Coprimes

From Rosetta Code
Coprimes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

p   and   q   are   coprimes   if they have no common factors other than   1.

Given the input pairs:   [21,15],[17,23],[36,12],[18,29],[60,15] display whether they are coprimes.

11l

Translation of: Python
F coprime(a, b)
   R gcd(a, b) == 1

print([(21, 15),
       (17, 23),
       (36, 12),
       (18, 29),
       (60, 15)].filter((x, y) -> coprime(x, y)))
Output:
[(17, 23), (18, 29)]

8080 Assembly 

puts:	equ	9
	org	100h
	lxi	h,pairs
load:	mov	b,m	; Load the current pair into (B,C)
	inx	h
	mov	c,m
	inx	h
	xra	a	; Load C into A and set flags
	ora	c
	rz 		; If zero, we've reached the end
	push	b	; Keep the current pair
	call	gcd	; Calculate GCD
	pop	b	; Restore the pair
	dcr	a	; If GCD = 1, then GCD-1 = 0
	jnz	load	; If not, then try the next pair
	push	h	; Keep the pair and the pointer
	push	b	
	mov	a,b	; Print the first item
	call	pnum
	pop	b
	mov	a,c	; Then the second item
	call	pnum
	lxi	d,nl	; Then print a newline
	mvi	c,puts
	call	5
	pop	h	; Restore the pointer
	jmp 	load
	;;;	Let A = GCD(A,B) using the subtraction algorithm
	;;;	(The 8080 does not have division in hardware)
gcd:	cmp	b	; Compare A and B
	rz		; If A == B, stop
	jc	gcdsw	; If A < B, then swap them
gcdsub:	sub	b	; Otherwise, A = A - B
	jmp	gcd
gcdsw:	mov	c,a	; Swap A and B
	mov	a,b
	mov	b,c
	jmp	gcdsub
	;;;	Print the decimal value of A
pnum:	lxi	d,nbuf	; End of output buffer
	mvi	c,10	; Divisor
pdgt:	mvi	b,-1	; Quotient	
pdgdiv:	inr	b	; Division by trial subtraction
	sub	c
	jnc	pdgdiv
	adi	'0'+10	; ASCII digit
	dcx	d	; Store in buffer
	stax 	d
	xra 	a	; Continue with quotient
	ora	b
	jnz	pdgt	; If not zero
	dcr	c	; CP/M syscall to print a string is 9
	jmp	5
	;;;	Pairs to test
pairs:	db	21,15	; 2 bytes per pair
	db	17,23
	db	36,12
	db	18,29
	db	60,15
	db	0,0	; end marker 
	db	'***'	; Number output buffer
nbuf:	db	' $'
nl:	db	13,10,'$'
Output:
17 23
18 29

8086 Assembly 

puts:	equ	9		; MS-DOS syscall to print a string
	cpu	8086
	org	100h
section	.text
	mov	si,pairs
load:	lodsw			; Load pair into AH,AL
	test	ax,ax		; Stop on reaching 0
	jz	.done
	mov	cx,ax		; Keep a copy out of harm's way
	call	gcd		; Calculate GCD
	dec	al		; If GCD=1 then GCD-1=0
	jnz	load		; If that is not the case, try next pair
	mov	al,cl		; Otherwise, print the fist item
	call	pnum
	mov	al,ch		; Then the second item
	call 	pnum
	mov	dx,nl		; Then a newline
	call	pstr
	jmp	load		; Then try the next pair
.done:	ret
	;;;	AL = gcd(AH,AL)
gcd:	cmp	al,ah 		; Compare AL and AH
	je	.done		; If AL == AH, stop
	jg	.sub		; If AL > AH, AL -= AH
	xchg	al,ah		; Otherwise, swap them first 
.sub:	sub	al,ah
	jmp	gcd
.done:	ret
	;;;	Print the decimal value of AL
pnum:	mov	bx,nbuf		; Pointer to output buffer
.dgt:	aam			; AH = AL/10, AL = AL mod 10
	add	al,'0'		; Add ASCII 0 to digit
	dec	bx		; Store digit in buffer
	mov	[bx],al
	mov	al,ah		; Continue with rest of number
	test	al,al		; If not zero
	jnz	.dgt
	mov	dx,bx
pstr:	mov	ah,puts		; Print the buffer using MS-DOS
	int	21h
	ret
section	.data
	db	'***'		; Number output buffer
nbuf:	db	' $'
nl:	db	13,10,'$'	; Newline
pairs:	db	21,15
	db	17,23
	db	36,12
	db	18,29
	db	60,15
	dw	0
Output:
17 23
18 29

Action! 

