Go Factor!

399337=6162+1412399337=4642+4292\large 399\:337 = 616^2 + 141^2 \\ \large 399\:337 = 464^2 + 429^2 The number 399337399\:337 is the product of two prime numbers p×qp\times q. Determine these prime numbers without using a calculator.

Submit your answer as the sum p+qp + q.

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