Noble Prime Numbers (Asil Asal Sayilar)

These numbers are based on prime numbers. All noble numbers are prime numbers. So what is the difference? Let us take a prime number 7 and collect the remainders.

P = 7

              (Remainder)                  1*10 = 10

              (Remainder)                3*10 = 30

When we collect the remainders, we can find that every noble prime number starts rotating itself in P-1 times. Other numbers don't have this property.

In Figure 1. it can be  seen how an array is mixing forward and backward. (a) is the original array. In (b) we are generating an array from P=7 (array size is 7). Last element is 1. In (c) we change it to 7. This array can be used to mix any type of arrays. Because we know the mixing process, we can take it back to original state.

                                                                                                This array is generated from P=7

 (1, 2, 3, 4, 5, 6, 7)                                   (1, 3, 2, 6, 4, 5, 1) 

            (a)                                                      (b)

(1, 2, 3, 4, 5, 6, 7)                                   (1, 3, 2, 6, 4, 5, 7)

            (b)                                                      (c)

                                   Figure 1.

If we replace last 1 with 7, this will be the mixed version.

Some Noble      Prime Numbers

The Algorithm

Below you will find the algorithm of checking whether a prime number is a noble prime or just an ordinary prime.