Strong pseudoprimes to the first 9 prime bases

2012/06/30 by Yupeng Jiang, Jiang, Yupeng, Yingpu Deng +1
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Finite Group Theory Research #math.NT

paper · pdf · doi:10.48550/arxiv.1207.0063

12pages

arxiv created 2012/06/30 · arxiv updated 2012/07/03

Abstract

Define ψ_m to be the smallest strong pseudoprime to the first m prime bases. The exact value of ψ_m is known for 1≤ m ≤ 8. Z. Zhang have 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 prove the conjecture by algorithms.

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