What is a pimp number?

A pimp number is a positive integer that is the product of two distinct prime numbers, and the sum of those prime numbers is also a Prime number. For example, the number 15 is a pimp number because it is the product of the prime numbers 3 and 5, and their sum (3 + 5 = 8) is not prime. However, the number 21 (product of 3 and 7) is a pimp number because the sum (3 + 7 = 10) is also not prime. In essence, pimp numbers showcase a unique relationship between their prime factors and their sum.