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Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.

47 votes

Examples of algorithms requiring deep mathematics to prove correctness

The Miller-Rabin tests determines whether an integer $n$ is prime in time $O_{\epsilon}((\log n)^{4+\epsilon})$. The bound on the running time is conditional on the truth of the Generalized Riemann Hy …