On Prime number varieties and their applications

Prime numbers and their variations are extremely useful in applied research areas such as cryptography, feedback and control in engineering. In this paper we discuss about prime numbers, perfect numbers, even perfect and odd perfect numbers, amicable numbers, semiprimes, mersenne prime numbers, triangular numbers, distribution of primes, relation between π and prime numbers. In the process we also obtain interesting properties of some of them and raise a set of open problems for further exploration.