Primige

Primige refers to a concept primarily discussed within the field of number theory, specifically concerning properties of integers. It is a term that has been used to denote a number that is either prime or the square of a prime number. Therefore, a primige number is of the form $p$ or $p^2$, where $p$ is a prime number. For example, 2, 3, 4 (which is $2^2$), 5, 7, 9 (which is $3^2$), 11, 13, 16 (which is $4^2$, but 4 is not prime, so 16 is not a primige), 17, 19, 23, 25 (which is $5^2$), and so on, are primige numbers.

The definition of primige numbers is not universally standardized and may appear in various contexts with slightly different interpretations or primarily as a term introduced for specific problem-solving or theoretical explorations. Some sources might refer to a related concept where a number is considered "primigenic" if its prime factorization consists of at most two prime factors, counting multiplicity, and these factors must be the same prime. This aligns with the $p$ or $p^2$ definition.

The study of numbers with specific prime factorizations, such as primiges, is a common area of interest in number theory. Understanding these numbers can contribute to broader investigations into the distribution of prime numbers, the properties of composite numbers, and the structure of the integers. While not a widely recognized term in mainstream number theory literature, "primige" serves as a descriptive label for a specific subset of integers with a clear mathematical definition.