INT FUNC Gcd(INT a,b)
  INT tmp

  IF a<b THEN
    tmp=a a=b b=tmp
  FI

  WHILE b#0
  DO
    tmp=a MOD b
    a=b b=tmp
  OD
RETURN (a)

PROC Test(INT a,b)
  CHAR ARRAY s0="not ",s1="",s

  IF Gcd(a,b)=1 THEN
    s=s1
  ELSE
    s=s0
  FI
  PrintF("%I and %I are %Scoprimes%E",a,b,s)
RETURN

PROC Main()
  Test(21,15)
  Test(17,23)
  Test(36,12)
  Test(18,29)
  Test(60,15)
RETURN
Output:

Screenshot from Atari 8-bit computer 

21 and 15 are not coprimes
17 and 23 are coprimes
36 and 12 are not coprimes
18 and 29 are coprimes
60 and 15 are not coprimes

ALGOL 68 

BEGIN # test the coprime-ness of some number pairs #
    # iterative Greatest Common Divisor routine, returns the gcd of m and n #
    PROC gcd = ( INT m, n )INT:
         BEGIN
            INT a := ABS m, b := ABS n;
            WHILE b /= 0 DO
                INT new a = b;
                b        := a MOD b;
                a        := new a
            OD;
            a
         END # gcd # ;
    # pairs numbers to test #
    [,]INT pq = ( ( 21, 15 ), ( 17, 23 ), ( 36, 12 ), ( 18, 29 ), ( 60, 15 ) );
    INT p pos = 2 LWB pq;
    INT q pos = 2 UPB pq;
    # test the pairs #
    FOR i FROM LWB pq TO UPB pq DO
        IF gcd( pq[ i, p pos ], pq[ i, q pos ] ) = 1 THEN
            # have a coprime pair #
            print( ( whole( pq[ i, p pos ], 0 ), " ", whole( pq[ i, q pos ], 0 ), newline ) )
        FI
    OD
END
Output:
17 23
18 29

ALGOL W

Translation of: MAD
BEGIN % check whether sme numbers are coPrime (their gcd is 1) or not %
    LOGICAL PROCEDURE COPRM ( INTEGER VALUE X, Y ) ; GCD( X, Y ) = 1;
    INTEGER PROCEDURE GCD ( INTEGER VALUE A, B ) ;
    BEGIN
        INTEGER AA, BB;
        AA := A;
        BB := B;
        WHILE AA NOT = BB DO BEGIN
            IF AA > BB THEN AA := AA - BB;
            IF AA < BB THEN BB := BB - AA
        END WHILE_AA_NE_BB  ;
        AA
    END GCD ;
    INTEGER ARRAY P, Q ( 0 :: 4 );
    INTEGER POS;
    POS := 0; FOR I := 21, 17, 36, 18, 60 DO BEGIN P( POS ) := I; POS := POS + 1 END;
    POS := 0; FOR I := 15, 23, 12, 29, 15 DO BEGIN Q( POS ) := I; POS := POS + 1 END;
    WRITE( "COPRIMES" );
    FOR I := 0 UNTIL 4 DO BEGIN
        INTEGER PP, QQ;
        PP := P( I );
        QQ := Q( I );
        IF COPRM( PP, QQ ) THEN WRITE( I_W := 4, S_W := 0, PP, QQ )
    END FOR_I
END.
Output:
COPRIMES
  17  23
  18  29

APL

Works with: Dyalog APL
(⊢(/⍨)1=∨/¨) (21 15)(17 23)(36 12)(18 29)(60 15)
Output:
┌─────┬─────┐
│17 23│18 29│
└─────┴─────┘

AppleScript 

on hcf(a, b)
    repeat until (b = 0)
        set x to a
        set a to b
        set b to x mod b
    end repeat
    
    if (a < 0) then return -a
    return a
end hcf

local input, coprimes, thisPair, p, q
set input to {{21, 15}, {17, 23}, {36, 12}, {18, 29}, {60, 15}}
set coprimes to {}
repeat with thisPair in input
    set {p, q} to thisPair
    if (hcf(p, q) is 1) then set end of coprimes to thisPair's contents
end repeat
return coprimes
Output:
{{17, 23}, {18, 29}}


or, composing a definition and test from more general functions: 

------------------------- COPRIME ------------------------

-- coprime :: Int -> Int -> Bool
on coprime(a, b)
    1 = gcd(a, b)
end coprime


--------------------------- TEST -------------------------
on run
    
    script test
        on |λ|(xy)
            set {x, y} to xy
            
            coprime(x, y)
        end |λ|
    end script
    
    filter(test, ¬
        {[21, 15], [17, 23], [36, 12], [18, 29], [60, 15]})
end run


