Prime towers

Number Theory Level 5

Find the last three digits of the sum of all (positive) primes \(p<1000,\) such that for some integer \(n\), the expression \(n^2-pn\) is a prime power.

Details and assumptions

A prime power is a number of the form \( q^m \) where \(q\) is a prime and \(m\) is a positive integer.

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