There are numerous hypotheses about prime numbers that have yet to be resolved. For example, since Euclid’s time, it’s been known that the sequence of prime numbers is infinite, but it is still unknown if an infinity of prime numbers *p* exists, such that *p* + 2 is also a prime number. And another one is that, on average, there are as many prime numbers for which the sum of decimal digits is even as prime numbers for which it is odd—or, more simply put, that the sum of digits of prime numbers is evenly distributed. This hypothesis was proposed by Russian mathematician Alexandre Gelfond in 1968, and now, it has been proven to be true. Why study such complex theories about prime numbers? Like many things in mathematics, such studies—besides being exciting to theoretical mathematicians—have important implications and applications in digital simulations and cryptography.