------------------------- GENERIC ------------------------

-- abs :: Num -> Num
on abs(x)
    -- Absolute value.
    if 0 > x then
        -x
    else
        x
    end if
end abs


-- filter :: (a -> Bool) -> [a] -> [a]
on filter(p, xs)
    tell mReturn(p)
        set lst to {}
        set lng to length of xs
        repeat with i from 1 to lng
            set v to item i of xs
            if |λ|(v, i, xs) then set end of lst to v
        end repeat
        lst
    end tell
end filter


-- gcd :: Int -> Int -> Int
on gcd(a, b)
    set x to abs(a)
    set y to abs(b)
    repeat until y = 0
        if x > y then
            set x to x - y
        else
            set y to y - x
        end if
    end repeat
    return x
end gcd


-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
    -- 2nd class handler function lifted into 1st class script wrapper. 
    if script is class of f then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn
Output:
{{17, 23}, {18, 29}}

Arturo 

coprimes?: function [a b] -> 1 = gcd @[a b]

loop [[21 15] [17 23] [36 12] [18 29] [60 15]] 'pair [
    print [pair\0 "and" pair\1 "ara" (coprimes? pair\0 pair\1)? -> "coprimes." -> "not coprimes."]
]
Output:
21 and 15 ara not coprimes. 
17 and 23 ara coprimes. 
36 and 12 ara not coprimes. 
18 and 29 ara coprimes. 
60 and 15 ara not coprimes.

AWK 

# syntax: GAWK -f COPRIMES.AWK
BEGIN {
    n = split("21,15;17,23;36,12;18,29;60,15",arr1,";")
    for (i=1; i<=n; i++) {
      split(arr1[i],arr2,",")
      a = arr2[1]
      b = arr2[2]
      if (gcd(a,b) == 1) {
        printf("%d %d\n",a,b)
      }
    }
    exit(0)
}
function gcd(p,q) {
    return(q?gcd(q,(p%q)):p)
}
Output:
17 23
18 29

BASIC 

10 DEFINT A-Z
20 READ N
30 FOR I=1 TO N
40 READ P,Q
50 A=P
60 B=Q
70 IF B THEN C=A: A=B: B=C MOD B: GOTO 70
80 IF A=1 THEN PRINT P;Q
90 NEXT I
100 DATA 5
110 DATA 21,15
120 DATA 17,23
130 DATA 36,12
140 DATA 18,29
150 DATA 60,15
Output:
 17  23
 18  29

BCPL 

get "libhdr"

let gcd(a,b) = b=0 -> a, gcd(b, a rem b)
let coprime(a,b) = gcd(a,b) = 1

let start() be
$(  let ps = table 21, 17, 36, 18, 60
    let qs = table 15, 23, 12, 29, 15
    let n = 5
    
    for i=0 to n-1
        if coprime(ps!i, qs!i) do writef("%N %N*N", ps!i, qs!i)
$)
Output:
17 23
18 29

BQN 

GCD ← {𝕨(|𝕊⍟(>⟜0)⊣)𝕩}
SelectCoprimes ← (1=GCD´¨)⊸/

SelectCoprimes ⟨21‿15,17‿23,36‿12,18‿29,60‿15⟩
Output:
⟨ ⟨ 17 23 ⟩ ⟨ 18 29 ⟩ ⟩

C 

#include <stdio.h>

int gcd(int a, int b) {
    int c;
    while (b) {
        c = a;
        a = b;
        b = c % b;
    }
    return a;
}

struct pair {
    int x, y;
};

void printPair(struct pair const *p) {
    printf("{%d, %d}\n", p->x, p->y);
}

int main() {
    struct pair pairs[] = {
        {21,15}, {17,23}, {36,12}, {18,29}, {60,15}
    };
    
    int i;
    for (i=0; i<5; i++) {
        if (gcd(pairs[i].x, pairs[i].y) == 1)
            printPair(&pairs[i]);
    }
    return 0;
}
Output:
{17, 23}
{18, 29}

C++ 

#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>

int gcd(int a, int b) {
    int c;
    while (b) {
        c = a;
        a = b;
        b = c % b;
    }
    return a;
}

int main() {
    using intpair = std::pair<int,int>;
    std::vector<intpair> pairs = {
        {21,15}, {17,23}, {36,12}, {18,29}, {60,15}
    };
    
    pairs.erase(
        std::remove_if(
            pairs.begin(),
            pairs.end(),
            [](const intpair& x) {
                return gcd(x.first, x.second) != 1;
            }
        ),
        pairs.end()
    );
    
    for (auto& x : pairs) {
        std::cout << "{" << x.first 
                  << ", " << x.second 
                  << "}" << std::endl;
    }
    
    return 0;
}
Output:
{17, 23}
{18, 29}

Cowgol 

include "cowgol.coh";

