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 $n$?

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