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Very well. What do you think, are there arbitrary large squares possible or not?
I think not. Even in binary notations NxN and above, probably don't exist for an N, large enough.
I'm pretty sure arbitrarily large squares are possible. Here's an argument that assumes primes behave like random numbers, which is often okay to assume. By the prime number theorem, the chance that an N-digit number is prime is proportional to 1/N. So the chance that N^2 random digits arranged in a square will form 2N primes (N rows and N columns) is about 1/N^(2N). But the number of ways to select N^2 digits is 10^(N^2) which easily overwhelms that.