Question

If $a$, $a+2$ and $a+4$ are prime numbers, then the number of possible solutions for $a$ is:

• A. one
• B. two
• C. three
• D. more than three

Hint:

When checking for primes in a sequence, start with the smallest prime numbers and test for divisibility by smaller primes.

Answer 1

The Correct Option is A

The numbers $a$, $a+2$, and $a+4$ must all be prime numbers. Checking small prime numbers, we find that $a = 3$ is the only solution where all three numbers are prime. Thus, the number of solutions for $a$ is 1.