Some comments from Jose

1. Almost no one got 4 points in problem 3. One issue was not considering that 1 can be in the list at all. Another issue was assuming that all the numbers should be prime.
2. For the two induction problems, you need to state clearly what the inductive hypothesis is, what type of induction you are using (basic or strong) and what the inductive step really is. This applies specially in Problem 6. I did not take a point from the people who did not state the I.H correctly, but used the correct assumption later in the proof. This is the last time I'll allow something like this. Please also review strong induction!!!
3. I will mark homeworks that are poorly presented with an asterisk. A poor presentation is just something that is hard to read, because of sloppy handwriting, bad organization of the paper or just hard to read (like if someone is writing with pencil and erases poorly).