The computation time used by the Extensive Air Showers (EAS) simulators is an important variable to be considered when generating shower simulated libraries. The thinning method implemented in the EAS simulator codes has been a fundamental tool when the computational resources were limited, nevertheless at present the computers allows to perform more calculations in a shorter time. Computer tools are such that the use of thinning nowadays is an option that can be avoided and one can perform simulations without it, achieving the totality of the information generated along the EAS development. This, anyway, imply the use of the maximum calculation time, on the other hand, it is always more efficient to have the option that allows a less time consuming, useful for example in the first stages of an EAS simulation analysis. It thus arise, naturally, the question about what is the optimal thinning that should be applied to perform the required EAS simulation, minimizing computer error and fluctuations.

We present an analysis of the convergence of the fluctuations of the observable of interest as a function of the thinning used, which allows to find the suitable thinning value and the number of simulated EAS needed in order to get the required observables with a value that guarantee the minimization of its artificial fluctuations.

We prove that the computation time can be optimized in a controlled way that allows to know which are the minimum numbers of EAS to average, the thinning value to be considered, which will allow to obtain a convergent value of the desired physical observable related to the fluctuations

between EAS.