Miller–Rabin primality test: Difference between revisions

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For Number types >= 2**64 you may have to use an external library.

<lang Ada>with Ada.Text_IO;

with Ada.Numerics.Discrete_Random;

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Ada.Text_IO.Put_Line ("What is it? " & Result_Type'Image (Is_Prime (N, K)));

end Miller_Rabin;</lang>

Output:

<pre> 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997.

Enter a Number: 1234567

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=={{header|ALGOL 68}}==

{{works with|ALGOL 68|Standard - with preludes manually inserted }}

{{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}

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FI

OD</lang>

Sample output:

<pre>

937 941 947 953 967 971 977 983 991 997

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=={{header|bc}}==

Requires a <tt>bc</tt> with long names.

(A previous version worked with [[GNU bc]].)

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=={{header|C}}==

'''miller-rabin.h'''

<lang c>#ifndef _MILLER_RABIN_H_

#define _MILLER_RABIN_H

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bool miller_rabin_test(mpz_t n, int j);

#endif</lang>

'''miller-rabin.c'''

For <code>decompose</code> (and header <tt>primedecompose.h</tt>), see [[Prime decomposition#C|Prime decomposition]].

<lang c>#include <stdbool.h>

#include <gmp.h>

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return res;

}</lang>

'''Testing'''

<lang c>#include <stdio.h>

#include <stdlib.h>

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}</lang>

=={{header|C sharp}}==

=={{header|C sharp|C#}}==

<lang csharp>public static class RabinMiller

public static class RabinMiller

{

public static bool IsPrime(int n, int k)

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return true;

}

}</lang>

}

<lang csharp>// Miller-Rabin primality test as an extension method on the BigInteger type.

</lang>

// Miller-Rabin primality test as an extension method on the BigInteger type.

// Based on the Ruby implementation on this page.

public static class BigIntegerExtensions

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return true;

}

}</lang>

}

</lang>

=={{header|Common Lisp}}==

<lang lisp>(defun factor-out (number divisor)

"Return two values R and E such that NUMBER = DIVISOR^E * R,

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=={{header|E}}==

<lang e>def millerRabinPrimalityTest(n :(int > 0), k :int, random) :boolean {

if (n <=> 2 || n <=> 3) { return true }

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return true

}</lang>

<lang e>for i ? (millerRabinPrimalityTest(i, 1, entropy)) in 4..1000 {

print(i, " ")

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=={{header|Erlang}}==

<lang erlang>-module(miller_rabin).

-module(miller_rabin).

-compile([export_all]).

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end,

L),

ok.

ok.</lang>

</lang>

<pre>

42> miller_rabin:first_1000().

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=={{header|Fortran}}==

For the module ''PrimeDecompose'', see [[Prime decomposition#Fortran|Prime decomposition]].

<lang fortran>module Miller_Rabin

use PrimeDecompose

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end module Miller_Rabin</lang>

'''Testing'''

<lang fortran>program TestMiller

use Miller_Rabin

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end program TestMiller</lang>

''Possible improvements'': create bindings to the [[:Category:GMP|GMP library]], change <code>integer(huge)</code> into something like <code>type(huge_integer)</code>, write a lots of interfaces to allow to use big nums naturally (so that the code will be unchanged, except for the changes said above)

=={{header|Go}}==

Go has it in the standard library. [http://golang.org/pkg/big/#ProbablyPrime ProbablyPrime]

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=={{header|Haskell}}==

* Ideas taken from [http://primes.utm.edu/prove/prove2_3.html Primality proving]

* Functions witns and isMillerRabinPrime follow closely the code outlined in [http://www.jsoftware.com/jwiki/Essays/Primality%20Tests#Miller-Rabin J/Essays]

* A useful powerMod function is taken from [http://rosettacode.org/wiki/Multiplicative_order#Haskell]

Another Miller Rabin test can be found in D. Amos's Haskell for Math module [http://www.polyomino.f2s.com/david/haskell/numbertheory.html Primes.hs]

