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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.
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Computational :: Number Theory
593: A Leyland number, =2^9+9^2; they're good tests for primality proving algorithms: easy to calculate, but the factorization isn't obvious
primeoftheday (Prime of the Day) Tue, 29 Sep 2009 07:03:07 -0000
593: A Leyland number, =2^9+9^2; they're good tests for primality proving algorithms: easy to calculate, but the factorization isn't obvious
Detecting False Reports in Primality Tests by the Oddcomp(z) Method - Suggests to measure reliability of probabilistic primality tests by applying them to odd composites. No false prime reports found in Maple's isprime.
Least Primitive Root of Prime Numbers - Empirical and statistical results showing the smallest base required to prove a number is prime. Includes theory and conjectures.
Lucas Sequences in Cryptography - Focus on their use in primality testing, with pseudo-code. Includes an explanation of the strong Lucas PRP test.
MathWorld: Primality Testing - Articles on many different tests and related subjects.
Pseudoprimes/Probable Primes - Papers on primality tests and Frobenius pseudoprimes by Jon Grantham.
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