Primality Testing for Numbers of the Form h·2~n± 1 |
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摘 要: | This paper studies the problem of primality testing for numbers of the form h · 2~n± 1,where h 2~n is odd, and n is a positive integer. The authors describe a Lucasian primality test for these numbers in certain cases, which runs in deterministic quasi-quadratic time. In particular, the authors construct a Lucasian primality test for numbers of the form 3 · 5 · 17 · 2~n± 1, where n is a positive integer, in half of the cases among the congruences of n modulo 12, by means of a Lucasian sequence with a suitable seed not depending on n. The methods of Bosma(1993), Berrizbeitia and Berry(2004), Deng and Huang(2016) can not test the primality of these numbers.
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Primality Testing for Numbers of the Form h · 2n ± 1 |
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Authors: | Huang Dandan Kang Yunling |
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Abstract: | Journal of Systems Science and Complexity - This paper studies the problem of primality testing for numbers of the form h · 2n ± 1, where h &;lt; 2n is odd, and n is a positive... |
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