# C# Program - Find all Prime Numbers in a given Interval

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 in a given internal.

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

In the example below, a function 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.

```using System;

class MyProgram {
static void primenumber(int MyNum) {
int n = 0;
for(int i = 2; i < (MyNum/2+1); i++) {
if(MyNum % i == 0){
n++;
break;
}
}
if (n == 0) {
Console.Write(MyNum + " ");
}
}

static void Main(string[] args) {
int x = 10;
int y = 50;
Console.WriteLine("Prime numbers between {0} and {1} are: ",x ,y);
for(int i = x; i < y + 1; i++) {
}
}
}
```

The above code will give the following output:

```Prime numbers between 10 and 50 are:
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.
```using System;

class MyProgram {
static void primenumber(int MyNum) {
int n = 0;
if (MyNum == 2 || MyNum == 3){
Console.Write(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){
Console.Write(MyNum + " ");
}
}
}

static void Main(string[] args) {
int x = 100;
int y = 200;
Console.WriteLine("Prime numbers between {0} and {1} are: ",x ,y);
for(int i = x; i < y + 1; i++) {
}
}
}
```

The above code will give the following output:

```Prime numbers between 100 and 200 are:
101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
```

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