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We describe an explicit generalized Lucasian test to determine the primality of numbers $h\cdot2^n\pm1$ when $h\nequiv0\pmod{17}$. This test is by means of fixed seeds which depend only on $h$. In particular when $h=16^m-1$ with $m$ odd, our paper gives a primality test with some fixed seeds depending only on $h$. Comparing the results of W. Bosma(1993) and P. Berrizbeitia and T. G. Berry(2004), our result adds new values of $h$ along with this line. Octic and bioctic reciprocity are used to deduce our result.

Explicit primality criteria for h\cdot 2^n\pm 1