Number Theory

    

A Recurrent Formula Inspired by Rowland’s Formula and Based on Smarandache Function Which Might be a Criterion for Primality

Authors: Marius Coman

Studying the two well known recurrent relations with the exceptional property that they generate only values which are equal to 1 or are odd primes, id est the formula which belongs to Eric Rowland and the one that belongs to Benoit Cloitre, I managed to discover a formula based on Smarandache function, from the same family of recurrent relations, which, instead to give a prime value for any input, seems to give the same value, 2, if and only if the value of the input is an odd prime; also, for any value of input different from 1 and different from an odd prime, the value of output is equal to n + 1. I name this relation the Coman-Smarandache criterion for primality and the exceptions from this rule, if they exist, Coman-Smarandache pseudoprimes.

Comments: 2 Pages.

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Submission history

[v1] 2014-02-01 00:09:09
[v2] 2014-02-03 01:35:50

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