论文标题
Kummer表面用于原始测试
Kummer surfaces for primality testing
论文作者
论文摘要
我们使用与高纤维曲线的Jacobian相关的Kummer表面的算术来研究该形式的整数$ 4M^2 5^n-1 $。我们提供了一种算法，能够证明这些家庭中大多数整数的原始性或综合性，并详细讨论在计算机中实现此算法的必要步骤。尽管不确定是可能的，但在这种情况下，应该使用另一种初始参数的选择，我们证明达到这种情况的概率极低，并且以$ n $的形式下降。
We use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form $4m^2 5^n-1$. We provide an algorithm capable of proving the primality or compositeness of most of the integers in these families and discuss in detail the necessary steps to implement this algorithm in a computer. Although an indetermination is possible, in which case another choice of initial parameters should be used, we prove that the probability of reaching this situation is exceedingly low and decreases exponentially with $n$.
