I search a prime factor of the huge number
3^(3^(3^3))+2^(2^(2^2))
The number is too large to apply elliptic curve method or even pollard-rho because it has about 3.6 * 10^12 digits. But it has a special form (the first power has a very large and special exponent).
How can I efficiently search for a prime factor of the given number ? Is trial division the only feasible method ?