primes and non-prime numbers

Note :

A) N€{3, 5, 7, 9, 11, 13, 15, 17, 19, ...}

B) (N^4)=N.N.N.N; (N^3)=N.N.N; (N^2)=N.N; (N^1)=N; (N^0)=1; (A^2)=A.A.

C) The general form of the 4th degree equation (or Quartic) is: ax4 +
bx3 + cx2 + dx + e = 0

Quartics have 4 roots.

The 4 roots can be represented this way:

http://www.josechu.com/ecuaciones_polinomicas/cuartica_solucion.htm



___ NON-PRIMES ___



THEOREM :



A non-primes <=> -(N^4)+2.(N^3)--2.(A-2).(N^2)-2.A.(N^1)-(A^2).(N^0)=0;

N€{3, 5, 7, 9, 11, 13, 15, 17, 19, ....}
AND M=(A/N)



___ PRIMES ___



THEOREM :



A primes <=> -(N^4)+2.(N^3)--2.(A-2).(N^2)-2.A.(N^1)-(A^2).(N^0)=0;
[N€{3, 5, 7, 9, 11, 13, 15, 17, 19, ...}]'

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URL : http://groups.google.com/group/primes

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