Question 3: Counting Prime Numbers [100 marks]

Programming language: Python

A prime number is an integer number greater than 1 that is not a product of two smaller integer numbers. In other words, a prime number has only two positive divisors: one and itself. Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Do you know during history scientists have always been looking for mysterious properties of prime numbers? Do you know one of the Millennium Prize Problems is about the distribution of prime numbers? Well, if this introduction motivated you enough, now, it is time to write a program about prime numbers.

In this part of the assignment, you are asked to create a program, called PrimeFinder, to count the number of prime numbers in a sequence of numbers provided by the user. PrimeFinder should work as follows:

First, PrimeFinder should ask how many numbers the user has decided to pass to PrimeFinder using the message 'How many numbers do you want to check? '. Lets call the provided number by user n.

For n times PrimeFinder should print 'Enter a positive integer: ' and take a positive integer from the user.

For each prime number, PrimeFinder prints out 'X is a prime number.' where X is the number provided by the user in that round.

For each nonprime number PrimeFinder does not print out a message.

PrimeFinder assumes that its users are smart enough not to enter a float number.

If the user inserts a negative number PrimeFinder should ignore it and inform the user by the message 'PrimeFinder ignores negative numbers!'. For instance, if n=2 the user-provided sequence of numbers can be 3, 5 or 2, -4, -7, 5. In other words, PrimeFinder will continue working until it gets exactly n positive integers.

Finally, PrimeFinder prints out the total count of prime numbers received from the user, Y , in the following format: 'Total prime numbers: Y'.