John Grieve: Grieve''s Twin Prime Conjecture    
 Grieve''s Twin Prime Conjecture3 comments
24 Aug 2008 @ 15:14, by John Grieve



This is a restatement of the classic Twin Prime conjecture in a more particular and provocative form

If you take any prime number greater than 2 and square it then take the next prime above the original one and square that,then the intervening numbers will always contain at least two pairs of twin primes.

example: 3 squared is 9 and 5 squared is 25 and between the numbers 9 and 25 you will find two pairs of twin primes namely 11,13 and 17,19

Comments appreciated


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3 comments

8 Mar 2009 @ 10:22 by harmonyone : Twin Primes
Fascinating, and fun! I've been working with solving magic math puzzles and have always been intrigued with the patterns which prime numbers form in them. As a matter of fact, with the ones I have put up on the net, I have all the prime numbers in bold.

I looked at your post in context with two of my puzzles:

Five Magic Math Square
http://www.geocities.com/Athens/Agora/7076/5square.html

Seven Magic Math Square
http://www.geocities.com/Athens/Agora/7076/7square.html

There are 2 pairs between 25 and 49: 29,31 and 41,43.

Will continue exploring this in the future, thanks!

Harmony

Magic Math, Prime Numbers and Mystery
http://www.geocities.com/Athens/Agora/7076/magicmath.html  

11 Mar 2009 @ 10:20 by johnjoseph : Twin Primes and Magic squares
Thanks Harmony for this comment
Your research looks very interesting and resonates with my own speculations. I believe that the magic square imposes and reveals the underlying symmetries hidden in the prime numbers. If you look at the twin primes rather than all of them and colour them accordingly,You might find some sort of fractal patterns emerging such as you mention elsewhere.

john  

12 Mar 2009 @ 14:02 by harmonyone : Twin Primes
Hi John, thanks for that suggestion- will start implementing it and see what happens.  

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