The Probability that a Random Probable Prime is Composite

@inproceedings{Kim2010ThePT,
  title={The Probability that a Random Probable Prime is Composite},
  author={Su Hee Kim and Carl Pomerance},
  year={2010}
}
Consider a procedure which (1) chooses a random odd number n < x, (2) chooses a random number 6, 1 < b < n — 1, and (3) accepts n if bn~l = 1 (mod n). Let P(x) denote the probability that this procedure accepts a composite number. It is known from work of Erdös and the second author that P(x) —> 0 as x —► oo. In this paper, explicit inequalities are established for P(x)\ For example, it is shown that P(10100) < 2.77 x 10~8 and that P(x) < (logx)"197 for x > 101()5. Introduction. Suppose one… CONTINUE READING