For any integer n (n ≥ 4) there exist two prime numbers p1 and p2 such that p1 + p2 = n. In a problem we might need to find the number of essentially different pairs (p1, p2), satisfying the condition in the conjecture for a given even number n (4 ≤ n ≤ 2 15). (The word ‘essentially’ means that for each pair (p1, p2) we have p1 ≤ p2.)
What's missing in the above excerpt is that n must be even. Goldbach's Conjecture is not valid for all odd numbers. For example, 27 cannot be expressed as a sum of two primes.