1. The statement claims that if $n$ is a prime number, then $2n + 1$ is also a prime number. 2. To test this, choose an example where $n$ is prime. Let's take $n = 3$, which is a prime number. 3. Calculate $2n + 1$: $$2 \times 3 + 1 = 6 + 1 = 7$$ Here, 7 is prime, so it fits the statement. 4. Now, let's try $n = 5$, which is also prime. 5. Calculate $2n + 1$: $$2 \times 5 + 1 = 10 + 1 = 11$$ Here, 11 is prime as well. 6. But we need to find an example where $2n + 1$ is *not* prime to prove the statement wrong. 7. Try $n = 7$, prime number. 8. Calculate $2n + 1$: $$2 \times 7 + 1 = 14 + 1 = 15$$ 9. The number 15 is *not* prime since it can be divided by 3 and 5. 10. This example shows the statement is false. Just because $n$ is prime does not guarantee $2n + 1$ is prime. **Final answer:** The statement is wrong. For example, when $n=7$, $2n + 1=15$ which is not a prime number.