There are too many. Not just more than could fit in every database on Earth. More than could fit on every database if every star in the sky had an Earth, each with as many databases as there are on Earth.

This is nothing specific to cryptography or prime numbers. Fun fact: if you shuffle a deck of cards correctly, it's almost certain that no one in history has ever had a deck in the exact same order. https://www.math.hmc.edu/funfacts/ffiles/10002.4-6.shtml