(Ir)regularity of the set of primes. Since antiquity it is known that there is an infinite number of primes. The proof is simple. Suppose the set of primes P is finite. Now multiply all elements of P and add 1. The resulting number cannot be divided by any member of P, so P is incomplete. An estimation of the density of the prime numbers given by the Prime Number Theorem (see entry in Encyclopaedia Britannica on Prime Number Theorem  [OIR]).  It states that the gaps between primes in the set of natural numbers of size n is roughly \( \ln n\), where \(\ln\) is the natural logarithm based on Euler’s number e. A refinement of the density estimation is given by the so-called Riemannn hypothesis, formulated by him in 1859 (Goodman and Weisstein 2019  [OIR]),  which is commonly regarded as deepest unsolved problems in mathematics, although most mathematicians consider the hypothesis to be true.