\[\vartheta (x)= \sum_{p \leqslant x}^{ } ln(p) \\ over \ all \ prime \ numbers \ p \leqslant x \] \[\vartheta (x)= ln(~\prod_{p \leqslant x}^{ }(p)~) =ln(x\#)\] \[\\ x\# \ is \ the \ primorial\]