NEW MODELLING OF PRIME NUMBER SERIES, IN-PAR

Abstract

The objective of the work was aimed at the modeling of the series of Prime numbers using the ROR methodology and using the IN-PAR methodology as an improvement of the previous one. From the methodological conception, the Objective Regressive Methodology, ROR and the IN-PAR methodology were used, in addition, there was a database of our own elaboration that consists of

25  cases of  prime numbers less  than  100.  Later  they were modeled according to  the  ROR methodology and with the IN-PAR methodology, this series using the first 25 cases, the errors of the predicted values were calculated with respect to the real values and the descriptive statistics of the corresponding errors were obtained. Perfect models for the series of prime numbers were obtained using both methodologies. The IN-PAR methodology described errors with zero mean as well as the ROR methodology and the standard deviation less than the ROR methodology. Both methodologies gave  excellent  results  for  prime  numbers. Our  work  showed  that  the  IN-PAR methodology obtains better results than the ROR in the case of the series of prime numbers. Perfect models were obtained for all series using both methodologies. The IN-PAR methodology offered better results for prime numbers than the ROR methodology. This alternative ROR methodology is very interesting for the Artificial Intelligence of computing machines and both could mean a saving in machine time in the search for the prime numbers that are so important in Cryptography.