What is the method to find the sum of two odd primes as 36?

Answer 1

trial and error, also called guess and check, but not quite

let x = 1st odd prime, and y = 2nd odd prime

the y can be 1,3,5,7,11,13,17,19,23,29,31

then x+y = 36, or x = 36 - y, by substitution

x = 36 - 1 = 35 not prime so not a solution

x = 36 - 3 = 33 not prime

x = 36 - 5 = 31 prime

x = 36 - 7 = 29 prime

x = 36 - 11 = 25 not prime

x = 36 - 13 = 23 prime

x = 36 - 17 = 19 prime

x = 36 - 19 = 17 prime (but a repeat of another solution)

so (5+31), and (7+29), and (13+23), and (17+19) are all solutions

For your question about the method, maybe it is called the method of exhaustion. List all possibilities for one number and exhaust (solve and check) for all other solutions.