Yes.
The mathematical formula is:
P(n,r) = n! / (n - r)!
= 2048! / (2048 - 2048)!
= 1.672691931e+5894.
Meaning 1 in 1.672691931e+5894 chance.
The e+5894 means 5894 extra zeros.
There are less atoms in the entire universe than this number.
The risk of two being identical is close to 0.
But even if there were two identical out there it would not compromise your security.
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