5 + 19
7 + 17
11 + 13
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5 and 3 are two prime numbers which on adding give 8.
They are: 359+2 = 361
No two prime numbers can add to 119.
No two prime numbers satisfy that request.
There is no solution. For two numbers to add to an odd total, one of them must be even. If that number is also a prime it must be 2. But if one of the numbers is 2 and the two sum to 289, the other must be 287. But 287 is not a prime and the question required two primes to be added.