The Riemann hypothesis is the Holy Grail of mathematics. Bernhard Riemann (1826–1866), one of the greatest mathematicians of the 19th century, formulated it in 1859 in his Über die Anzahl der Primzahlen unter einer gegebenen Größe. This conjecture bridges two areas of mathematics that a priori have nothing to do with each other: prime numbers and an analytic function, the ζ ("zeta") function. For more than 150 years, mathematicians have therefore been trying—so far in vain—to turn this conjecture into a theorem.
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The harmonic series diverges ---------------------------
What is the zeta function? The basic building block of the zeta function is the Dirichlet series
ζ(s)=∑n=1+∞1ns=1+12s+13s+14s+15s+…\zeta(s)=\sum\limits_{n=1}^{+\infty}\frac{1}{n^{s}}=1+\frac{1}{2^{s}}+\frac{1}{3^{s}}+\frac{1}{4^{s}}+\frac{1}{5^{s}}+\dots