Objectives Experiment #1 Introduction to Algorithms

Prime Numbers:
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors
other than 1 and itself. One of the most common problems is finding the Prime numbers in a
certain range, this can be done using:
1. Brute Force algorithm:
By testing all numbers one by one.
2. Sieve of Eratosthenes
Algorithm:
To find all the prime numbers less than or equal to a given integer n by Sieve method:
Requirements
1. Create a list of consecutive integers from 2 to n: (2, 3, 4, ..., n).
2. Initially, let p equal 2, the first prime number.
3. Starting from p, count up in increments of p and mark each of these numbers greater
than p itself in the list. These numbers will be 2p, 3p, 4p, etc.; note that some of them
may have already been marked.
4. Find the first number greater than p in the list that is not marked.If there was no such
number, stop. Otherwise, let p now equal this number (which is the next prime), and
repeat from step 3.
When the algorithm terminates, all the numbers in the list that are not marked are
prime.
1- Implement the two algorithms described above.
2- Run both algorithms on the following data
a. 100
b. 1000
c. 10000
d. 100000
e. 200000
3- For the previous data fill the following table.
input Brute Force Sieve
Time in MS Time in MS
100
1000
10000
100000
200000
Winter 2012 Experiment #1 3/5