sub gcd(a: uint8, b: uint8): (r: uint8) is
    while b != 0 loop
        r := a;
        a := b;
        b := r % b;
    end loop;
    r := a;
end sub;

record Pair is
    x: uint8;
    y: uint8;
end record;

sub printPair(p: [Pair]) is
    print_i8(p.x);
    print_char(' ');
    print_i8(p.y);
    print_nl();
end sub;

var pairs: Pair[] := {
    {21,15}, {17,23}, {36,12}, {18,29}, {60,15}
};

var i: @indexof pairs := 0;
while i < @sizeof pairs loop
    if gcd(pairs[i].x, pairs[i].y) == 1 then
        printPair(&pairs[i]);
    end if;
    i := i + 1;
end loop;

Delphi

Works with: Delphi version 6.0
Library: SysUtils,StdCtrls


function GreatestCommonDivisor(A,B: integer): integer;
begin
if B = 0 then Result:=A
else Result:=GreatestCommonDivisor( B, A mod B);
end;


function IsCoprime(A,B: integer): boolean;
begin
Result:=GreatestCommonDivisor(A,B)=1;
end;


const TestNumbers: array [0..4] of TPoint =
((X:21;Y:15),(X:17;Y:23),(X:36;Y:12),(X:18;Y:29),(X:60;Y:15));


procedure ShowCoprimes(Memo: TMemo);
var I: integer;
var S: string;
var TN: TPoint;
begin
for I:=0 to High(TestNumbers) do
	begin
	TN:=TestNumbers[I];
	S:=IntToStr(TN.X)+' '+IntToStr(TN.Y)+' is ';
	if IsCoprime(TN.X,TN.Y) then S:=S+'coprime'
	else S:=S+'not coprime';
	Memo.Lines.Add(S);
	end;
end;
Output:
21 15 is not coprime
17 23 is coprime
36 12 is not coprime
18 29 is coprime
60 15 is not coprime
Elapsed Time: 5.729 ms.


EasyLang 

func gcd a b .
   while b <> 0
      h = b
      b = a mod b
      a = h
   .
   return a
.
proc test p[] . .
   if gcd p[1] p[2] = 1
      print p[]
   .
.
pairs[][] = [ [ 21 15 ] [ 17 23 ] [ 36 12 ] [ 18 29 ] [ 60 15 ] ]
for i to len pairs[][]
   test pairs[i][]
.
Output:
[ 17 23 ]
[ 18 29 ]

F# 

// Coprimes. Nigel Galloway: May 4th., 2021
let rec fN g=function 0->g=1 |n->fN n (g%n)
[(21,15);(17,23);(36,12);(18,29);(60,15)] |> List.filter(fun(n,g)->fN n g)|>List.iter(fun(n,g)->printfn "%d and %d are coprime" n g)
Output:
17 and 23 are coprime
18 and 29 are coprime

Factor

Works with: Factor version 0.98
USING: io kernel math prettyprint sequences ;

: coprime? ( seq -- ? ) [ ] [ simple-gcd ] map-reduce 1 = ;

{
    { 21 15 }
    { 17 23 }
    { 36 12 }
    { 18 29 }
    { 60 15 }
    { 21 22 25 31 143 }
}
[ dup pprint coprime? [ " Coprime" write ] when nl ] each
Output:
{ 21 15 }
{ 17 23 } Coprime
{ 36 12 }
{ 18 29 } Coprime
{ 60 15 }
{ 21 22 25 31 143 } Coprime

Fermat 

Func Is_coprime(a, b) = if GCD(a,b)=1 then 1 else 0 fi.

FOCAL 

01.10 S P(1)=21; S Q(1)=15
01.20 S P(2)=17; S Q(2)=23
01.30 S P(3)=36; S Q(3)=12
01.40 S P(4)=18; S Q(4)=29
01.50 S P(5)=60; S Q(5)=15
01.60 F N=1,5;D 3
01.70 Q

02.10 I (A-B)2.2,2.6,2.4
02.20 S B=B-A
02.30 G 2.1
02.40 S A=A-B
02.50 G 2.1
02.60 R

03.10 S A=P(N)
03.20 S B=Q(N)
03.30 D 2
03.40 I (A-1)3.6,3.5,3.6
03.50 T %4,P(N),Q(N),!
03.60 R
Output:
=   17=   23
=   18=   29

