Question 70
The sequence of positive integers $\{a_n\}_{n \ge 1}$ is such that
$$
a_n \le 1000^{1000^{\sqrt{\log_2 n}}}, \quad \forall n = 1, 2, 3, \dots
$$
It is known that any number appears in the sequence at most $5000$ times. Prove that there are infinitely many primes, each of which divides at least one member of the sequence.
$$
a_n \le 1000^{1000^{\sqrt{\log_2 n}}}, \quad \forall n = 1, 2, 3, \dots
$$
It is known that any number appears in the sequence at most $5000$ times. Prove that there are infinitely many primes, each of which divides at least one member of the sequence.