There are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no known simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, the statistical behaviour of primes in the large, can be modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n.
How many prime numbers exist? Who established the amount of prime numbers in existence? What type of behavior in primes is it possible to determine? What theorem states that the probability that a number n is prime is inversely proportional to its logarithm? When was the prime number theorem proven?