FreeBASIC 

function gcdp( a as uinteger, b as uinteger ) as uinteger
    'returns the gcd of two positive integers
    if b = 0 then return a
    return gcdp( b, a mod b )
end function

function gcd(a as integer, b as integer) as uinteger
    'wrapper for gcdp, allows for negatives
    return gcdp( abs(a), abs(b) )
end function

function is_coprime( a as integer, b as integer ) as boolean
    return (gcd(a,b)=1)
end function

print is_coprime(21,15)
print is_coprime(17,23)
print is_coprime(36,12)
print is_coprime(18,29)
print is_coprime(60,15)
Output:


false
true
false
true
false

Frink 

pairs = [ [21,15],[17,23],[36,12],[18,29],[60,15] ]
for [a,b] = pairs
   println["[$a, $b] are " + (gcd[a,b] == 1 ? "" : "not ") + "coprime"]
Output:
[21, 15] are not coprime
[17, 23] are coprime
[36, 12] are not coprime
[18, 29] are coprime
[60, 15] are not coprime

Go

Library: Go-rcu

Uses the same observation as the Wren entry. 

package main

import (
    "fmt"
    "rcu"
)

func main() {
    pairs := [][2]int{{21, 15}, {17, 23}, {36, 12}, {18, 29}, {60, 15}}
    fmt.Println("The following pairs of numbers are coprime:")
    for _, pair := range pairs {
        if rcu.Gcd(pair[0], pair[1]) == 1 {
            fmt.Println(pair)
        }
    }
}
Output:
The following pairs of numbers are coprime:
[17 23]
[18 29]

Haskell 

------------------------- COPRIMES -----------------------

coprime :: Integral a => a -> a -> Bool
coprime a b = 1 == gcd a b


--------------------------- TEST -------------------------
main :: IO ()
main =
  print $
    filter
      ((1 ==) . uncurry gcd)
      [ (21, 15),
        (17, 23),
        (36, 12),
        (18, 29),
        (60, 15)
      ]
Output:
[(17,23),(18,29)]


J 

([#~1=+./"1) >21 15;17 23;36 12;18 29;60 15
Output:
17 23
18 29

jq

Works with: jq

Works with gojq, the Go implementation of jq 

# Note that jq optimizes the recursive call of _gcd in the following:
def gcd(a;b):
  def _gcd:
    if .[1] != 0 then [.[1], .[0] % .[1]] | _gcd else .[0] end;
  [a,b] | _gcd ;

# Input: an array
def coprime: gcd(.[0]; .[1]) == 1;

The task 

"The following pairs of numbers are coprime:",
([[21,15],[17,23],[36,12],[18,29],[60,15]][]
 | select(coprime))
Output:
The following pairs of numbers are coprime:
[17,23]
[18,29]

Julia 

filter(p -> gcd(p...) == 1, [[21,15],[17,23],[36,12],[18,29],[60,15],[21,22,25,31,143]])
Output:


3-element Vector{Vector{Int64}}:



[17, 23]
[18, 29]
[21, 22, 25, 31, 143]

MAD 

            NORMAL MODE IS INTEGER
            
            INTERNAL FUNCTION COPRM.(X,Y) = GCD.(X,Y).E.1
            
            INTERNAL FUNCTION(A,B)
            ENTRY TO GCD.
            AA=A
            BB=B
LOOP        WHENEVER AA.E.BB, FUNCTION RETURN AA
            WHENEVER AA.G.BB, AA = AA-BB
            WHENEVER AA.L.BB, BB = BB-AA
            TRANSFER TO LOOP
            END OF FUNCTION
                        
            VECTOR VALUES P = 21, 17, 36, 18, 60
            VECTOR VALUES Q = 15, 23, 12, 29, 15
            
            PRINT COMMENT $ COPRIMES $
                 
            THROUGH SHOW, FOR I=0, 1, I.GE.5
            PP=P(I)
            QQ=Q(I)
SHOW        WHENEVER COPRM.(PP, QQ), PRINT FORMAT FMT, PP, QQ
            
            VECTOR VALUES FMT = $I4,I4*$
            END OF PROGRAM
Output:
COPRIMES
  17  23
  18  29

Mathematica /Wolfram Language 

CoprimeQ @@@ {{21, 15}, {17, 23}, {36, 12}, {18, 29}, {60, 15}}
Output:
{False, True, False, True, False}

MATLAB 

disp(coprime([21, 17, 36, 18, 60], [15, 23, 12, 29, 15]));

function coprimes = coprime(a,b)
gcds = gcd(a,b) == 1;
coprimes(1,:) = a(gcds);
coprimes(2,:) = b(gcds);
end
Output:
    17    18
    23    29

Maxima 

/* Taken the list of pairs and making a sublist of those pairs that are coprimes */
pairs:[[21,15],[17,23],[36,12],[18,29],[60,15]]$
sublist(pairs,lambda([x],apply('gcd,x)=1));
Output:
[[17,23],[18,29]]

Nim 

import math

for (a, b) in [(21, 15), (17, 23), (36, 12), (18, 29), (60, 15)]:
  echo a, " and ", b, " are ", if gcd(a, b) == 1: "coprimes." else: "not coprimes."
Output:
21 and 15 are not coprimes.
17 and 23 are coprimes.
36 and 12 are not coprimes.
18 and 29 are coprimes.
60 and 15 are not coprimes.

