Powerful, Power-packed, Power-driven..........Primes!

How many prime numbers less than 100100 are there which can be expressed in the form an+bna^{n}+b^{n} where a,ba,b and nn are all natural numbers and n2n≥2.

Details and Assumptions:

  • aa and bb can be non-distinct natural numbers.
  • Don't double count the primes.
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