Prove that for all odd prime numbers $p_1$ and $p_2$, there exist prime numbers(exclude 2) $p_3$ and $p_4$ such that $$p_3 + p_4 = p_1 + p_2 + 2.$$

Hints would be appreciated.

• What is the source of this problem? – user236182 Nov 8 '15 at 0:49

For $p_1=2,p_2=7$, we have $p_1+p_2+2=11$, but there are no pairs of primes $(p_3,p_4)$ such that $$11=p_3+p_4.$$