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 $10^{15}$.

翻译：贝利利- PSW 初等测试结合了 Fermat 和 Lucas 可能的主要测试。 它报告一个数字要么是合成的, 要么可能是质的。 如果参数以适当方式选择, 没有异常的复合整数被报告通过这种初等测试的组合。 这里, 我们描述这个测试的显著增强, 几乎没有额外的计算成本。 通过在测试中加入我们称之为卢卡斯- V 伪金, 其中只有不到 10 15 美元。