It is proved that there exist two odd prime numbers, pi and pj , such that pi + pj = 2r + 2(r ⩾ 2), where pn denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, hi and hj , such that hi + hj = r(r ⩾ 2), where hn = (pn − 1)/2，(pn ⩾ 3).Then we complete the proof.