What is fake prime?

Fake primes are numbers that appear to be prime but are actually composite. These numbers can be created using different methods, such as the Fermat primality test or the Miller-Rabin primality test.

One reason for creating fake primes is to try to break cryptographic systems that rely on the difficulty of factoring large composite numbers. An attacker can create a fake prime and use it to create a trapdoor in the system, allowing them to easily factor the composite numbers and break the encryption.

Fake primes can also be used in other computational tasks, such as generating random numbers or testing the performance of primality testing algorithms. However, it is important to use reliable methods for generating these fake primes to avoid introducing vulnerabilities in the systems that rely on them.