That isn't possible. 7 + 7 = 14, and 7 x 7 = 49. You can't get higher than that, if you split 14 into two parts.
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It is impossible for the product of two prime numbers to be prime. It is impossible for the sum of two prime numbers to be prime as long as one of the numbers isn't 2.
17 and 3 are two prime numbers whose sum is 20. Their product is 51.
12
There are no such numbers.
391