17 and 37. 17+37=54
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what prime numbers have the sum of 54
If two prime number have a sum of 54 they cannot have a sum of 84, and conversely.
Two prime numbers can have only one sum, not three different sums!
The numbers are 13 and 41. And you do not need to know that they are prime in order to find the answer. The sum (54) and difference (28) provide all the necessary information.
The prime numbers (factors) of 54 are: 2 and 3