Could Miller-Rabin primality test give false negative, for example when test prime number and gives...

skylsn

skylsn

Answered

2022-06-27

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

Answer & Explanation

America Barrera

America Barrera

Expert

2022-06-28Added 23 answers

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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