Let P(n) be the statement : `10n + 3` is prime. Is P(3) true ?

Answer

To determine whether the statement \( P(3) \) is true, we need to evaluate the expression \( 10n + 3 \) for \( n = 3 \) and check if the result is a prime number.

### Step-by-Step Solution:

1. **Substitute \( n = 3 \) into the expression**:
\[ P(3) = 10 \cdot 3 + 3 \]

2. **Calculate the value**:
\[ P(3) = 30 + 3 = 33 \]

3. **Check if 33 is a prime number**:
- A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself.
- The factors of 33 can be determined:
- 33 can be divided by 1, 3, 11, and 33.
- Specifically, \( 33 = 3 \times 11 \).

4. **Conclusion**:
- Since 33 has divisors other than 1 and itself (3 and 11), it is not a prime number.
- Therefore, \( P(3) \) is **not true**.

### Final Answer:
The statement \( P(3) \) is false because 33 is not a prime number.

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