I did a similar one before but this one is different.
Take the numbers 1 and 14. Multiply them to get 14 and add them to get 15. Now add the results to get 29 which is a prime number. Now take 4 and 11 which yields 44 and 15 for the results. Adding the results gives 59 which is a prime number.
Let's try 1 and 15. The results are 15 and 16 which upon adding yields the prime number 31. With 11 and 5, the results are 55 and 16 which yields the prime number 71 after adding.
At this point you should notice a pattern and the question is how far can this be extended? Would this work with numbers that don't have repeated digits? Would this work with more than two numbers at a time?