How to find the value of this giant?

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How can I find the value of this giant exponent: "2 raised to the power of 1717986918400"? Should one need a supercomputer to calculate this number? Is there any theory in math that can specify how many digits would this value have?

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This number has

$$\left\lfloor1717986918400\frac{\log2}{\log10}\right\rfloor+1=517165594597$$ digits.

Written in ASCII code, this takes half a terabyte and doesn't fit in the memory of a PC.

Using a bignum library able to swap to disk, I would expect a few hours of work.