Primes and Powers.

Note that:

( 2 1 ) ! + 1 = 2 1 ( 3 1 ) ! + 1 = 3 1 ( 5 1 ) ! + 1 = 5 2 (2-1)!+1=2^1\\ (3-1)!+1=3^1\\ (5-1)!+1=5^2

Are there any other primes p > 5 p>5 such that ( p 1 ) ! + 1 (p-1)!+1 is a power of p p ?

Yes. No.

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