Accession Number : ADA181192

Title :   A New Method for Finding Prime-Rich Equations of the Type I=X2-X+C,

Corporate Author : NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD

Personal Author(s) : Sery,R S

PDF Url : ADA181192

Report Date : Dec 1986

Pagination or Media Count : 22

Abstract : A new method has been discovered for finding prime-rich equations of the type I=x-squared-x+c where c=2N-1 and N=1,2,3,..... 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 I=X-squared+x-r where r=2N-1 and N=1,2,3,..... 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 0(mod 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 0(mod 3,5,7 and 11) tend to be prime rich.

Descriptors :   *EQUATIONS, *PRIME NUMBERS, ARRAYS, CELLS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE