skylsn

2022-06-27

Could Miller-Rabin primality test give false negative, for example when test prime number and gives it as composite?

America Barrera

Expert

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.

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