Frobenius素性检验的有效性评价
Evaluation of the Effectiveness of the Frobenius Primality Test
摘要：
Frobenius素性检验是基于剩余域的二次扩张的弗罗贝尼乌斯自同构的性质。虽然这是概率的，但我们表明这“很少出错”。到目前为止，这种方法还没有反例，有理由相信它们根本不存在。在本文中，我们提出了一个版本的Frobenius测试，并证明它不会失败的数字小于$2^{64}$。我们还表明，“Frobenius pseudoprime”将必然有一个素除子大于3000。
英文摘要：
The Frobenius primality test is based on the properties of the Frobenius automorphism of the quadratic extension of the residue field. Although it is probabilistic, we show that is "very rarely wrong". To date there are no counterexamples to this method and there are reasons to believe that they do not exist at all. In this paper, we suggest a version of the Frobenius test and prove that it does not fail for numbers less than $2^{64}$. We also show that a "Frobenius pseudoprime" will necessarily have a prime divisor greater than 3000.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
