Extremely difficult question

If x,y are positive real integers such that x can be expressed as an infinite sum of $\frac{a}{\frac{b}{\frac{b}{\frac{b}{\cdots}+\frac{c}{\cdots}}+\frac{c}{\frac{b}{\cdots}+\frac{c}{\cdots}}}+\frac{b}{\frac{b}{\frac{b}{\cdots}+\frac{c}{\cdots}}+\frac{c}{\frac{b}{\cdots}+\frac{c}{\cdots}}}}$ and a is the least prime number whicn has the property that any sum of two consecutive integers is divisible by it. C is defined recursively, where c=$\frac{a}{\frac{b}{\frac{b}{\frac{b}{\cdots}+\frac{c}{\cdots}}+\frac{c}{\frac{b}{\cdots}+\frac{c}{\cdots}}}+\frac{b}{\frac{b}{\frac{b}{\cdots}+\frac{c}{\cdots}}+\frac{c}{\frac{b}{\cdots}+\frac{c}{\cdots}}}}$. B has the property that it is the first prime number which is not a factor of any other prime number, and it also does not equal to C. Y has the property that the sum of an infinite geometric sequence with a scale factor of 1/2 with starting term one is equal to y plus $e^{\pi i}$. What is x+y?