Abstract:

Amongst a list of all the ODD numbers (≥3), one may reveal ALL the PRIMES (P) simply be identifying ALL the NO-PRIMES (NP).

Two new methods:

1.) algebraic;

2.) algebraic geometry;

—identify ALL the NP from any list of sequential ODD numbers.

1.) *NP = 6yx ± y (let x = 1, 2, 3,..., and y = ODD number) is the pure algebraic method. It was derived from and is easily visualized within the 2.) algebraic geometry method. (*The exponentials of 3, as 3^x, must be added to the algebraic method.)

The latter method is built into the matrix grid depicting the Inverse Square Law, known as the BBS–ISL Matrix or BIM for short.

The enclosed geometry on one part of the BIM identifies ALL the NP numbers. When eliminated from the remaining Inner Grid geometry, ALL the PRIMES (≥3) are revealed.

Both methods produce identical results. Given enough CPU cycles, ALL PRIMES can potentially be identified, including those larger than—and between—the Mersenne Primes.