Refining the confidence factor in isProbablePrime

Question

My question is about the confidence factor for the method isProbablePrime()for BigInteger. The Java API claims that it is:

"a measure of the uncertainty that the caller wants to endure"

This is a percentage of uncertainty or some other factor. I need 2 simple numbers 512 bits.

Answer 1

From the JavadocsBigInteger isProbablePrime method for :

certainty is a measure of the uncertainty that the caller can tolerate: if the call returns true, the probability that this BigInteger simply exceeds (1 - 1/2 ^certainty )

, certainty, , , .. 100 , 1 - (1/2) ¹⁰⁰ 1.

Java , -, certainty ( Lucas-Lehmer).