OCaml 

let rec is_coprime a = function
  | 0 -> a = 1
  | b -> is_coprime b (a mod b)

let () =
  let p (a, b) =
    Printf.printf "%u and %u are%s coprime\n" a b (if is_coprime a b then "" else " not")
  in
  List.iter p [21, 15; 17, 23; 36, 12; 18, 29; 60, 15]
Output:
21 and 15 are not coprime
17 and 23 are coprime
36 and 12 are not coprime
18 and 29 are coprime
60 and 15 are not coprime

Perl

Library: ntheory
use strict;
use warnings;
use ntheory 'gcd';

printf "%7s %s\n", (gcd(@$_) == 1 ? 'Coprime' : ''), join ', ', @$_
     for [21,15], [17,23], [36,12], [18,29], [60,15], [21,22,25,31,143];
Output:
        21, 15
Coprime 17, 23
        36, 12
Coprime 18, 29
        60, 15
Coprime 21, 22, 25, 31, 143

Phix 

function gcd1(sequence s) return gcd(s)=1 end function
?filter({{21,15},{17,23},{36,12},{18,29},{60,15}},gcd1)
Output:
{{17,23},{18,29}}

A longer set/element such as {21,22,25,30,143} would also be shown as coprime, since it is, albeit not pairwise coprime - for the latter you would need something like: 

function pairwise_coprime(sequence s)
    for i=1 to length(s)-1 do
        for j=i+1 to length(s) do
            if gcd(s[i],s[j])!=1 then return false end if
        end for
    end for
    return true
end function
?filter({{21,15},{17,23},{36,12},{18,29},{60,15},{21, 22, 25, 31, 143}},pairwise_coprime)

Output is the same as the above, because this excludes the {21, 22, 25, 31, 143}, since both 22 and 143 are divisible by 11.

PL/M 

100H:
BDOS: PROCEDURE (FN, ARG);
    DECLARE FN BYTE, ARG ADDRESS;
    GO TO 5;
END BDOS;

PRINT: PROCEDURE (STRING);
    DECLARE STRING ADDRESS;
    CALL BDOS(9, STRING);
END PRINT;

PRINT$BYTE: PROCEDURE (N);
    DECLARE S (5) BYTE INITIAL ('... $');
    DECLARE P ADDRESS, (N, C BASED P) BYTE;
    P = .S(3);
DIGIT:
    P = P - 1;
    C = N MOD 10 + '0';
    N = N / 10;
    IF N > 0 THEN GO TO DIGIT;
    CALL PRINT(P);
END PRINT$BYTE;

PRINT$PAIR: PROCEDURE (P, Q);
    DECLARE (P, Q) BYTE;
    CALL PRINT$BYTE(P);
    CALL PRINT$BYTE(Q);
    CALL PRINT(.(13,10,'$'));
END PRINT$PAIR;

GCD: PROCEDURE (A, B) BYTE;
    DECLARE (A, B, C) BYTE;
    DO WHILE B <> 0;
        C = A;
        A = B;
        B = C MOD B;
    END;
    RETURN A;
END GCD;

DECLARE P (5) BYTE INITIAL (21, 17, 36, 18, 60);
DECLARE Q (5) BYTE INITIAL (15, 23, 12, 29, 15);
DECLARE I BYTE;

DO I = 0 TO LAST(P);
    IF GCD(P(I), Q(I)) = 1 THEN
        CALL PRINT$PAIR(P(I), Q(I));
END;
CALL BDOS(0,0);
EOF
Output:
17 23
18 29

Python 

'''Coprimes'''

from math import gcd


# coprime :: Int -> Int -> Bool
def coprime(a, b):
    '''True if a and b are coprime.
    '''
    return 1 == gcd(a, b)


# ------------------------- TEST -------------------------
# main :: IO ()
def main():
    '''List of pairs filtered for coprimes'''

    print([
        xy for xy in [
            (21, 15), (17, 23), (36, 12),
            (18, 29), (60, 15)
        ]
        if coprime(*xy)
    ])


# MAIN ---
if __name__ == '__main__':
    main()
Output:
[(17, 23), (18, 29)]


Quackery

gcd is defined at Greatest common divisor#Quackery. 

