Understanding Antiprimes: Properties and Applications

Antiprimes are numbers that are not prime, but have the property that they cannot be expressed as a product of smaller prime factors. In other words, a number is an antiprime if it is not prime, but it cannot be factored into simpler prime factors.

For example, the number 12 is not prime because it can be factored into 2 x 2 x 3, but it is also not an antiprime because it can be expressed as a product of smaller prime factors. On the other hand, the number 15 is not prime because it can be factored into 3 x 5, but it is an antiprime because it cannot be expressed as a product of smaller prime factors.

Antiprimes were first studied by the mathematician Paul Erdős in the 1930s, and they have been the subject of ongoing research in number theory ever since. There are many interesting properties and applications of antiprimes, and they continue to be an active area of study in mathematics.