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Challenge 2: Primes Near Powers

How many prime numbers are there that are 1 less than a square? How many prime numbers are there that are 1 less than a cube? What about primes of the form nk – 1 for k > 3?

How many prime numbers are there that are 1 less than a square? 

How many prime numbers are there that are 1 less than a cube? 

What about primes of the form nk – 1 for k > 3?