A harmonic series is a form of the zeta function : .
When has a value less than or equal to one the function outputs infinity. Euler found that when , the zeta function outputs . Euler also realized that since every number is the multiplication of some order of primes, then the zeta function is equal to
Riemann found that when complex numbers are the input to the zeta function, the resulting graph is that which aids in the finding of the exact value of or the number of primes less than or equal to .