The original purpose of defining the Riemann zeta, was to investigate the distribution of prime numbers, particularly the function \pi(x), which counts the number of primes less than a given quantity. Riemann’s efforts in his 1859 article, “On the Number of Prime Numbers Less Than a Given Quantity,” made significant waves in the world of mathematics. Still, he could not prove the conjecture initially noticed by Legendre in 1797.

However, building on Riemann’s theory of the zeta function, Jacques Hadamard and Charles Jean de la Vallée-Poussin independently proved the conjecture in 1896.