Ramanujan's infinite nested radical states that $$\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\cdots}}}}=3.$$
Now instead, consider the following infinite nested radical $$\sqrt{1+p_1\sqrt{1+p_2\sqrt{1+p_3\sqrt{1+\cdots}}}}$$ where $p_n$ represents the $n$-th prime. How to solve this infinite nested radical?