<lang Haskell>import System.Random

import Data.List

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=={{header|Icon}} and {{header|Unicon}}==

The following code works in both languages:

<lang unicon>procedure main()

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return n

end</lang>

Sample run:

<pre>->mrpt

907 911 919 929 937 941 947 953 967 971 977 983 991 997

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=={{header|Java}}==

The Miller-Rabin primality test is part of the standard library (java.math.BigInteger)

<lang java>import java.math.BigInteger;

public class MillerRabinPrimalityTest

public class MillerRabinPrimalityTest {

public static void main(String[] args) {

{

public static void main(String[] args)

{

BigInteger n = new BigInteger(args[0]);

int certainty = Integer.parseInt(args[1]);

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}

}</lang>

Sample output:

<pre>java MillerRabinPrimalityTest 123456791234567891234567 1000000

123456791234567891234567 is probably prime</pre>

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];

,{k}];

Print[test] ]

Print[test] ]</lang>

<lang mathematica>MillerRabin[17388,10]

Example output (not using the PrimeQ builtin):

MillerRabin[17388,10]

->False</lang>

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===Built-in===

<lang parigp>MR(n,k)=ispseudoprime(n,k);</lang>

===Custom===

<lang parigp>sprp(n,b)={

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1

};</lang>

===Deterministic version===

A basic deterministic test can be obtained by an appeal to the ERH (as proposed by Gary Miller) and a result of Eric Bach (improving on Joseph Oesterlé). Calculations of Jan Feitsma can be used to speed calculations below 264 (by a factor of about 250).

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(NIL (_prim? N D S))

T ) ) ) )</lang>

Output:

<pre>: (filter '((I) (prime? I)) (range 937 1000))

-> (937 941 947 953 967 971 977 983 991 997)

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: (prime? 4547337172376300111955330758342147474062293202868155909393)

-> NIL</pre>

=={{header|PureBasic}}==

<lang PureBasic>Enumeration

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=={{header|Python}}==

<lang python>import random

import random

_mrpt_num_trials = 5 # number of bases to test

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return False

return True # no base tested showed n as composite

return True # no base tested showed n as composite</lang>

</lang>

=={{header|REXX}}==

With a K of 1, there seems to be a not uncommon number of failures, but

~~ ~~with a K ≥ 2, the failures are rare,

:with a K ≥ 2, the failures are rare,

~~ ~~with a K ≥ 3, rare as hen's teeth.

:with a K ≥ 3, rare as hen's teeth.

This would be in the same vein as: 3 is prime, 5 is prime, 7 is prime, all odd numbers are prime.

<lang rexx>/*REXX program puts Miller-Rabin primality test through its paces. */

/*REXX program puts Miller-Rabin primality test through its paces. */

arg limit accur . /*get some arguments (if any). */

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!.j=1 /*and keep filling the water jar.*/

end /*j*/ /*this comment not left blank. */

return /*whew! All done with the primes*/

return /*whew! All done with the primes*/</lang>

</lang>

Output when using the input of:

10000 10

They're 1229 primes <= 10000

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p primes = (1..100).find_all {|i| miller_rabin_prime?(i,10)}</lang>

=={{header|Smalltalk}}==

Smalltalk handles big numbers naturally and trasparently (the parent class <tt>Integer</tt> has many subclasses, and <cite>a subclass is picked according to the size</cite> of the integer that must be handled)

<lang smalltalk>Integer extend [

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]

].</lang>

<lang smalltalk>1 to: 1000 do: [ :n |

(n millerRabinTest: 10) ifTrue: [ n printNl ]

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=={{header|Standard ML}}==

<lang sml>open LargeInt;

open LargeInt;

val mr_iterations = Int.toLarge 20;

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then (n,t)

else findPrime t end

in List.tabulate (10, fn e => findPrime 0) end;

in List.tabulate (10, fn e => findPrime 0) end;</lang>

</lang>

Sample run:

<pre>

...

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(349239056313926786302179212509,7),(565349019043144709861293116613,126)]

: (int * int) list

</pre>

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}

}</lang>

produces

<pre>1

2