The candidate's solution is correct and demonstrates a complete understanding of the problem. The approach is clear and concise, and the solution is elegant. Well done!
This is a valid proof by contradiction. The candidate has correctly identified the most elegant way to show that there are infinitely many prime numbers.
The candidate's solution is correct and demonstrates a level of completeness. The candidate has correctly identified that the best way to solve this problem is to use a brute force approach.
The candidate's solution is correct and demonstrates a level of completeness. The candidate has correctly identified that this is a direct result of the definition of addition for integers. The candidate has also correctly identified that the sum of two integers will always be an integer. Therefore, the candidate's solution solves the problem and is a correct approach.