We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of $log t$ term. Our analysis covers the entire parameter regions with respect to the replica number $n$ and the conformal dimension $h_O$ of the primary operator which creates the excitation. We numerically analyse relevant vacuum conformal blocks by using Zamolodchikovs recursion relation. We find that the behavior of the conformal blocks in two dimensional CFTs with a central charge $c$, drastically changes when the dimensions of external primary states reach the value $c/32$. In particular, when $h_Ogeq c/32$ and $ngeq 2$, we find a new universal formula $Delta S^{(n)}_Asimeq frac{nc}{24(n-1)}log t$. Our numerical results also confirm existing analytical results using the HHLL approximation.
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