The two prime numbers are 31 and 19 and their product is 589.
Step-by-step explanation:
Let the numbers be x and y.
We will consider all the prime numbers between 1 and 50 is 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47.
First we will find all the possibilities,
3+ 47 = 50 and their product is 141.
43+ 7 = 50 and their product is 301.
13+ 37 = 50 and their product is 481
19+ 31 = 50 and their product is 589
Among these combinations, the biggest possible product of 2 prime numbers is 589 and the 2 prime numbers are 31 and 19.