
Mathematics 2012
Hexile Sieve Analysis of Prime and Composite IntegersAbstract: Here we demonstrate a sieve for analysing primes and their composites, using equivalence classes based on the modulo 6 return value as applied to the Natural numbers. Five features of this 'Hexile' sieve are reviewed. The first aspect, is that it narrows the search for primes to onethird of the Natural numbers. The second feature is that we can obtain from the equivalence class formulae, a property of its diophantine equations to distinguish between primes and composites resulting from multiplication of these primes. Thirdly we can from these diophantine formulations ascribe a nonrandom occurence to not only the composites in the two equivalence classes but by default and as a consequence : nonrandomness of occurence to the resident primes. Fourthly we develop a theoretical basis for sieving primes. Of final mention is that the diophantine equations allows another route to a prime counting function using combinatorics or numerical analysis.
