Pseudoprime

A pseudoprime is a composite number that has certain properties in common with prime numbers.

Introduction
To find out if a given number is a prime number, one can test it for properties that all prime numbers share. One property of a prime number is that it is only divisible by one and itself. This is a defining property: it holds for all primes and no other numbers.

However, other properties hold for all primes and also some other numbers. For instance, every prime number greater than 3 has the form $$6n - 1\ $$ or $$6n + 1\ $$ (with n an integer), but there are also composite numbers of this form: 25, 35, 49, 55, 65, 77, 85, 91, &hellip;. So, we can say that 25, 35, 49, 55, 65, 77, 85, 91, &hellip; are pseudoprimes with respect to the property of being of the form $$6n - 1\ $$ or $$6n + 1\ $$. There exist better properties, which lead to special pseudoprimes, as outlined below.