Strong pseudoprimes to the first 9 prime bases

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 have found a 19-decimal-digit number $Q_{11}=3825123056546413051$ which is a strong pseudoprime to the first 11 prime bases and he conjectured that $${\psi }_9={\psi }_{10}={\psi }_{11}=Q_{11}.$$ We prove the conjecture by algorithms.

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