Skip to content

Primality test can return true for composites #29

@randombit

Description

@randombit

It appears the Miller-Rabin test implemented in bigi always chooses the base from the set of primes < 1000, however it is possible to construct a composite that appears prime relative to any fixed set of witnesses, and the paper https://math.dartmouth.edu/~carlp/PDF/reliable.pdf has a proof that there exist integers with no small witnesses at all.

The best fix is probably to choose the witnesses randomly from the range [2,n) which avoids the problem entirely.

Metadata

Metadata

Assignees

No one assigned

    Labels

    Type

    No type

    Projects

    No projects

    Milestone

    No milestone

    Relationships

    None yet

    Development

    No branches or pull requests

    Issue actions