Sentence:  In 1859, Riemann attempted to give a complete proof of the <WSD>prime number theorem</WSD> using the zeta function for complex variables "s". Although he was not successful in proving the <WSD>prime number theorem</WSD> he established many properties of the zeta function and showed that the <WSD>prime number theorem</WSD> depended on the zeros of the zeta function. 
Meaning of the word marked with <WSD> tags:  The theorem that the number of prime numbers less than "n" asymptotically approaches "n" / ln("n") as "n" approaches infinity.