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# Haskell Program to Display Prime Numbers Between Two Intervals

In Haskell, we can display Prime Numbers between Two Intervals using user-defined functions and list comprehension. In the first example, we are going to use (isPrime and primesInRange) user-defined functions and in the second example, we are going to use list comprehension.

### Algorithm

**Step 1**− The Data.List library is imported.**Step 2**− The user-defined isPrime function is defined.**Step 3**− Program execution will be started from main function. The main() function has whole control of the program.**Step 4**− The variables named, “lower” and “upper” are being initialized. It will hold the range between which the prime numbers is to be printed.**Step 5**− The resultant prime numbers under the defined range is printed to the console using ‘print’ function after the function is called.

### Example 1

In this example, we are going to see that how we can display prime numbers between two interval using user defined functions.

import Data.List (filter) isPrime :: Integer -> Bool isPrime n | n <= 1 = False | n == 2 = True | n `mod` 2 == 0 = False | otherwise = all (\x -> n `mod` x /= 0) [3,5..(floor (sqrt (fromIntegral n)))] primesInRange :: Integer -> Integer -> [Integer] primesInRange a b = filter isPrime [a..b] main :: IO () main = do let lower = 10 upper = 20 print (primesInRange lower upper)

### Output

[11,13,17,19]

### Example 2

In this example, we are going to see that how we can display prime numbers between two interval using list comprehension.

import Data.List (filter) isPrime :: Integer -> Bool isPrime n | n <= 1 = False | n == 2 = True | n `mod` 2 == 0 = False | otherwise = all (\x -> n `mod` x /= 0) [3,5..(floor (sqrt (fromIntegral n)))] primesInRange :: Integer -> Integer -> [Integer] primesInRange a b = filter isPrime [a..b] main :: IO () main = do let lower = 10 upper = 20 print (primesInRange lower upper)

### Output

[11,13,17,19]

## Conclusion

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In Haskell, to display the prime numbers between two interval we can use user-defined functions and list comprehension.

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