All positive integers greater than $2$ are written on a board. First we erase number $3$ and $5$. 

With 4 positive integers $a,b,c,d$ satisfying $a+b=c+d$, if $ab$ is erased, then $cd$ can be erased, otherwise $cd$ cannot be erased. 

For example, $3=3 \times 1$, $3+1=4=2+2$ , then $2 \times 2 = 4$ is erased.

a. What are the conditions of a number that can be erased ?

b. If not only $3$ and $5$, but every prime number is erased at the beginning, can all other numbers be erased as well? If not, what are the conditions of a number to be erased ?

(Sorry for my last question, English is my second language)