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Prime numbers and Rubik cube
Submitted by mdlazreg on Fri, 03/07/2008 - 20:32.The most fascinating thing about prime numbers is how to predict one.
For example in the following list:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
only 2, 5, 7, 11, 13, 17 and 19 are prime numbers.
Now if we look at the Rubik cube's positions, we can also count them, something like:
U D F B L R U' D' F' B' L' R' UU UD UF UB UL UR UU' UD' UF' UB' UL' UR'....
Similar to the prime number concept we can come up with the prime cube position concept. So in the above list UU' is not a prime position.
In prime numbers theory, the following theorem has been proved:
P(x)~x/ln(x) where P(x) is the prime numbers counting function.
For example in the following list:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
only 2, 5, 7, 11, 13, 17 and 19 are prime numbers.
Now if we look at the Rubik cube's positions, we can also count them, something like:
U D F B L R U' D' F' B' L' R' UU UD UF UB UL UR UU' UD' UF' UB' UL' UR'....
Similar to the prime number concept we can come up with the prime cube position concept. So in the above list UU' is not a prime position.
In prime numbers theory, the following theorem has been proved:
P(x)~x/ln(x) where P(x) is the prime numbers counting function.
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