  [ gcd 1 = ]          is coprime ( n n --> b )

  ' [ [ 21 15 ]
      [ 17 23 ]
      [ 36 12 ]
      [ 18 29 ]
      [ 60 15 ] ]

  witheach
    [ unpack 2dup swap
      echo say " and " echo
      say " are"
      coprime not if
         [ say " not" ]
      say " coprime." cr ]
Output:
21 and 15 are not coprime.
17 and 23 are coprime.
36 and 12 are not coprime.
18 and 29 are coprime.
60 and 15 are not coprime.

R 

factors <- function(n) c(Filter(function(x) n %% x == 0, seq_len(n %/% 2)), n)
isCoprime <- function(p, q) all(intersect(factors(p), factors(q)) == 1)
output <- data.frame(p = c(21, 17, 36, 18, 60), q = c(15, 23, 12, 29, 15))
print(transform(output, "Coprime" = ifelse(mapply(isCoprime, p, q), "Yes", "No")))
Output:
   p  q Coprime
1 21 15      No
2 17 23     Yes
3 36 12      No
4 18 29     Yes
5 60 15      No

Racket

There is a coprime? function in the math/number-theory library to show off (more useful if you're using typed racket). 

#lang racket/base

;; Rename only necessary so we can distinguish it 
(require (rename-in math/number-theory [coprime? number-theory/coprime?]))

(define (gcd/coprime? . ns)
  (= 1 (apply gcd ns)))

(module+ main
  (define ((Coprimes name coprime?) test)
    (printf "~a: ~a -> ~a~%" name (cons 'coprime? test) (apply coprime? test)))
  (define tests '([21 15] [17 23] [36 12] [18 29] [60 15] [21 15 27] [17 23 46]))

  (for-each (λ (n f) (for-each (Coprimes n f) tests))
            (list "math/number-theory"
                  "named gcd-based function"
                  "anonymous gcd-based function")
            (list number-theory/coprime?
                  gcd/coprime?
                  (λ ns (= 1 (apply gcd ns))))))
Output:
math/number-theory: (coprime? 21 15) -> #f
math/number-theory: (coprime? 17 23) -> #t
math/number-theory: (coprime? 36 12) -> #f
math/number-theory: (coprime? 18 29) -> #t
math/number-theory: (coprime? 60 15) -> #f
math/number-theory: (coprime? 21 15 27) -> #f
math/number-theory: (coprime? 17 23 46) -> #t
named gcd-based function: (coprime? 21 15) -> #f
named gcd-based function: (coprime? 17 23) -> #t
named gcd-based function: (coprime? 36 12) -> #f
named gcd-based function: (coprime? 18 29) -> #t
named gcd-based function: (coprime? 60 15) -> #f
named gcd-based function: (coprime? 21 15 27) -> #f
named gcd-based function: (coprime? 17 23 46) -> #t
anonymous gcd-based function: (coprime? 21 15) -> #f
anonymous gcd-based function: (coprime? 17 23) -> #t
anonymous gcd-based function: (coprime? 36 12) -> #f
anonymous gcd-based function: (coprime? 18 29) -> #t
anonymous gcd-based function: (coprime? 60 15) -> #f
anonymous gcd-based function: (coprime? 21 15 27) -> #f
anonymous gcd-based function: (coprime? 17 23 46) -> #t

Raku

How do you determine if numbers are co-prime? Check to see if the Greatest common divisor is equal to one. Since we're duplicating tasks willy-nilly, lift code from that task, (or in this case, just use the builtin). 

say .raku, ( [gcd] |$_ ) == 1 ?? ' Coprime' !! '' for [21,15],[17,23],[36,12],[18,29],[60,15],[21,22,25,31,143]

[21, 15]
[17, 23] Coprime
[36, 12]
[18, 29] Coprime
[60, 15]
[21, 22, 25, 31, 143] Coprime

REXX

Version 1

/*REXX prgm tests number sequences (min. of two #'s, separated by a commas) if comprime.*/
parse arg @                                      /*obtain optional arguments from the CL*/
if @='' | @==","  then @= '21,15 17,23 36,12 18,29 60,15 21,22,25,143 -2,0 0,-3'

       do j=1  for words(@);     say             /*process each of the sets of numbers. */
       stuff= translate( word(@, j), , ',')      /*change commas (,) to blanks for  GCD.*/
       cofactor= gcd(stuff)                      /*get  Greatest Common Divisor  of #'s.*/
       if cofactor==1  then say  stuff  " ─────── are coprime ───────"
                       else say  stuff  " have a cofactor of: "       cofactor
       end   /*j*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gcd:   procedure; parse arg $                    /*╔═══════════════════════════════════╗*/
          do #=2  for arg()-1;   $= $  arg(#)    /*║This GCD handles multiple arguments║*/
          end   /*#*/                            /*║ & multiple numbers per argument, &║*/
       parse var  $    x  z  .                   /*║negative numbers and non-integers. ║*/
       if x=0  then x= z;        x= abs(x)       /*╚═══════════════════════════════════╝*/
          do j=2  to words($);   y= abs( word($, j) );               if y=0  then iterate
             do  until _==0;     _= x // y;            x= y;         y= _
             end   /*until*/
          end      /*j*/
       return x
output   when using the default inputs:
21,15  have a cofactor of:  3

