Strong pseudoprimes to the first eight prime bases
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- by Yupeng Jiang and Yingpu Deng PDF
- Math. Comp. 83 (2014), 2915-2924 Request permission
Abstract:
Define $\psi _m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi _m$ is known for $1\le m \le 8$. Z. Zhang has found a 19-decimal-digit number $Q_{11}=3825 12305 65464 13051$ which is a strong pseudoprime to the first 11 prime bases and he conjectured that $\psi _9=\psi _{10}=\psi _{11}=Q_{11}.$ We tabulate all the strong pseudoprimes $n\le Q_{11}$ to the first eight prime bases, and prove Zhang’s conjecture.References
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Additional Information
- Yupeng Jiang
- Affiliation: Key Laboratory of Mathematics Mechanization, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, 100190
- Email: jiangyupeng@amss.ac.cn
- Yingpu Deng
- Affiliation: Key Laboratory of Mathematics Mechanization, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, 100190
- Email: dengyp@amss.ac.cn
- Received by editor(s): August 23, 2012
- Received by editor(s) in revised form: January 26, 2013, and April 5, 2013
- Published electronically: May 5, 2014
- Additional Notes: This research was supported by the NNSF of China (Grant Nos. 11071285, 61121062), 973 Project (2011CB302401) and the National Center for Mathematics and Interdisciplinary Sciences, CAS
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 83 (2014), 2915-2924
- MSC (2010): Primary 11Y11, 11A51
- DOI: https://doi.org/10.1090/S0025-5718-2014-02830-5
- MathSciNet review: 3246815