Abstract
Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3n+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=k2m3n+1.
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Bibliography
Ireland, K., Rosen, M.,A Classical Introduction to Modern Number Theory, Springer 1982.
Riesel, H.,Prime Numbers and Computer Methods for Factorization, Birkhäuser 1985.
Robinson, R. M.,The converse of Fermat's theorem, Amer. Math. Monthly 64, 703–710 (1957).
Williams, H. C., Zarnke, C. R.,Some prime numbers of the forms 2A3n+1and 2A3n−1, Math. Comp. 26, 995–998 (1972).
Williams, H. C.,A note on the primality of 62n+1and 102n+1, Fibonacci Quarterly 26, 296–305 (1988).
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Guthmann, A. Effective primality tests for integers of the formsN=k3n+1 andN=k2m3n+1. BIT 32, 529–534 (1992). https://doi.org/10.1007/BF02074886
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DOI: https://doi.org/10.1007/BF02074886