14.4.27 ** Find all prime numbers that can be expressed both as the sum of two prime numbers and as the difference of two prime numbers.
The prime number $r$ that satisfies the condition is only one, which is 5. In fact, the sum and difference of two odd primes are even numbers, so $r=p+2=q-2$, where $p$ and $q$ are odd primes. Thus, $p, r=p+2, q=r+2$ are three consecutive odd primes. At this point, there is only one unique set: $3,5,7$ (since among any two consecutive odd numbers, one must be divisible by 3). Therefore, $r=5=3+2=7-2$.