A New Method for Finding Prime-Rich Equations of the Type I=X2-X+C,
NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD
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A new method has been discovered for finding prime-rich equations of the type Ix-squared-xc where c2N-1 and N1,2,3,..... It is based on an analysis of an array described in NSWC TR-85-120. The array can be defined by stating that all its columns are described by the above equations while simultaneously all its rows are described by the equations IX-squaredx-r where r2N-1 and N1,2,3,..... Primitive cells and primitive cell arrays are derived from the above special array by determining and then indicating in table form which columns are empty of integers which are congruent to 0mod F where P is prime. The primitive cell array can be thought of as being constructed by the translation in the c and r directions of the primitive cell. Analysis of the superposition of two or more such primitive cell arrays reveals which columns are empty of two or more divisors. For example, columns which have no integers congruent to 0mod 3,5,7 and 11 tend to be prime rich.
- Numerical Mathematics