prime

Not on Stackage, so not searched. prime number tools

Wrapper for prime elements of a. It is supposed to be constructed by nextPrime / precPrime. and eliminated by unPrime. One can leverage Enum instance to generate lists of primes. Here are some examples.

• Generate primes from the given interval:

>>> :set -XFlexibleContexts

>>> [nextPrime 101 .. precPrime 130]
[Prime 101,Prime 103,Prime 107,Prime 109,Prime 113,Prime 127]

• Generate an infinite list of primes:

[nextPrime 101 ..]
[Prime 101,Prime 103,Prime 107,Prime 109,Prime 113,Prime 127...

• Generate primes from the given interval of form p = 6k+5:

>>> [nextPrime 101, nextPrime 107 .. precPrime 150]
[Prime 101,Prime 107,Prime 113,Prime 131,Prime 137,Prime 149]

• Get next prime:

>>> succ (nextPrime 101)
Prime 103

• Get previous prime:

>>> pred (nextPrime 101)
Prime 97

• Count primes less than a given number (cf. approxPrimeCount):

>>> fromEnum (precPrime 100)
25

• Get 25-th prime number (cf. nthPrimeApprox):

>>> toEnum 25 :: Prime Int
Prime 97

Identifier ends in Integer many primes.

Deprecated: This module is a perpetual draft and will therefore be removed from xmonad-contrib in the near future.

A Prime is a function that transforms an XConfig. It's not a monad, but we turn on RebindableSyntax so we can abuse the pretty do notation.

Module for finding the greatest prime number that is less than or equal to a given number

Like primElemRepSizeB but assumes pointers/words are 8 words wide. This can be useful to compute the size of a rep as if we were compiling for a 64bit platform.

The prime prefix; primePrefix mempty == mempty for monoids.

The prime suffix; primeSuffix mempty == mempty for monoids.

Efficient, purely functional generation of prime numbers This Haskell library provides an efficient lazy wheel sieve for prime generation inspired by Lazy wheel sieves and spirals of primes by Colin Runciman and The Genuine Sieve of Eratosthenes by Melissa O'Neil.

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.

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 wheelSieve directly.

Ascending list of primes.

>>> take 10 primes
[Prime 2,Prime 3,Prime 5,Prime 7,Prime 11,Prime 13,Prime 17,Prime 19,Prime 23,Prime 29]

primes is a polymorphic list, so the results of computations are not retained in memory. Make it monomorphic to take advantages of memoization. Compare

>>> primes !! 1000000 :: Prime Int -- (5.32 secs, 6,945,267,496 bytes)
Prime 15485867

>>> primes !! 1000000 :: Prime Int -- (5.19 secs, 6,945,267,496 bytes)
Prime 15485867

against

>>> let primes' = primes :: [Prime Int]

>>> primes' !! 1000000 :: Prime Int -- (5.29 secs, 6,945,269,856 bytes)
Prime 15485867

>>> primes' !! 1000000 :: Prime Int -- (0.02 secs, 336,232 bytes)
Prime 15485867

primeCount n == π(n) is the number of (positive) primes not exceeding n. For efficiency, the calculations are done on 64-bit signed integers, therefore n must not exceed primeCountMaxArg. Requires O(n^0.5) space, the time complexity is roughly O(n^0.7). For small bounds, primeCount n simply counts the primes not exceeding n, for bounds from 30000 on, Meissel's algorithm is used in the improved form due to D.H. Lehmer, cf. http://en.wikipedia.org/wiki/Prime_counting_function#Algorithms_for_evaluating_.CF.80.28x.29.

Maximal allowed argument of primeCount. Currently 8e18.

An infinite list of Eisenstein primes. Uses primes in Z to exhaustively generate all Eisenstein primes in order of ascending norm.

• Every prime is in the first sextant, so the list contains no associates.
• Eisenstein primes from the whole complex plane can be generated by applying associates to each prime in this list.

>>> take 10 primes
[Prime 2+ω,Prime 2,Prime 3+2*ω,Prime 3+ω,Prime 4+3*ω,Prime 4+ω,Prime 5+3*ω,Prime 5+2*ω,Prime 5,Prime 6+5*ω]

An infinite list of the Gaussian primes. Uses primes in Z to exhaustively generate all Gaussian primes (up to associates), in order of ascending magnitude.

>>> take 10 primes
[Prime 1+ι,Prime 2+ι,Prime 1+2*ι,Prime 3,Prime 3+2*ι,Prime 2+3*ι,Prime 4+ι,Prime 1+4*ι,Prime 5+2*ι,Prime 2+5*ι]

Get the name of the equality type.