| 寻找关于几个素数基的两类强伪素数 |
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| 引用本文： | 谢蕊蕊.寻找关于几个素数基的两类强伪素数[J].安徽师范大学学报(自然科学版),2011(2). |
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| 作者姓名： | 谢蕊蕊 |
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| 作者单位： | 安徽师范大学数学计算机科学学院; |
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| 基金项目： | 国家自然科学基金(10726074) |
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| 摘 要： | 给出了用四次剩余特征为主要工具找K8-强伪素数和K7/2-强伪素数(具有形式n=pq,其中p,q是奇素数且q-1=k(p-1),k=8,7/2的强伪素数)的方法,表列出所有小于1024的关于前6个素数基的K8-强伪素数和关于前4个素数基的K7/2-强伪素数,总共有111个K8-强伪素数和173个K7/2-强伪素数.进一步验证了张振祥的一个论断,即PR(n)值越接近1/4时,n成为关于较多个基的强伪素数的可能性就越大.
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| 关 键 词： | 素性测定 强伪素数 Miller测试 四次剩余特征 孙子定理 |
Finding Two Kinds of Strong Pseudoprimes to Several Prime Bases |
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| XIE Rui-rui.Finding Two Kinds of Strong Pseudoprimes to Several Prime Bases[J].Journal of Anhui Normal University(Natural Science Edition),2011(2). |
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| Authors: | XIE Rui-rui |
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| Institution: | XIE Rui-rui(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | In this paper,we first follow Zhang Zhenxiang and Tang Min's work to give the method of using biquadratic residue characters as main tools to find all strong pseudoprimes(spsp's) n<1024 to the first six or four prime bases,which have the form n=pq with p,q odd primes and q-1=k(p-1),k=8,7/2;then we tabulate all K8-spsp's<1024 to the first six prime bases and K7/2-spsp's<1024 to the first four prime bases.There are in total 111 K8-spsp's and 173 K7/2-spsp's.As a result we further test and verify one of Zhang ... |
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| Keywords: | primality testing strong pseudoprimes Miller tests biquadratic residue characters Chinese remainder theorem |
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