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Question 19

The number of integers from 2 to 100 that can be written as $$p \times q$$, where $$p$$ and $$q$$ are different prime numbers, is ______.


Correct Answer: 30

Count the products $$pq \le 100$$ with $$p < q$$ both prime. For $$p = 2$$ the prime $$q$$ can be any of the 14 primes from 3 to 47, for $$p = 3$$ any of the 9 primes from 5 to 31, for $$p = 5$$ any of $$7, 11, 13, 17, 19$$, and for $$p = 7$$ either 11 or 13. No larger $$p$$ works, so the total is $$14 + 9 + 5 + 2 = 30$$.

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