论文标题
加强Baillie-PSW原始测试
Strengthening the Baillie-PSW primality test
论文作者
论文摘要
Baillie-PSW原始测试结合了Fermat和Lucas可能的主要测试。它报告一个数字是复合材料或可能是素数。据报道，如果以适当的方式选择参数，则尚无奇数复合整数通过这种原始测试的组合。在这里，我们描述了该测试的重大加强，几乎没有额外的计算成本。这是通过在测试中包括我们所谓的Lucas-V pseudaprimes来实现的，其中只有5美元小于$ 10^{15} $。
The Baillie-PSW primality test combines Fermat and Lucas probable prime tests. It reports that a number is either composite or probably prime. No odd composite integer has been reported to pass this combination of primality tests if the parameters are chosen in an appropriate way. Here, we describe a significant strengthening of this test that comes at almost no additional computational cost. This is achieved by including in the test what we call Lucas-V pseudoprimes, of which there are only five less than $10^{15}$.
