Explicit Bound of $\pmb{|ζ\left(1+it\right)|}$

Abstract: In this work, we show that for all $t\geq e$, [|\zeta(1+it)|\leq 0.6443 \log t. ] The equality is achieved when $t=17.7477$. We also use the Riemann-Siegel formula and numerical computations to show that [|\zeta(1+it)|\leq\frac{1}{2}\log t+0.6633\hspace{1cm}\text{when}\;t\geq e.]When $t\geq 100$, the bound $\frac{1}{2}\log t+0.6633$ is better than the bound $0.6443\log t$.