1, 17 and 289.
578
1 x 289, 17 x 17
1 x 289 = 289
1 and 36 289 and 324
289 = 17 x 17
The prime number (factor) of 289 is: 17
17*17 = 289
1, 17, 289.
289 - 256 = 33
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.
It is: 289/2 = 144.5