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Mathematics of Computation

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Explicit primality criteria for $ h\cdot 2\sp k\pm 1$

Author: Wieb Bosma
Journal: Math. Comp. 61 (1993), 97-109, S7
MSC: Primary 11A51; Secondary 11Y11
MathSciNet review: 1197510
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Abstract: Algorithms are described to obtain explicit primality criteria for integers of the form $ h \cdot {2^k} \pm 1$ (in particular with h divisible by 3) that generalize classical tests for $ {2^k} \pm 1$ in a well-defined finite sense. Numerical evidence (including all cases with $ h < {10^5}$) seems to indicate that these finite generalizations exist for every h, unless $ h = {4^m} - 1$ for some m, in which case it is proved they cannot exist.

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Article copyright: © Copyright 1993 American Mathematical Society

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