Oct 14, 2019 · A quick look at Shor's algorithm (1995) suggests only thousands of qubits are needed to factor a 2048 bit number. This is deduced as follows: We need to perform a Quantum Fourier Transform (QFT) of size Q where Q is a 4096 or 4097 bit number . This QFT requires the calculation of a special function x^a mod N.
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The number (n) must be >=3. While 2 is a prime number, for our purposes we have no interest in numbers less than 3. Do a bitwise and (n&1). If the result is not 0 then we know the number is even and can throw it out. Check that n%p is 0 (in other words, that n is not divisible evenly by p) for all primes <1000.
corresponding to 64 elements of 32 bits each = 2048 bits, in current specifications from Intel (Intel, 2014a). The high-end CPUs are currently available with 8 or more cores and a clock frequency of 3 – 4 GHz. Some models are capable of running two threads in each core, but this may not be useful for CPU-intensive code because both threads are
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For the 2048-bit case, the first decimal digit can only be 0, 1, 2, or 3. So it's not "exact". The 2048 bits are comparable to the length of a number with somewhere between …