Number theory and especially primes are an infinite source of inspirational ideas in elementary mathematics. Many of these ideas can be understood and some also explained with very basic mathematical knowledge. In our paper we explain the cycle which appears between the first six multiples of the decimal expression of and explore an inspiringly simple relation between primes, which somehow makes them gather into mysterious groups. And while exploring these simple questions, we are led to unveil some aspects of the power and limits of human mind and those of a computer.