Primes 6 apart
Weekly Problem 30 - 2017
The prime numbers p and q are the smallest primes that differ by 6. What is the value of p+q?
The prime numbers p and q are the smallest primes that differ by 6. What is the value of p+q?
Age
11 to 14
Challenge level
Problem
The prime numbers $p$ and $q$ are the smallest primes that differ by $6$. What is the value of $p+q$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
The table below shows the possible values of $p$, the value of $p+6$ and whether this is prime.
| $p$ | $p+6$ | Prime? |
|---|---|---|
| 2 | 8 | No |
| 3 | 9 | No |
| 5 | 11 | Yes |
Therefore the values of $p$ and $q$ are $5$ and $11$, so their sum is $16$.