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@MaxAlekseyev No, it isn't. In post you mentioned we treat numbers of the form $N =k \cdot b^n-1$ with base $b$ being an even number not divisible by $3$ .
@MaxAlekseyev Actually this is a generalization of Inkeri's primality test for Fermat numbers...Reference : Tests for primality, Ann. Acad. Sci. Fenn. Ser. A I 279 (1960), 1-19.