Prime Pickle

Let pp and qq be prime numbers and rr be a whole number, such that (p)(p+3)+(q)(q+3)=(r)(r+3)(p)(p+3)+(q)(q+3)=(r)(r+3). Find the sum of all possible values of pp.

Details:

\bullet rr needn't be a prime number.

\bullet 11 is nether prime nor composite.

\bullet You may use the fact that all primes except 22 and 33 can be expressed in the form 6k±16k \pm 1.

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