** ** ** ** * ** ******** * * ** ** ** ** ** ** ** * ** ** * * ** *** *** ** ** ** ** * ** ** ** * * **** ** ** *** ** ****** ** * ** ***** * * ** * * ** * * * * * ******************************************************************
Here's a pretty (decimal) PrP, even if the "circle" is trivial: 11111111111111111111111111111111111111111111111111111111111 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000100000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 10000000000000000000000000000000000000000000000000000000001 11111111111111111111111111111111111111111111111111111111111 (33 rows by 59 columns with the extra "1" in the exact centre to save you counting.) Note: Entirely hollow rectangles are always divisible by 3 or 11. Andy
participants (6)
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Andy Steward -
Edwin Clark -
Eugene Salamin -
John McCarthy -
Jon Perry -
Michael B Greenwald