Strong pseudoprimes to the first eight prime bases

Yupeng Jiang; Yingpu Deng

doi:10.1090/S0025-5718-2014-02830-5

Strong pseudoprimes to the first eight prime bases

Yupeng Jiang
, Yingpu Deng

CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Define ψm to be the smallest strong pseudoprime to the first m prime bases. The exact value of ψm is known for 1 ≤ m ≤ 8. Z. Zhang has found a 19-decimal-digit number Q₁₁ = 3825 12305 65464 13051 which is a strong pseudoprime to the first 11 prime bases and he conjectured that ψ9 = ψ10 = ψ11 ≤ Q₁₁. We tabulate all the strong pseudoprimes n ≤ Q₁₁ to the first eight prime bases, and prove Zhang's conjecture.

Original language	English
Pages (from-to)	2915-2924
Number of pages	10
Journal	Mathematics of Computation
Volume	83
Issue number	290
DOIs	https://doi.org/10.1090/S0025-5718-2014-02830-5
State	Published - 2014
Externally published	Yes

Keywords

Chinese remainder theorem
Strong pseudoprimes

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10.1090/S0025-5718-2014-02830-5

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abstract = "Define ψm to be the smallest strong pseudoprime to the first m prime bases. The exact value of ψm is known for 1 ≤ m ≤ 8. Z. Zhang has found a 19-decimal-digit number Q11 = 3825 12305 65464 13051 which is a strong pseudoprime to the first 11 prime bases and he conjectured that ψ9 = ψ10 = ψ11 ≤ Q11. We tabulate all the strong pseudoprimes n ≤ Q11 to the first eight prime bases, and prove Zhang's conjecture.",

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AU - Jiang, Yupeng

AU - Deng, Yingpu

PY - 2014

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N2 - Define ψm to be the smallest strong pseudoprime to the first m prime bases. The exact value of ψm is known for 1 ≤ m ≤ 8. Z. Zhang has found a 19-decimal-digit number Q11 = 3825 12305 65464 13051 which is a strong pseudoprime to the first 11 prime bases and he conjectured that ψ9 = ψ10 = ψ11 ≤ Q11. We tabulate all the strong pseudoprimes n ≤ Q11 to the first eight prime bases, and prove Zhang's conjecture.

AB - Define ψm to be the smallest strong pseudoprime to the first m prime bases. The exact value of ψm is known for 1 ≤ m ≤ 8. Z. Zhang has found a 19-decimal-digit number Q11 = 3825 12305 65464 13051 which is a strong pseudoprime to the first 11 prime bases and he conjectured that ψ9 = ψ10 = ψ11 ≤ Q11. We tabulate all the strong pseudoprimes n ≤ Q11 to the first eight prime bases, and prove Zhang's conjecture.

KW - Chinese remainder theorem

KW - Strong pseudoprimes

UR - https://www.scopus.com/pages/publications/84916898648

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DO - 10.1090/S0025-5718-2014-02830-5

M3 - 文章

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SN - 0025-5718

VL - 83

SP - 2915

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JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 290

ER -

Strong pseudoprimes to the first eight prime bases

Abstract

Keywords

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