Are you asking how hard it is to take 2^{332,199,893}1 and expand it to its full decimal form vs checking it to see if it is prime?
The first is very fast. Faster than the old machines could display it. The second is slow.
If you have some complex formula to calculate the number vs checking it to see if it is prime, even that, calculating the number is faster than checking it (in almost every case).
