In computer science efficiency of a program solely depends on time factor of processing statement or statement block. Further the amount of memory it is being used for processing also matters in calculating the space complexity of the program. All computer languages support sequencing, selection and iteration and file handling methods. The syntax and semantics in a language differs because of construction compiler or an interpreter is different in nature. This manuscript specifically examines the execution of checking the given number fall under category of prime number or not using Lucas Mathematical Model. A Lucas prime sequence generated and stored on secondary storage device to check the prime number and further comparing with the normal approach of checking a prime number. In addition to this time complexity and space complexity of Lucas prime sequence is examined. The purpose is to provide a alternative methodology for checking the prime numbers.