# Sum of Prime Numbers in Java

In this section, we will create Java programs to find the sum of all the prime numbers in a given range. Before moving ahead in this section, let's see the important facts about prime numbers.

• A prime number is a number that is greater than 1 and can be divided by 1 and itself without leaving a remainder.
• The numbers 0 and 1 are not prime numbers.
• The only even prime number is 2. All other even numbers are divisible by 2.

## Steps to Find the Sum of Prime Numbers

• Read or initialize the lower and upper limit.
• Iterate a loop (for or while) to find the prime numbers between the given range.
• If the number is prime, add that number to the variable sum and print the result.

Let's implement the above steps in a Java program.

## Java Program to Find the Sum of Prime Numbers

There are the following ways to find the sum of prime numbers:

Let's create the Java program for each.

### Using for Loop

Output:

```The Sum of Prime Numbers from 1 to 200 is: 4227
```

### Using while Loop

In the following program, we have used a while loop instead of for loop. The logic is the same as above.

Output:

```The Sum of Prime Numbers from 1 to 100 is: 1060
```

## Using Function

Output:

```The sum of all the prime number between the given range is: 328
```

### Using Dynamic Programming

The logic for the sum of prime numbers using dynamic programming is a bit tricky and difficult to implement. In this approach, we will use arrays. Let's see the steps.

1. Declare two arrays number[] and array[].
2. Initialize array[] to 0.
3. Iterate over the for loop till sqrt(uprlimit). If the array element is 0, consider it as prime and its multiple as non-prime. While marking the non-prime numbers, set the respective location to 1.
4. Update the number[] array that holds the sum of prime numbers. Each position of number[i] represents the sum of all prime numbers within a specified range i.e. [1, i].

Let's implement the above steps in a Java program.

Output:

```The sum of all the prime number between the given range is: 75067
```

### Feedback   