Without any doubt, primes are the most prominent numbers. They are, to say it in simple words, the base of calculations. All other natural, rational, or irrational numbers are resulting or expressed by them. True primes are natural numbers which can only be divided without remainder or residue by themselves or the number one. The trivial conclusion is that there are no other integer parts in primes. Already Euclid knew that the number of primes is infinite. Eratoshenes gave an algorithm for their construction, which is not surpassed. Today, there exists a comprehensive but in many aspects not sufficient knowledge about these numbers.There is also a practical aspect of primes in factorisation of natural numbers. Hunting great primes and prime twins is like a sport in mathematics.While the knowledge about primes can only be calles vast an a detailed treatment would fill thousands of pages, in this book, some important basic ideas can be found. The main goal is to show the connections with number theory. A choice of equations and theorems is often only shortly cited.