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Primality Test Via Quantum Factorization

H. F. Chau·H. -K. Lo
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Abstract

We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the primality of a number $N$, making it (asymptotically) the fastest known primality test. Thus, the potential power of quantum mechanical computers is once again revealed.

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H. F. Chau, H. -K. Lo. 1995-08-05. Primality Test Via Quantum Factorization. https://arxiv.org/abs/quant-ph/9508005

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