Sieve of Eratosthenes (individual assignment)

The first thing you'll need to do is to create a repository for your project using GitHub classroom. Visit this GitHub classroom link (which I've placed in Moodle). Log into GitHub if need to. GitHub should then hopefully respond with a screen that says "You're ready to go!" and will supply you with a link for the repository that you are creating. Click on that link, and you should be taken to the repository.

Since this is an individual assignment, you'll again use the my-work repl in Repl.it that you created. In Repl.it, start up your my-work repl, and then make sure that you are in your home directory in the terminal window. You can always navigate there by typing

cd ~

in the terminal window. To further confirm, type pwd (which is short for "print working directory.") You should see /home/runner. If you see something different, you're not in the home directory, so try again or ask for help.

In a different browser tab (leave the one with Repl.it open), visit our our class GitHub organization page online. Once you've landed there, you should see the GitHub repository you created in the GitHub Classroom step above. It should be named scheme-sieve-username (where username is your username). Contact us for help if the repository isn't there. Click on that repository title. This should take you to the home page for that repository. There is a green box on the page that says "Clone or download." Click that box, and make sure it says "Clone with HTTPS." Highlight the https link shown, and copy it to the clipboard. The link that you're copying should look something like

https://github.com/carleton251-term/scheme-sieve-username.git

… though your username and term will be different.

Then navigate back to the Repl.it tab with the repl that you created above, and click on the terminal window within your new repl. Your next step is to clone the repository from GitHub. To do that, type git clone, then a space, then paste in the URL from the github page that you copied from above. (To paste, you might need to right-click in the terminal window and choose paste rather than using a keyboard shortcut.)

For example, I would type the following, though your username and term will be different:

git clone https://github.com/carleton251-term/scheme-sieve-username.git

You'll be prompted to enter your GitHub username and password.

If all goes well, you should receive a directory, titled scheme-sieve-username. If you type ls at the prompt, you should be able to see it. It will also appear in your file browser window with Repl.it on the left. Then navigate into that directory by typing in:

cd scheme-sieve-username

… and you should be all set to work.

(seq first last)

This function takes two integers and returns an integer lazy list containing the sequence of values first, first+1, ... , last. This is just a renaming of the function gen-lazy-list from a previous assignment, so this one should be pretty easy.

(inf-seq first)

This function takes an integer and returns an integer lazy list containing the infinite sequence of values first,first+1, ....

(first-n lazy-list n)

This function takes a lazy list and an integer and returns an ordinary Scheme list containing the first n values in the lazy-list. If the lazy list contains fewer than n values, then all the values in the lazy list are returned. You may assume that n is an integer greater than or equal to 1. If the lazy list is empty, return an empty Scheme list.

(nth lazy-list n)

This function takes a lazy list and an integer and returns the n-th value in the lazy-list (counting from 1). If the lazy-list contains fewer than n values, then #f is returned.

(filter-multiples lazy-list n)

This function returns a new lazy list that has n and all integer multiples of n removed from lazy-list. For example, a non-lazy list version of filter-multiples would behave as follows:

(filter-multiples '(2 3 4 5 6) 2) --->  (3 5)
(filter-multiples  '(3 4 5 6 7 8) 3) ---> (4 5 7 8)

Create a function called count-smaller-primes that takes a single integer as a parameter, and counts the number of primes less than that number. For example:

(count-smaller-primes 11) ---> 4

You should be using your lazy list of primes to do this, rather than some other technique that generates prime numbers.

Create a function called twin-primes that generates an infinite lazy list of all twin prime pairs, in order. Twin primes are two prime numbers that are only two apart from each other. For example:

(first-n (twin-primes) 5) ---> ((3 . 5) (5 . 7) (11 . 13) (17 . 19) (29 . 31))