How Shor's Algorithm Factors 314191

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This video explains how Shor’s Algorithm factors the pseudoprime number 314191 into its prime factors using a quantum computer. The quantum computation relies on the number-theoretic analysis of the factoring problem via modular arithmetic mod N (where N is the number to be factored), and finding the order or period of a random coprime number mod N. The exponential speedup comes in part from the use of the quantum fast fourier transform which achieves interference among frequencies that are not related to the period (period-finding is the goal of the QFT FFT).


RSA Numbers (sample large numbers to try factoring)


Modulo Multiplication Group Tables

Difference of squares factorization

Euclid’s Algorithm

Rational sieve for factoring

General Number field Sieve

Scott Aaronson blog post about Shor’s Algorithm

Experimental implementation of Shor’s Algorithm (factoring 15, 21, and 35)

Adiabatic Quantum Computation factoring the number 291311

Scott Aaronson course notes

Shor’s Algorithm on Quantiki

TLS And SSL use RSA encryption

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Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Created by Henry Reich