#### CSCI 3104 - Algorithms - Fall 2010

### Problem Set #3

#### Due: 12pm, Feb 2nd, 2011

1. Text problem 1.16.
2. Text problem 1.20. Do not use a computer; show your work.

3. What is the smallest integer that is simultaneously a 2-pseudoprime, a
3-pseudoprime and a 2011-pseudoprime? Use a computer to search;
include your source code.

4. Write a python function `getrand100()` to generate random 100-digit
positive numbers. Write
a second function `nextprime(i)` to
find the next prime ≥ `i`. What is `nextprime(2011**50)`?
Include the answer along with your source code.

5. Using your code from above, write a python program that computes the
average distance from a selected integer to the nextprime after it.
Use 1 thousand samples to obtain your average. In other words, let
`s=getrand100()` and then compute the average value of
`nextprime(s)-s` using 1000 samples. Include source code
with your answer.