Editing Primality test (section)

=== Other tests ===
[[Leonard Adleman]] and Ming-Deh Huang presented an errorless (but expected polynomial-time) variant of the [[Elliptic curve primality proving|elliptic curve primality test]]. Unlike the other probabilistic tests, this algorithm produces a [[primality certificate]], and thus can be used to prove that a number is prime.<ref name=AH92>{{cite book |first1=Leonard M. |last1=Adleman |author1-link=Leonard Adleman |first2=Ming-Deh |last2=Huang |title=Primality testing and Abelian varieties over finite field |series=Lecture notes in mathematics |volume=1512 |year=1992 |isbn=3-540-55308-8 |publisher=[[Springer-Verlag]]}}</ref> The algorithm is prohibitively slow in practice.

If [[quantum computer]]s were available, primality could be tested [[Big O notation|asymptotically faster]] than by using classical computers. A combination of [[Shor's algorithm]], an integer factorization method, with the [[Pocklington primality test]] could solve the problem in <math>O((\log n)^3 (\log\log n)^2 \log\log\log n)</math>.<ref>{{cite arXiv |last1=Chau |first1=H. F. |last2=Lo |first2=H.-K. |year=1995 |eprint=quant-ph/9508005 |title=Primality Test Via Quantum Factorization}}</ref>