Let \( p_1 \) and \( p_2 \) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \( p_1 \) and \( p_2 \)?
Show Hint
- \( p_1 + p_2 \) is not a prime number.
- \( p_1 p_2 \) is not a prime number.
- \( p_1 + p_2 + 1 \) is a prime number.
- \( p_1 p_2 + 1 \) is a prime number.
The Correct Option is B
Solution and Explanation
For any two arbitrary prime numbers \( p_1 \) and \( p_2 \), their product \( p_1 p_2 \) will always have more than two divisors (i.e., 1, \( p_1 \), \( p_2 \), and \( p_1 p_2 \)), which means it cannot be a prime number.
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