modify the previous program to find every prime number less than or equal to the goldbach conjecture asserts that every even number is the sum of two prime numbers write program that gets number from the userchecks to make sure that it is evenand then finds two prime numbers that sum to the number the greatest common divisor (gcdof two values can be computed using euclid' algorithm starting with the values and nwe repeatedly apply the formulanm mn% until is at that pointn is the gcd of the original and write program that finds the gcd of two numbers using this algorithm write program that computes the fuel efficiency of multi-leg journey the program will first prompt for the starting odometer reading and then get information about series of legs for each legthe user enters the current odometer reading and the amount of gas used (separated by spacethe user signals the end of the trip with blank line the program should print out the miles per gallon achieved on each leg and the total mpg for the trip modify the previous program to get its input from file heating and cooling degree-days are measures used by utility companies to estimate energy requirements if the average temperature for day is below then the number of degrees below is added to the heating degree-days if the temperature is above the amount over is added to the cooling degree-days write program that accepts sequence of average daily temps and computes the running total of cooling and heating degree-days the program should print these two totals after all the data has been processed modify the previous program to get its input from file write program that graphically plots regression linethat isthe line with the best fit through collection of points first ask the user to specify the data points by clicking on them in graphics window to find the end of inputplace small rectangle labeled "donein the lower left corner of the windowthe program will stop gathering points when the user clicks inside that rectangle the regression line is the line with the following equationy ( xwhere xi yi nxy mp xi nx is the mean of the -valuesy is the mean of the -valuesand is the number of points as the user clicks on pointsthe program should draw them in the graphics window and keep track of the count of input values and the running sum of xyx and xy values when the user clicks inside the "donerectanglethe program then computes value of (using the equations abovecorresponding to the values at the left and right edges of the window to