This number is a composite.
3^(2^3 x 3^4) - 2 is prime and 3^(2^3 x 3^4 x 4^5) - 2 = 3^663552 - 2 has no prime factor less than 2^32. [Kulsha]
3^(2^3 x 3^4) - 2 is prime and 3^(2^3 x 3^4 x 4^5) - 2 = 3^663552 - 2 has no prime factor less than 2^32. [Kulsha]