Show that
$$ 7^{40 353 606} \equiv 0 \pmod {40 353 607} $$
Is $40 353 607$ prime?
Trial and error leads us to
$7^9 \equiv 40353607 \equiv 0 \pmod {40353607}$
We also have $40353606 = 9 \times 4483734$. And so
$7^{40353606} \equiv (7^9)^{4483734} \equiv 0^{4483734} \equiv 0 \pmod {40353607}$
We have shown above that 40353607 has factors of 7, and so is not a prime.