47 and 53
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An example of two numbers which add together to make 100 are 47 and 53.
47+53
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.
If you meant "what two prime numbers have a sum of 36?" the answer is 19 and 17.
Two prime numbers can have only one sum, not three different sums!