17,23  ─────── are coprime ───────

36,12  have a cofactor of:  12

18,29  ─────── are coprime ───────

60,15  have a cofactor of:  15

21,22,25,143  ─────── are coprime ───────

-2,0  have a cofactor of:  2

0,-3  have a cofactor of:  3

Version 2

Libraries: How to use
Library: Numbers
Library: Functions
Library: Settings
Library: Abend

Gcd() is in library Numbers. 

include Settings

say version; say 'Coprimes'; say
numeric digits 10
call ShowResults
say Format(Time('e'),,3) 'seconds'
exit

ShowResults:
say 'Coprimes (1 = Yes, 0 = No)'
say '21,15' IsCoprime(21,15)
say '17,23' IsCoprime(17,23)
say '36,12' IsCoprime(36,12)
say '18,29' IsCoprime(18,29)
say '60,15' IsCoprime(60,15)
return

Coprime:
/* Are 2 numbers coprime? */
procedure expose glob.
arg x,y
/* Formula */
return (Gcd(x,y) = 1)

include Numbers
include Functions
include Abend
Output:
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024
Coprimes

Coprimes (1 = Yes, 0 = No)
21,15 0
17,23 1
36,12 0
18,29 1
60,15 0

0.000 seconds

Ring 

see "working..." + nl
row = 0
Coprimes = [[21,15],[17,23],[36,12],[18,29],[60,15]]
input = "input: [21,15],[17,23],[36,12],[18,29],[60,15]"
see input + nl
see "Coprimes are:" + nl

lncpr = len(Coprimes)
for n = 1 to lncpr
    flag = 1
    if Coprimes[n][1] < Coprimes[n][2]
       min = Coprimes[n][1]
    else
       min = Coprimes[n][2]
    ok
    for m = 2 to min
        if Coprimes[n][1]%m = 0 and Coprimes[n][2]%m = 0 
           flag = 0
           exit
        ok 
    next  
    if flag = 1
       row = row + 1
       see "" + Coprimes[n][1] + " " + Coprimes[n][2] + nl
    ok     
next

see "Found " + row + " coprimes" + nl
see "done..." + nl
Output:
working...
input: [21,15],[17,23],[36,12],[18,29],[60,15]
Coprimes are:
17 23
18 29
Found 2 coprimes
done...

RPL

GCD is defined at Greatest common divisor

Works with: HP version 28
≪ → pairs
  ≪ { }
     1 pairs SIZE FOR j 
        pairs j GET 
        DUP LIST→ DROP 
        IF GCD 1 == THEN 1 →LIST + ELSE DROP END
     NEXT
≫ '→COPR' STO

{{21 15} {17 23} {36 12} {18 29} {60 15}} →COPR
Output:
1: { { 17 23 } { 18 29 } }

Ruby 

pairs = [[21,15],[17,23],[36,12],[18,29],[60,15]]
pairs.select{|p, q| p.gcd(q) == 1}.each{|pair| p pair}
Output:
[17, 23]
[18, 29]

Sidef 

var pairs = [[21,15],[17,23],[36,12],[18,29],[60,15]]
say "The following pairs of numbers are coprime:"
pairs.grep { .gcd == 1 }.each { .say }
Output:
The following pairs of numbers are coprime:
[17, 23]
[18, 29]

Wren

Library: Wren-math

Two numbers are coprime if their GCD is 1. 

import "./math" for Int

var pairs = [[21,15],[17,23],[36,12],[18,29],[60,15]]
System.print("The following pairs of numbers are coprime:")
for (pair in pairs) if (Int.gcd(pair[0], pair[1]) == 1) System.print(pair)
Output:
The following pairs of numbers are coprime:
[17, 23]
[18, 29]

XPL0 

func GCD(A, B);         \Return greatest common divisor of A and B
int  A, B;
[while A#B do
  if A>B then A:= A-B
         else B:= B-A;
return A;
];

int Input, N, A, B;
[Input:= [[21,15], [17,23], [36,12], [18,29], [60,15]];
for N:= 0 to 4 do
    [A:= Input(N, 0);  B:= Input(N, 1);
    if GCD(A, B) = 1 then 
        [IntOut(0, A);  ChOut(0, ^,);  IntOut(0, B);  CrLf(0)];
    ];
]
Output:
17,23
18,29
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