Could Miller-Rabin primality test give false negative, for example when test prime number and gives it as composite?
I know that it could give false positive (giving composite number as prime), but I am not sure about the reverse.
2025-01-13 02:06:05.1736733965
Could Miller-Rabin primality test give false negative?
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No, it will not indicate composite when given a prime.
The Miller-Rabin test, like many primality tests, uses properties that are always true for primes, but are rarely true for composites. Hence, barring implementation defects, it will always return true (PROBABLY PRIME) when given a prime. Most composites will return false (DEFINITELY COMPOSITE). Some composites, which we call pseudoprimes to the particular test, will also return true.