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Currently there is no known efficient formula for primes. Besides that, primenumbers have great importance in e.g., information technology such aspublic-key cryptography, and their position and possible or impossiblefunctional generation among the natural numbers is an ancient dilemma. Theproperties of the functions 2ab+a+b in the domain of natural numbers areintroduced, analyzed, and exhibited to illustrate how these single out all theprime numbers from the full set of odd numbers. The characterization of oddprimes vs. odd non-primes can be done with 2ab+a+b among the odd naturalnumbers as an analogue to the other, well known type of fundamentalcharacterization for irrational and rational numbers among the real numbers.The prime number theorem, twin primes and erratic nature of primes, are alsocommented upon with respect to selection, as well as with the Fermat and Eulernumbers as examples.

On the statistical distribution of prime numbers, a view from where the distribution of prime numbers is not erratic