# C Program - Find all Prime Numbers less than the given Number

A Prime number is a natural number greater than 1 and divisible by 1 and itself only, for example: 2, 3, 5, 7, etc.

Objective: Write a C code to find all prime numbers less than a given number.

### Method 1: Using method to find prime number

In the example below, a method called primenumber() is created which takes a number as argument and checks it for prime number by dividing it with all natural numbers starting from 2 to N/2.

```#include <stdio.h>

int n = 0;
for(int i = 2; i < (MyNum/2+1); i++) {
if(MyNum % i == 0) {
n++;
break;
}
}
if (n == 0) {
printf("%i ", MyNum);
}
}

int main() {
int x = 50;
printf("Prime numbers less than %i are:\n", x);
for(int i = 2; i < x + 1; i++) {
}
return 0;
}
```

The above code will give the following output:

```Prime numbers less than 50 are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
```

### Method 2: Optimized Code

• Instead of checking the divisibility of given number from 2 to N/2, it is checked till square root of N. For a factor larger than square root of N, there must the a smaller factor which is already checked in the range of 2 to square root of N.
• Except from 2 and 3, every prime number can be represented into 6k ± 1.
```#include <stdio.h>

int n = 0;
if (MyNum == 2 || MyNum == 3) {
printf("%i ", MyNum);
}
else if (MyNum % 6 == 1 || MyNum % 6 == 5) {
for(int i = 2; i*i <= MyNum; i++) {
if(MyNum % i == 0){
n++;
break;
}
}
if (n == 0) {
printf("%i ", MyNum);
}
}
}

int main() {
int x = 100;
printf("Prime numbers less than %i are:\n", x);
for(int i = 2; i < x + 1; i++) {
}
return 0;
}
```

The above code will give the following output:

```Prime numbers less than 100 are:
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
```

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