A New Method for Finding Prime-Rich Equations of the Type I=X2-X+C,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1986
- Accession Number
- ADA181192
Entities
People
- R. S. Sery
Organizations
- Naval Ordnance Laboratory