HASKELL TEST FOR PRIME NUMBER

REVISED: Thursday, February 8, 2024

1. INTRODUCTION

The search is on for larger and larger prime numbers. This tutorial will show a method for testing large positive integers to see if they are prime numbers.

The largest explicitly known prime keeps growing. For example,  (2^32582657 - 1),  (2^43112609 - 1) and (2^74207281 - 1)  were recently discovered very large prime numbers. Methods for quickly testing to see if very large positive integers are prime numbers are important tools used in the search for larger prime numbers.

2. HASKELL PROGRAM

The Haskell program we will use in this tutorial to test a positive integer for prime is as follows:

-- C:\Users\Tinnel\Haskell2024\test.hs

import Data.List
import System.IO

main :: IO ()  -- Has type I/O action.
main = do {  putStrLn ""  -- putStrLn Has type I/O action.
           ; putStrLn "=========================================================="
           ; putStrLn ""
           ; putStrLn "Type a positive integer you want to test for prime then press Enter."
           ; s <- getLine -- getLine is a function, getLine :: IO String
           ; let n = (read s)::Integer
           ; putStrLn ""
           ; putStrLn "=========================================================="
           ; putStrLn ""
           ; let test = if (p n == 0 || m n == 0) && n /= 1
                        then "True"
                        else if (n == 2 || n == 3)
                             then "True"
                             else if (n == 0 || n == 1)
                                  then "False"
                                  else "False"
           ; putStrLn "QUESTION: True or False, is the number you entered a prime number?"
           ; putStrLn ""
           ; putStrLn ("ANSWER: " ++ test ++ ".")
           ; putStrLn ""
           ; putStrLn "=========================================================="
           ; putStrLn ""
          }

-- Adds 1 and divides by 6; a remainder means False.
p :: Integral a => a -> a
p n = (n + 1) `mod` 6

-- Subtracts 1 and divides by 6; a remainder means False.
m :: Integral a => a -> a
m n = (n - 1) `mod` 6

3. GHCi RUN

Prelude> :l test
[1 of 1] Compiling Main             ( test.hs, interpreted )
Ok, modules loaded: Main.

*Main> main

=========================================================================

Type a positive integer you want to test for prime then press Enter.
29996224275833

=========================================================================

QUESTION: True or False, is the number you entered a prime number?

ANSWER: True.

=========================================================================

*Main>

4. CONCLUSION

The above Haskell program is a quick way to determine if very large positive integers are prime numbers.

5. REFERENCES

Bird, R. (2015). Thinking Functionally with Haskell. Cambridge, England: Cambridge University Press.

Davie, A. (1992). Introduction to Functional Programming Systems Using Haskell. Cambridge, England: Cambridge University Press.

Goerzen, J. & O'Sullivan, B. &  Stewart, D. (2008). Real World Haskell. Sebastopol, CA: O'Reilly Media, Inc.

Hutton, G. (2007). Programming in Haskell. New York: Cambridge University Press.

Lipovača, M. (2011). Learn You a Haskell for Great Good!: A Beginner's Guide. San Francisco, CA: No Starch Press, Inc.

Thompson, S. (2011). The Craft of Functional Programming. Edinburgh Gate, Harlow, England: Pearson Education Limited.