Yes, it is possible to have a number system with a fixed number of "prime" or atomic numbers. Such a number system would be called a fixed-base number system.
In a typical number system like the decimal system (base-10), we have ten digits (0-9) that can be combined to represent any number. However, in a fixed-base number system, we would have a fixed set of "prime" or atomic numbers that cannot be further decomposed into other numbers within the system.
For example, let's consider a hypothetical fixed-base number system with four atomic numbers: {0, 1, 2, 3}. In this system, we have only four digits to represent any number. We can use these digits to form different numbers by combining them according to the rules of the number system.
Using this system, we can represent the following numbers: 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, ...
Note that in this system, numbers like 4, 5, 6, etc., cannot be represented because they are not part of the fixed set of atomic numbers.
The properties and limitations of a fixed-base number system with a specific set of atomic numbers will depend on the rules and operations defined for that system. It may have different arithmetic operations, algorithms, and representations compared to traditional number systems like decimal or binary.