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Let p1 and p2 denote two arbitrary prime numbers. Which one of the following statements is correct for all values of p1 and p2?

1. p1 + p2 is not a prime number.
2. p1p2 is not a prime number.
3. p1 + p2 + 1 is a prime number.
4. p1p2 + 1 is a prime number.

Correct answer: p1p2 is not a prime number.

Solution

The product of two prime numbers, p1 and p2, is always composite (not prime) because it has at least three distinct positive divisors: 1, p1, and p2. Therefore, option B is correct.

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