A quick look at prime numbers - Lillis, David (New Zealand Science Review, 2018)
​Since the time of the ancient Greeks, and probably long before then, we have been fascinated by prime numbers. One possible reason for our fascination with prime numbers is that the in-ter-relationships between them and the patterns that they appear to create are so difficult to understand. Another possible reason is that the primes appear to exhibit both deterministic behaviours (i.e. fully determined on the basis of naturally-occurring relationships) and random behaviours (i.e. occurring by chance). Nobody has succeeded in creating mathematical models that predict the magnitudes of prime numbers exactly or the numbers of prime numbers up to a given natural number. Other reasons for our fascination with primes may involve unexpected and quite exquisite relationships between prime numbers and certain mathematical functions and the seemingly disconnected islands of prime numbers, each surrounded by a sea of numbers that are not prime but which are related mysteriously to one another.