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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | -- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Efficient, purely functional generation of prime numbers
--
-- This Haskell library provides an efficient lazy wheel sieve for prime
-- generation inspired by <i>Lazy wheel sieves and spirals of</i>
-- <i>primes</i> by Colin Runciman and <i>The Genuine Sieve of
-- Eratosthenes</i> by Melissa O'Neil.
@package primes
@version 0.2.1.0
-- | This Haskell library provides an efficient lazy wheel sieve for prime
-- generation inspired by <i>Lazy wheel sieves and spirals of</i>
-- <i>primes</i> by Colin Runciman
-- (<a>http://www.cs.york.ac.uk/ftpdir/pub/colin/jfp97lw.ps.gz</a>) and
-- <i>The Genuine Sieve of Eratosthenes</i> by Melissa O'Neil
-- (<a>http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf</a>).
module Data.Numbers.Primes
-- | This global constant is an infinite list of prime numbers. It is
-- generated by a lazy wheel sieve and shared across the whole program
-- run. If you are concerned about the memory requirements of sharing
-- many primes you can call the function <tt>wheelSieve</tt> directly.
primes :: Integral int => [int]
-- | This function returns an infinite list of prime numbers by sieving
-- with a wheel that cancels the multiples of the first <tt>n</tt> primes
-- where <tt>n</tt> is the argument given to <tt>wheelSieve</tt>. Don't
-- use too large wheels. The number <tt>6</tt> is a good value to pass to
-- this function. Larger wheels improve the run time at the cost of
-- higher memory requirements.
wheelSieve :: Integral int => Int -> [int]
-- | Checks whether a given number is prime.
--
-- This function uses trial division to check for divisibility with all
-- primes below the square root of the given number. It is impractical
-- for numbers with a very large smallest prime factor.
isPrime :: Integral int => int -> Bool
-- | Yields the sorted list of prime factors of the given positive number.
--
-- This function uses trial division and is impractical for numbers with
-- very large prime factors.
primeFactors :: Integral int => int -> [int]
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