C Program to Find Prime Number between 1 to 100
Prime Number between 1 to 100 in C
Here, on this page, we will discuss the program to find the prime numbers between 1 to 100 in C.
Generally this program is asked as Write a Program to print Prime Numbers from 1 to 100 in C
Methods Discussed in page
We have discussed the following methods
- Basic checking prime by only checking first n
- Basic checking prime by only checking first n/2 divisors
- Checking prime by only checking first √n divisors
- Checking prime by only checking first √n divisors, but also skipping even iterations.
Method 1
- Set lower bound = 1, upper bound = 100
- Run a loop in the iteration of (i) b/w these bounds.
- For each, i check if its prime or not using function checkPrime(i)
- If i is prime print it else move to next iteration
Method used to check prime
Here we use the usual method to check prime. If given number is prime then we print it else we move ahead to the next number and check if that is prime and keep going till 100
Code
#include <stdio.h>
int checkPrime(int num)
{
// 0, 1 and negative numbers are not prime
if(num < 2){
return 0;
}
else{
// no need to run loop till num-1 as for any number x the numbers in
// the range(num/2 + 1, num) won't be divisible anyways.
// Example 36 wont be divisible by anything b/w 19-35
int x = num/2;
for(int i = 2; i <=x; i++)
{
if(num % i == 0)
{
return 0;
}
}
}
// the number would be prime if we reach here
return 1;
}
int main()
{
int a = 1, b = 100;
for(int i=a; i <= b; i++){
if(checkPrime(i))
printf("%d ",i);
}
return 0;
}
//Time Complexity: O(N^2)
//Space Complexity O(1) Output
2 3 4 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
Method 2
- Run a loop in the iteration of (i) b/w 1 and 100 bounds.
- For each, i check if its prime or not using function checkPrime(i)
- If i is prime print it else move to the next iteration
Method used to check prime
Here we use the usual method to check prime. We however check the divisibility only till num/2.
As the range(num/2 + 1, num) won't be divisible anyways. Example 36 won't be divisible by anything b/w 19-35
As the range(num/2 + 1, num) won't be divisible anyways. Example 36 won't be divisible by anything b/w 19-35
Code
#include<stdio.h>
int checkPrime(int num)
{
// 0, 1 and negative numbers are not prime
if(num < 2){
return 0;
}
else{
// no need to run loop till num-1 as for any number x the numbers in
// the range(num/2 + 1, num) won't be divisible anyways.
// Example 36 wont be divisible by anything b/w 19-35
int x = num/2;
for(int i = 2; i < x; i++)
{
if(num % i == 0)
{
return 0;
}
}
}
// the number would be prime if we reach here
return 1;
}
int main()
{
for(int i=1; i <= 100; i++){
if(checkPrime(i))
printf("%d ",i);
}
return 0;
}
//Time Complexity: O(N^2)
//Space Complexity O(1) Output
2 3 4 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
Method 3
The outer logic remains the same. Only the method to check prime changes to make code more optimized. Has better time complexity of O(√N)
- Run a loop in the iteration of (i) b/w 1 and 100 bounds.
- For each, i check if its prime or not using function checkPrime(i)
- If i is prime print it else move to next iteration
Method used to check prime
A number n is not a prime if it can be factored into two factors a & b:
n = a * b
Now a and b can't be both greater than the square root of n, since then the product a * b would be greater than sqrt(n) * sqrt(n) = n.
So in any factorization of n, at least one of the factors must be smaller than the square root of n, and if we can't find any factors less than or equal to the square root, n must be a prime.
So we only need to run loop till sqrt(n) and not n or n/2
n = a * b
Now a and b can't be both greater than the square root of n, since then the product a * b would be greater than sqrt(n) * sqrt(n) = n.
So in any factorization of n, at least one of the factors must be smaller than the square root of n, and if we can't find any factors less than or equal to the square root, n must be a prime.
So we only need to run loop till sqrt(n) and not n or n/2
Code
#include<stdio.h>
#include<math.h>
int checkPrime(int num)
{
// 0, 1 and negative numbers are not prime
if(num < 2){
return 0;
}
else{
// A number n is not a prime, if it can be factored into two factors a & b:
// n = a * b
/*Now a and b can't be both greater than the square root of n, since
then the product a * b would be greater than sqrt(n) * sqrt(n) = n.
So in any factorization of n, at least one of the factors must be
smaller than the square root of n, and if we can't find any factors
less than or equal to the square root, n must be a prime.
*/
for(int i = 2; i < sqrt(num); i++)
{
if(num % i == 0)
{
return 0;
}
}
}
// the number would be prime if we reach here
return 1;
}
int main()
{
for(int i=1; i <= 100; i++){
if(checkPrime(i))
printf("%d ",i);
}
return 0;
}
//Time Complexity: O(N√N)
//Space Complexity O(1)
// This method is obviously faster as has better time complexity Output
2 3 4 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
Method 4
The outer logic remains the same. Only the method to check prime changes to make code more optimized. Has same time complexity of O(√N).
But makes around half lesser checks
- Run a loop in the iteration of (i) b/w 1 to 100 bounds.
- For each, i check if its prime or not using function checkPrime(i)
- If i is prime print it else move to next iteration
Method used to check prime
This method uses the assumption that –
We can simply check all divisors between [2, √num]
2 is the only even prime number
We can skip all even iterations in the loop
We can simply check all divisors between [2, √num]
2 is the only even prime number
We can skip all even iterations in the loop
Code
#include<stdio.h>
#include<math.h>
int checkPrime(int n)
{
// 0 and 1 are not prime numbers
// negative numbers are not prime
if (n <= 1)
return 0;
// special case as 2 is the only even number that is prime
else if (n == 2)
return 1;
// Check if n is a multiple of 2 thus all these won't be prime
else if (n % 2 == 0)
return 0;
// If not, then just check the odds
for (int i = 3; i <= sqrt(n); i += 2)
{
if (n % i == 0)
return 0;
}
return 1;
}
int main()
{
for(int i=1; i <= 100; i++){
if(checkPrime(i))
printf("%d ",i);
}
return 0;
}
//Time Complexity: O(N√N)
//Space Complexity O(1)
// This method is obviously faster as makes around half lesser comparision due skipping even iterations in the loop Output
2 3 4 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
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All the codes for this problem doesnt work because 4 is also getting printed. Writing an if block for 4 might help or we initialising count variable to 0 and writing is another way but its time complexity is not better as previous one.
easy one
#include
int main()
{
int i,j,cnt=0,c;
for(i=2;i<=100;i++)
{
for(j=1;j<=i;j++)
{
if(i%j==0)
c=cnt++;
}
if(c<2)
printf("%d\n",i);
cnt=0;
}
}
if(c<3)*
every number has 1 and itself as factors. or in the second for loop you can take it as for(j=2;j<=1;j++); omitting 1 then if(c<2) works.