Question 638960: Let n be a positive integer greater than 1. We call n prime if the only positive integers that (exactly) divide n are 1 and n itself. For example, the first seven primes are 2, 3, 5, 7, 11, 13, and 17.Use the method of exhaustion to show that every integer in the universe 4, 6, 8, . . . , 36, 38 can be written as the sum of two primes.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! This is simply a guess and check problem. Doing this will give you the following
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7
12 = 5 + 7
14 = 3 + 11
16 = 3 + 13
18 = 5 + 13
20 = 3 + 17
22 = 3 + 19
24 = 5 + 19
26 = 3 + 23
28 = 5 + 23
30 = 7 + 23
32 = 3 + 29
34 = 3 + 31
36 = 5 + 31
38 = 7 + 31
Note: This list is NOT unique. Notice how 16 = 3+13 and 16 = 5+11. Also, notice how 20 = 3+17 and 20 = 7+13. So there is more than one way to write some integers as a sum of two primes.
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