Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 𝐴.3ⁿ±1

Berrizbeitia, Pedro; Berry, T.

doi:10.1090/S0002-9939-99-04786-3

Cubic reciprocity and generalised Lucas-Lehmer tests for primality of $A.3^n\pm 1$
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by Pedro Berrizbeitia and T. G. Berry PDF

Proc. Amer. Math. Soc. 127 (1999), 1923-1925 Request permission

Abstract:

Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form $A.3^n \pm 1$. The test for $A.3^n-1$ is a minor improvement on a test derived by Williams by other means; the test for $A.3^n+1$ seems to be new.

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