1. The statement claims that if $n$ is a prime number, then $2n + 1$ will also be a prime number. 2. To test this, let's use an example with $n = 5$, which is a prime number. 3. Substitute $n = 5$ into the expression $2n + 1$: $$2 \times 5 + 1 = 10 + 1 = 11$$ 4. The number 11 is a prime number, so for $n=5$, the statement holds. 5. Now, try another prime number, $n=7$: $$2 \times 7 + 1 = 14 + 1 = 15$$ 6. The number 15 is not a prime number since it is divisible by 3 and 5. 7. Hence, using $n=7$ as a counterexample, the statement "If $n$ is prime, then $2n + 1$ is also prime" is proven false because it does not hold for all prime $n$. Final answer: The statement is incorrect as demonstrated by the counterexample $n=7$ where $2n + 1 = 15$ is not prime.