#### Hall 123

#### Prime Number Theorem

#### Karthick Babu

##### IMSc, Chennai

*In this talk, We will prove Riemann zeta function has no zeros in re(s) > 1- c/(log(t))^9 for |t|>2 and c > 0, where t= im(s) and using that We prove Prime Number theorem with error term O(x exp{-c(log x)^1/10}).*

Done