Shor's algorithm is a quantum algorithm designed to factor large numbers efficiently. The minimum number of qubits required to run Shor's algorithm depends on the size of the number being factored.
In general, Shor's algorithm requires a minimum of 2n+3 qubits, where n is the number of bits in the number being factored. This includes n qubits for storing the input, 2n qubits for performing quantum Fourier transform operations, and 3 additional qubits for ancillary operations.
For example, if you want to factor a 2048-bit number, Shor's algorithm would require a minimum of 4099 qubits (2048 for storing the input, 4096 for quantum Fourier transforms, and 3 ancillary qubits).
It's worth noting that the number of qubits required is just a theoretical lower bound. In practice, running Shor's algorithm on a large number is extremely challenging due to the fragility of qubits, error rates, and the need for error correction techniques. Current quantum computers have limited qubit numbers and are prone to errors, making it impractical to factor large numbers using Shor's algorithm at this time.