A primality test is an algorithm for determining whether an input number is prime. Amongst other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is prime, while others like Miller–Rabin prove that a number is composite. Therefore we might call the latter compositeness tests instead of primality tests.
Read more about Primality Test: Naive Methods, Probabilistic Tests, Fast Deterministic Tests, Complexity, Number-theoretic Methods
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“Experimental work provides the strongest evidence for scientific realism. This is not because we test hypotheses about entities. It is because entities that in principle cannot be ‘observed’ are manipulated to produce a new phenomena
[sic] and to investigate other aspects of nature.”
—Ian Hacking (b. 1936)