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  "body": "\n## Summary\n\nA primality test is an algorithm that decides whether a given natural number is [[prime|0SN0MAEKYX]].\nUnlike factorization, it does not need to find the factors of a composite number.\n\n## Remarks\n\nThe simplest test is [[trial division|0Z962ECCXR]] by the primes up to $\\sqrt{n}$, but it is slow for large $n$.\nProbabilistic tests, such as the [[Fermat test|0N5ZSZMYH6]] and the [[Miller–Rabin test|0SZCSYHW60]], are fast but can accept a composite number with a small probability.\nIn 2002, Agrawal, Kayal and Saxena gave the first deterministic test that runs in polynomial time without an unproven hypothesis.\n\n## Explanations\n\n### L1 human\n\nA primality test answers the question \"is $n$ prime?\".\nFor numbers with hundreds of digits, this is much easier than finding the factors of $n$.\n",
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