# Prime Pickle

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

Details:

$$\bullet$$ $$r$$ needn't be a prime number.

$$\bullet$$ $$1$$ is nether prime nor composite.

$$\bullet$$ You may use the fact that all primes except $$2$$ and $$3$$ can be expressed in the form $$6k \pm 1$$.

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