Carmichael numbers and a new primality test

A new algorithm which correctly identifies every positive integer tested as being either prime or composite is considered. In fact, the first one hundred Carmichael numbers were tested and each one resulted composite as expected. It is well known that other primality tests exist that can also identify Carmichael numbers as composites, but the given algorithm seems to work without any exception. Yet, it is not a practical test for large integers since the operations required to verify such numbers are not feasible from a computational point of view.