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APMO 1995 - Asian Pacific Mathematics Olympiad Question 2

APMO · APMO 1995 - Asian Pacific Mathematics Olympiad

Question 2

Let $a_1,a_2,\ldots,a_n$ be integers between $2$ and $1995$ such that (i) any two terms are relatively prime; (ii) each term is either a prime or a product of primes. Determine the smallest possible value of $n$ guaranteeing that the sequence contains a prime number.