For this Hands-On, you will compare five countries of your choice. You can see the countries in the gapminder data frame with the below command: levels(gapminder$country) This Hands-On will be graded, so be sure you complete all requirements. Please complete this Hands-On in a R script file, and submit it along with your presentation file below when completed. Requirements Choose five countries from the resulting list after running the above command. Then use them to answer each of these questions: Which country of the five you chose has the lowest per capita GDP in 1952? In 2007? Which has the highest per capita GDP in 1952? In 2007? Create a line plot with year on the horizontal axis and lifeExp on the vertical axis for the five countries; give each country a different color line. Describe the variations in life expectancy between the countries. Compute the median of lifeExp as a function of year for all the countries in the gapminder data frame. For what years is the life expectancy of each of the countries you selected above the median life expectancy for all countries? Tip! You will need to load the library dplyr, ggplot, and gapminder to complete this hands on! Create a presentation (MS Power Point or equivalent) to report out on your findings. Be sure to include any R code you used to get your findings and create your graphs. Add any additional insight you believe is warranted.

Comment must be added.Q1 [30 pts] Mersenne prime: is a prime number of the form Mp = 2^p – 1, where p isa prime number. For example, M5 = 2^5 – 1 = 31 is a Mersenne prime. Noticethat if p is not prime, then 2^p – 1 must be composite. To generate a Mersenneprime of a large size, take a small prime p, then compute n = 2^p – 1, useprimality test to check if n is prime. If so, then n is Mersenne prime of length pbits. Otherwise, n is called a Mersenne composite. Implement a Booleanfunction mersenne (p) that returns true if and only if Mp is a Mersenne prime.The function should call your primality test function is_prime (with k basesshown below).a) In the main program, use your function to print all the Mersenne primesMp for p between 2 and 29, (with k = 3 in the is_prime function).b) Repeat part (a) using k =1 (for base 2 only), and compare the resultsc) Report the outcomes of this experiment (in the PA2.report.pdf file)d) Test mersenne (31). How long does it take to test if M31 is a Mersenneprime? Report your observations with justification if any.Q2 [40 pts] Implement the modular exponentiation (a.k.a. fast exponentiation)function mod_exp (b, n, m) to compute b^n (mod m) more efficiently. (Hint: toread n bit-by-bit, use / and % operations repeatedly)a) Test your function for b = 3, n = 2^31 – 2, m = 2^31 – 1.b) Report the result and the time (in seconds) it takes to find the resultQ3 [30 pts] Modify your is_prime function to use the mod_exp (b, n, m) instead ofthe standard power operation (b**n % m). Rename it as is_prime2. Modify themersenne (p) function to use is_prime2, and call it mersenne2.a) Use the modified function mersenne2 to print all the Mersenne primesMp for p between 2 and 31 if possible, (with k = 3 in the is_primefunction). Compare the results with the ones found in Q1.b) Gradually increase the range of p to find more Mersenne primes (say upto p = 101 if possible). What is the largest Mersenne prime you canachieve here?c) Extend the work in part (b) and find the maximum Mersenne prime youcan get from this experiment in a reasonable amount of time (Saywithin two minutes).d) Report your findings in this experiment, and comment on the speed upachieved by implementing the fast exponentiation algorithm.---------------the code must be built on top of the below code:my_Primes = [2, 3, 5, 7, 11, 13, 17, 19] def is_prime(n, k): if n in my_Primes: return True # Fermat Theorem: if p prime, then b^(p-1) = 1 (mod p) # choose a base b co-prime to n, if b^(n-1) mod n != 1 then Not Prime for i in range (k): # i = 0,1,2, ..., k-1 base = my_Primes[i] if gcd(base, n) > 1 : return False elif ((base**(n-1)) % n) > 1 : return False return True #pseudoprime to all bases tested. # Main Program:for j in range (2, 2000): if is_prime (j, 3): # for k= 3, accuracy ~99.95% # for k= 2, accuracy ~99.90% counter += 1 print (j, end = " \t") print ("\nDone!")