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A Prime Conjecture

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0 and 1 are PRIME

Formulaic Definition of Primality by Diophantine Inequation

These statements seem to define 0 and 1 as being Prime Numbers. I think that this more formal definition makes the Primes more easily understood, but my investigations, using a spreadsheet program, leaves the question of discovering more Primes unclear to me. Does this approach make the Riemann hypothesis any easier to prove? Does the resemblance to fractal systems or cellular automata say anything particularly important?

Below is a table of the differences of the absolute values. There definitely seems to be some sort of hidden pattern. For instance, the bottom two diagonals only really change if the larger primes are altered to even rather than odd values, and they don't seem to have any real value in predicting the next prime, while the row directly beneath the primes is far more interesting, and yet far less regular. 

0 1 2 3 5 7 11 13 17 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
1 1 1 2 2 4 2 4 6 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8
0 0 1 0 2 -2 2 2 0 -4 4 -2 -2 2 2 0 -4 4 -2 -2 4 -2 2 2
0 1 -1 2 0 0 0 -2 4 0 -2 0 0 0 -2 4 0 -2 0 2 -2 0 0
1 0 1 -2 0 0 2 2 -4 2 -2 0 0 2 2 -4 2 -2 2 0 -2 0
-1 1 1 -2 0 2 0 2 -2 0 -2 0 2 0 2 -2 0 0 -2 2 -2
0 0 1 -2 2 -2 2 0 -2 2 -2 2 -2 2 0 -2 0 2 0 0
0 1 1 0 0 0 -2 2 0 0 0 0 0 -2 2 -2 2 -2 0
1 0 -1 0 0 2 0 -2 0 0 0 0 2 0 0 0 0 -2
-1 1 -1 0 2 -2 2 -2 0 0 0 2 -2 0 0 0 2
0 0 -1 2 0 0 0 -2 0 0 2 0 -2 0 0 2
0 1 1 -2 0 0 2 -2 0 2 -2 2 -2 0 2
1 0 1 -2 0 2 0 -2 2 0 0 0 -2 2
-1 1 1 -2 2 -2 2 0 -2 0 0 2 0
0 0 1 0 0 0 -2 2 -2 0 2 -2
0 1 -1 0 0 2 0 0 -2 2 0
1 0 -1 0 2 -2 0 2 0 -2
-1 1 -1 2 0 -2 2 -2 2
0 0 1 -2 2 0 0 0
0 1 1 0 -2 0 0
1 0 -1 2 -2 0
-1 1 1 0 -2
0 0 -1 2
0 1 1
1 0
-1

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