Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and in all of mathematics. It states:

"Every even integer greater than 2 can be expressed as the sum of two primes."

Efficient method to test if n is prime is to first test if n is divisible by 2 or 3, then to check through all the numbers of form 6k ± 1 that are <= of square root of n.

lets check if 2014 - 3 = 2011 is prime:

2011 is not divisible by 2 nor 3

square root of 2011 < 45

all the numbers of form 6k ± 1 that are <= 45 are:

5, 11, 13, 17, 19, 23, 29, 31, 37, 41 and 43

using trail check if 2011 is divisible by some of the above numbers

2011 is not divisible by any of 5, 11, 13, 17, 19, 23, 29, 31, 37, 41 and 43 thus 2011 is prime and:

2014 = 3 + 2011, a sum of two prime numbers 3 and 2011.