Exercise 2.4.6 (but $2047$ is not a strong pseudoprime to the base $3$)

Question

Show that $2047$ is composite by applying the strong pseudoprime test to the base $3$.

Richard Ganaye · Accepted Answer

\begin{proof} 
Since $$3^{2046} \equiv 1013 \pmod{2047},$$
 $2047$ is not a strong pseudoprime to the base $3$ (it is not even a pseudoprime to the base $3$).
 
 Therefore $2047$ is composite ($2047 = 23 	imes 89$).
\end{proof}

Exercise 2.4.6 (but $2047$ is not a strong pseudoprime to the base $3$)

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Exercise 2.4.6 (but $2047$ is not a strong pseudoprime to the base $3$)

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