Math 310: Problem set 6

Instructions: This problem set is due Friday, February 17, 2006.
  1. (2 points) Let m be the integer I emailed to you. Thus each of you has your own particular m. For each integer n from 34000+10m to 34000+10m+10, determine whether or not n is prime. List the ones that are prime. (If you have a calculator that can do this, fine. If not, you can use the web form on our class web site. Combine results in class as a test of the Prime Number Theorem, which gives an estimate on how many primes there are in a range of integers.)
  2. (8 points) Let n be a positive integer. Let r be the remainder when n is divided by 4. We will say n has class r. (Thus, for example, 10 has class 2, 83 has class 3, and every n has class either 0, 1, 2 or 3.)