jmc

There are five prime numbers between $4$ and $18:$ namely $5,$ $7,$ $11,$ $13,$ and $17.$ Hence the product of any two of these is odd and the sum is even. Because $$xy-(x+y)=(x-1)(y-1)-1$$increases as either $x$ or $y$ increases (since both $x$ and $y$ are bigger than $1$), the answer must be an odd number that is no smaller than $$23=5\cdot 7-(5+7)$$and no larger than $$191=13\cdot 17-(13+17).$$The only possibility among the options is $\boxed{119},$ and indeed $119=11\cdot 13-(11+13).$