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A primality test is an algorithm for determining whether an input number is prime. It is important to note the difference between primality testing and integer factorization — factorization is, as of 2006, a computationally hard problem, whereas primality testing, as shown below, is comparatively easy.
Naïve methods
The simplest primality test is as follows: Given an input number n, we see if any integer m from 2 to n-1 divides n. If n is divisible by any m then n is composite, otherwise it is prime.
More on [ Primality test ]
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2^33548+4471: A 10099-digit result of elliptic curve primality proving; ECPP, using many more groups than n+/-1, is strong vs. strong primes
primeoftheday (Prime of the Day) Mon, 07 Dec 2009 00:41:20 -0000
2^33548+4471: A 10099-digit result of elliptic curve primality proving; ECPP, using many more groups than n+/-1, is strong vs. strong primes
Primality Proving - Covers different types of primality tests, such as quick, classical and general purpose prime filters. Page includes bibliography.
Lucas's Primality Test with Factored N-1 - Kevin Brown explains the mathematics behind the classical N-1 method to prove primes.
Manindra Agrawal - Papers including PRIMES is in P by Agrawal, Kayal and Saxena (AKS). It presents a polynomial-time primality proving algorithm for any number.
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PRIMES is in P Little FAQ - Answers to some common questions about the proof that testing for primality is a polynomial-time problem. By Anton Stiglic.
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