, Volume 32, Issue 3, pp 529-534

Effective primality tests for integers of the formsN=k3 n +1 andN=k2 m 3 n +1

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Abstract

Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3 n +1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN−1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2 m 3 n +1.