Lets consider the sequence of consecutive prime numbers $p_1=2 , p_2=3 ,p_4=5 , \cdots$

. $(p_n,p_{j})$ is to be called good prime pair if $$\sum_{i =n }^{j}p_i= p_n p_{j}$$ Meaning the sum of set of consecutive term of the sequence of prime number equals to the product first and the last number of the set.

For example we have $$2+3+5=10= 2 \times 5$$Thus $(2,5)$ are good prime pairs . Similarly $$3+5+7+11+13=39=3 \times 13$$thus $(3,13)$ are good prime pairs And similarly $(5 ,31)$ is other such example . On this I have two questions

1) Are there infinitely many good prime pairs? and also 2) For every prime $p$ does there exist another prime $p'$ such that those form a good prime pair $(p , p')$