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The RSA algorithm works because, when n is sufficiently large, deriving d from a known e and n will be an impractically long calculation — unless we know p, in which case we can use the shortcut.
One company, also called RSA, shares quite a bit of history with the algorithm, but the patents have expired and now most implementations of RSA used throughout the internet did not come from them.
A quantum computer with a million qubits would be able to crack the vital RSA encryption algorithm, and while such machines don't yet exist, that estimate could still fall further ...