proof

I probably don't know enough about primes, but,

What properties/laws are you using that makes N prime?

Have you also considered that, under the number system that allows infinite digit integers, since [...11111] is the largest number, there must also be a largest prime number?

If we constructed a table in that method that contains n primes, the resulting N has m digits. Surely there exists some n that produces a table that contains a number larger than N, if not containing N outright. The table that we used with n = infinity produces some prime N with some m digits; m in this case is presumably infinity. Does our infinite list contain a number larger than N? Which infinite value has more "infinite-ness", n or m?