Is RSA public key unique?

rsa

Solution

As per Wikipedia, you are allocated a number (usually a prime number) in the range of 0 to:

RSA-2048 = 2519590847565789349402718324004839857142928212620403202777713783604366202070
           7595556264018525880784406918290641249515082189298559149176184502808489120072
           8449926873928072877767359714183472702618963750149718246911650776133798590957
           0009733045974880842840179742910064245869181719511874612151517265463228221686
           9987549182422433637259085141865462043576798423387184774447920739934236584823
           8242811981638150106748104516603773060562016196762561338441436038339044149526
           3443219011465754445417842402092461651572335077870774981712577246796292638635
           6373289912154831438167899885040445364023527381951378636564391212010397122822
           120720357

This number is huge. This number scales to that larger than the number of particles in the universe.

Statistically it will never clash with another number, nor will anyone have the computing power to brute force what it is. By the time they do, the message will be meaningless

(..and most of the universe would have imploded)

Problem

We use RSA 2048 public key on our server for user identifier, but now I have a doubt about unique of this identifier. Could I use RSA public key as unique user identifier on server or RSA does not guarantee this?

Original source