Math 2.0

Number theory Finite fields and computational number theory Concept

Primality test

Builds on Prime number

Summary

A primality test is an algorithm that decides whether a given natural number is prime. Unlike factorization, it does not need to find the factors of a composite number.

Remarks

The simplest test is trial division by the primes up to n\sqrt{n}, but it is slow for large nn. Probabilistic tests, such as the Fermat test and the Miller–Rabin test, are fast but can accept a composite number with a small probability. In 2002, Agrawal, Kayal and Saxena gave the first deterministic test that runs in polynomial time without an unproven hypothesis.

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To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Divisibility, definition, no evidence levelDivisibilitydefinitionPrime number, definition, no evidence levelPrime numberdefinitionPrimality test, concept, no evidence levelPrimality testconcept
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  1. Divisibility definition
  2. Prime number definition
  3. Primality test concept

Where this leads

3 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Primality_test, lead section
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