Modularity and prime number sequence I tried to solve this modular equation involving first $n$ prime numbers. And it is: 
$$2^{3+5+7+11+13+.....+p_{n-3}+p_{n-2}}\equiv p_{n-1}\ \left(\text{mod }p_{n}\right),$$
where $p_{n}$ is the $n$-th prime number.
I couldn't find any solution for this equation until first $300$ primes. Is there any solutions for $n$?

For what is worth, next solutions $\{n,p_n\}$ are:
$$
\{306\,311,4\,353\,467\}\\
\{859\,825,13\,174\,621\}\\
\{1\,700\,098,27\,291\,793\}\\
$$
There are no more with $n\le10^7$.
