# Consecutive Prime Powers

Number Theory Level 4

Find the sum of all positive integers $$N$$ such that $$N-1$$, $$N$$, and $$N+1$$ are all prime powers.

Details and assumptions

A prime power is a positive integer that can be expressed in the form $$p^a$$, where $$p$$ is a prime and $$a$$ is a positive integer.

The question has been updated to standardize the definition of a prime power.

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