This document discusses prime numbers and the Sieve of Eratosthenes algorithm for finding prime numbers. It defines a prime number as a whole number greater than 1 that is only divisible by 1 and itself. It then presents an approach to determine if a number is prime or composite by checking if it has any smaller factors. Finally, it provides pseudocode and a C++ implementation of the Sieve of Eratosthenes algorithm, which involves iteratively marking as composite the multiples of each prime, producing the primes sequentially.

2. Prime Number
Md. Al-Mamun Riyadh

3. Prime Number
•An Integer number greater than 1 having factor one (1) and itself.
•A Prime number has exactly two factors 1 and N.
•No factor between 2 to N-1.
•No smaller factor/divisor for a Prime number N but one (1).

4. A Different Approach
• Let a number be N.
• How can we state that whether it is Prime or not?
• If a number N has a smaller factor/divisor than it is not a Prime
number (Composite Number).
• If a number N has a smaller factor/divisor then, of course, the
number N is a multiples of that smaller number.
• Multiples of a number is not a Prime number.

5. Algorithm
•Initially all the number are not multiples of other numbers.
•Let all the integer number are prime numbers.
•we are starting from two (2) as zero and one are not a prime number
by definition.
•Two (2) is a prime number.
•Multiples of Two (2) are not prime.
•Three (3) is also a prime number.
•Again multiples of Three (3) are not a prime number.

6. Simulation
Source: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
2 3 5 7
11 13 17 19
23 29
31 37
41 43 47
53 59
61 67
71 73 79
83 89
97

7. C++ Code
#include<stdio.h>
int p = 999;
bool prime[1000];
int main(){
int i,c=0;
generatePrime();
for(i=2;i<=100;i++){
if(prime[i]){
printf("%d ",i);
c++;
}
}
printf("nPrime: %d",c);
return 0;
}
void generatePrime(){
int i,j;
prime[0]=prime[1]=false;
for(i=2;i<=p;i++)
prime[i]=true;
for(i=2;i*i<=p;i++){
if(prime[i]){
for(j=i*i;j<=p;j+=i)
prime[j]=false;
}
}
}

8. Sieve of Eratosthenes
Source: https://en.wikipedia.org/wiki/Sieve_theory

9. Thank you
Q/A