A swarm of prey, when attacked by a predator, is known to rely on their cooperative interactions to escape. Understanding such interactions of collectively moving prey and the emerging patterns of their escape trajectories still remain elusive. In this paper, we investigate how the range of cooperative interactions within a prey group affects the survival chances of the group while chased by a predator. As observed in nature, the interaction range of prey may vary due to their vision, age, or even physical structure. Based on a simple theoretical prey-predator model, here, we show that an optimality criterion for survival can be established on the interaction range of prey. Very short-range or long-range interactions are shown to be inefficient for the escape mechanism. Interestingly, for an intermediate range of interaction, the survival probability of the prey group is found to be maximum. Our analysis also shows that the nature of the escape trajectories strongly depends on the range of interactions between prey and corroborates with the naturally observed escape patterns. Moreover, we find that the optimal survival interaction regime varies depending on the prey group size and also on the strength of the predator and the prey interactions.