Essential genes are considered to be the necessary genes that are required to sustain life of different organisms. These genes encode proteins which maintain central metabolism, DNA replications, translation of Genes, basic cellular structure and mediate transport process within and out of the cell. The identification of essential genes is one of the essential problems in computational genomics. In this present study, in order to discriminate essential genes from the other genes from the non-biologist’s perspective, the purine and pyrimidine (Pu-Py) distribution over the essential genes of four exemplary species namely: Homo Sapiens (HS), Arabidopsis Thaliana (AT), Drosophila Melanogaster (DM) and DanioRerio (DR) are thoroughly experimented using some quantitative methods. Moreover, the Indigent classification method has also been deployed for classification on the essential genes of the said species. Based on Shannon entropy (SE), Fractal dimension (FD), Hurst exponent (HE), purine and pyrimidine (Pu-Py) bases distribution the ten different clusters have been generated for the essential genes of the four species. Some proximity results are also reported herewith the clusters of the essential genes.