Special properties are mathematical properties that are not shared by all mathematical objects. For example, the property of being a prime number is a special property, because not all numbers are prime numbers.

Here are some properties of special properties:

* Special properties are often defined in terms of other mathematical properties.

* For example, the property of being a prime number can be defined in terms of the property of being divisible by only 1 and itself.

* Special properties can be used to classify mathematical objects.

* For example, the set of prime numbers can be classified as a special subset of the set of natural numbers.

* Special properties can be used to solve mathematical problems.

* For example, the fact that prime numbers are the building blocks of all natural numbers can be used to prove a variety of results about natural numbers.

* Special properties can be used to create new mathematical structures.

* For example, the set of prime numbers can be used to create a variety of algebraic structures, such as rings and fields.

* Some special properties that can be studied are periodicity, continuity, differentiability, symmetry, computability, recurrence, solvability, self-similarity, etc.