Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design st...Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers;and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.展开更多
本文研究了清末数学家方士(钅荣)的《数根丛草》。在李善兰素数论的基础上,方士(钅荣)在1896年完成的《数根丛草》中提出了20种判别素数的方法,不少具有独创性,其中最重要的是威尔逊(Wilson)定理,他和德国数学家亥尔维茨(A. Hurwitz)同...本文研究了清末数学家方士(钅荣)的《数根丛草》。在李善兰素数论的基础上,方士(钅荣)在1896年完成的《数根丛草》中提出了20种判别素数的方法,不少具有独创性,其中最重要的是威尔逊(Wilson)定理,他和德国数学家亥尔维茨(A. Hurwitz)同一年将该定理应用于素数判别,并且早于记载在迪克逊(L. E. Dickson)《数论史》中的一些西方数学家。《数根丛草》还改进了依据素数定义的判别方法和李善兰《考数根法》中的方法。展开更多
文摘Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers;and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.
文摘本文研究了清末数学家方士(钅荣)的《数根丛草》。在李善兰素数论的基础上,方士(钅荣)在1896年完成的《数根丛草》中提出了20种判别素数的方法,不少具有独创性,其中最重要的是威尔逊(Wilson)定理,他和德国数学家亥尔维茨(A. Hurwitz)同一年将该定理应用于素数判别,并且早于记载在迪克逊(L. E. Dickson)《数论史》中的一些西方数学家。《数根丛草》还改进了依据素数定义的判别方法和李善兰《考数根法》中的方法。
