5) Consider the following languages: PRIME = {ai where i is a prime number}, PRIME′ = {ai where i is not prime} i) Prove that PRIME′ is nonregular (hint: prove that PRIME is nonregular first - this is a challenge, since you'll have to choose your pumping factor K in a very clever way) ii) Show that PRIME′ does satisfy the pumping lemma (that is, it can't be proven nonregular using the pumping lemma) iii) How can this be? g

Develop the program incrementally: a) start by reading and displaying each line of the input file to make sure you are reading the data set correctly. b) use the split string method to extract information from each line into a list. print the list to prove that this step is working correctly. d) convert the exam scores to type int and calculate the student’s average. display those items to prove this step is working correctly. e) create a tuple containing the six items for each student (name, exam scores, exam mean). display the tuples to prove this step is working correctly. (optionally, you may want to have the exam scores in a list so your tuple is (name, scores_list, f) append each tuple to a list. display the list to prove this step is working correctly. g) use the sort list method to re-order the tuples in the list. display the list to prove this step is working correctly. h) use a for statement to display the contents of the list as a table (with appropriate formatting). i) use a for statement to calculate the average of all scores on exam #1, then display the results. note that you could have calculated this average within the first loop, but we are explicitly requiring you to do this calculation by looping though your list of tuples. j) add the logic to calculate the average of all scores on exam #2, then display the results.