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Prime triplets

From Rosetta Code
Prime triplets 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

Find and show members of prime triples (p, p+2, p+6), where p < 5500


See also



11l

Translation of: Nim
F is_prime(n)
   I n == 2
      R 1B
   I n < 2 | n % 2 == 0
      R 0B
   L(i) (3 .. Int(sqrt(n))).step(2)
      I n % i == 0
         R 0B
   R 1B

print(‘   p  p+2  p+6’)
V count = 0
L(n) (3.<5500).step(2)
   I is_prime(n) & is_prime(n + 2) & is_prime(n + 6)
      print(f:‘{n:4} {n + 2:4} {n + 6:4}’)
      count++

print("\nFound "count‘ primes triplets for p < 5500.’)
Output:
   p  p+2  p+6
   5    7   11
  11   13   17
  17   19   23
  41   43   47
 101  103  107
 107  109  113
 191  193  197
 227  229  233
 311  313  317
 347  349  353
 461  463  467
 641  643  647
 821  823  827
 857  859  863
 881  883  887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483

Found 43 primes triplets for p < 5500.

Action!

Library: Action! Sieve of Eratosthenes
INCLUDE "H6:SIEVE.ACT"

PROC Main()
  DEFINE MAX="5499"
  BYTE ARRAY primes(MAX+1)
  INT i,count=[0]

  Put(125) PutE()
  Sieve(primes,MAX+1)
  FOR i=2 TO MAX-6
  DO
    IF primes(i)=1 AND primes(i+2)=1 AND (primes(i+6))=1 THEN
      PrintF("(%I %I %I) ",i,i+2,i+6)
      count==+1
    FI
  OD
  PrintF("%E%EThere are %I prime triplets",count)
RETURN
Output:

Screenshot from Atari 8-bit computer 

(5 7 11) (11 13 17) (17 19 23) (41 43 47) (101 103 107) (107 109 113) (191 193 197) (227 229 233) (311 313 317) (347 349 353)
(461 463 467) (641 643 647) (821 823 827) (857 859 863) (881 883 887) (1091 1093 1097) (1277 1279 1283) (1301 1303 1307)
(1427 1429 1433) (1481 1483 1487) (1487 1489 1493) (1607 1609 1613) (1871 1873 1877) (1997 1999 2003) (2081 2083 2087)
(2237 2239 2243) (2267 2269 2273) (2657 2659 2663) (2687 2689 2693) (3251 3253 3257) (3461 3463 3467) (3527 3529 3533)
(3671 3673 3677) (3917 3919 3923) (4001 4003 4007) (4127 4129 4133) (4517 4519 4523) (4637 4639 4643) (4787 4789 4793)
(4931 4933 4937) (4967 4969 4973) (5231 5233 5237) (5477 5479 5483)

There are 43 prime triplets

ALGOL 68

Using code from Successive_prime_differences#ALGOL_68 

BEGIN # find primes p where p+2 and p+6 are also prime                    #
    # reurns a list of primes up to n #
    PROC prime list = ( INT n )[]INT:
         BEGIN
            # sieve the primes to n #
            INT no = 0, yes = 1;
            [ 1 : n ]INT p;
            p[ 1 ] := no; p[ 2 ] := yes;
            FOR i FROM 3 BY 2 TO n DO p[ i ] := yes OD;
            FOR i FROM 4 BY 2 TO n DO p[ i ] := no  OD;
            FOR i FROM 3 BY 2 TO ENTIER sqrt( n ) DO
                IF p[ i ] = yes THEN FOR s FROM i * i BY i + i TO n DO p[ s ] := no OD FI
            OD;
            # replace the sieve with a list #
            INT p pos := 0;
            FOR i TO n DO IF p[ i ] = yes THEN p[ p pos +:= 1 ] := i FI OD;
            p[ 1 : p pos ]
         END # prime list # ;
    # prints the elements of list #
    PROC print list = ( INT width, []INT list )VOID:
         BEGIN
            print( ( "[" ) );
            FOR i FROM LWB list TO UPB list DO print( ( " ", whole( list[ i ], width ) ) ) OD;
            print( ( " ]" ) )
         END # print list # ;
    # attempts to find patterns in the differences of primes and prints the results #
    PROC try differences = ( []INT primes, []INT pattern )VOID:
         BEGIN
            INT    pattern length = ( UPB pattern - LWB pattern ) + 1;
            [ 1 :  pattern length + 1 ]INT first; FOR i TO UPB first DO first[ i ] := 0 OD;
            [ 1 :  pattern length + 1 ]INT last;  FOR i TO UPB last  DO last[  i ] := 0 OD;
            INT    count := 0;
            FOR p FROM LWB primes + pattern length TO UPB primes DO
                BOOL matched := TRUE;
                INT e pos    := LWB pattern;
                FOR e FROM p - pattern length TO p - 1
                WHILE matched := primes[ e + 1 ] - primes[ e ] = pattern[ e pos ]
                DO
                    e pos +:= 1
                OD;
                IF matched THEN
                    # found a matching sequence #
                    count +:= 1;
                    print list( -4, primes[ p - pattern length : p ] );
                    IF count MOD 6 = 0 THEN print( ( newline ) ) ELSE print( ( " " ) ) FI
                FI
            OD;
            print( ( newline, "Found ", whole( count, 0 ), " prime sequence(s) that differ by: " ) );
            print list( 0, pattern );
            print( ( newline ) )
        END # try differences # ;
    INT max number = 5 500;
    []INT    p list = prime list( max number - 1 );
    print( ( "Prime triplets under ", whole( max number, 0 ), ":", newline ) );
    try differences( p list, ( 2, 4 ) )
END
Output:
Prime triplets under 5500:
[    5    7   11 ] [   11   13   17 ] [   17   19   23 ] [   41   43   47 ] [  101  103  107 ] [  107  109  113 ]
[  191  193  197 ] [  227  229  233 ] [  311  313  317 ] [  347  349  353 ] [  461  463  467 ] [  641  643  647 ]
[  821  823  827 ] [  857  859  863 ] [  881  883  887 ] [ 1091 1093 1097 ] [ 1277 1279 1283 ] [ 1301 1303 1307 ]
[ 1427 1429 1433 ] [ 1481 1483 1487 ] [ 1487 1489 1493 ] [ 1607 1609 1613 ] [ 1871 1873 1877 ] [ 1997 1999 2003 ]
[ 2081 2083 2087 ] [ 2237 2239 2243 ] [ 2267 2269 2273 ] [ 2657 2659 2663 ] [ 2687 2689 2693 ] [ 3251 3253 3257 ]
[ 3461 3463 3467 ] [ 3527 3529 3533 ] [ 3671 3673 3677 ] [ 3917 3919 3923 ] [ 4001 4003 4007 ] [ 4127 4129 4133 ]
[ 4517 4519 4523 ] [ 4637 4639 4643 ] [ 4787 4789 4793 ] [ 4931 4933 4937 ] [ 4967 4969 4973 ] [ 5231 5233 5237 ]
[ 5477 5479 5483 ]
Found 43 prime sequence(s) that differ by: [ 2 4 ]

Arturo 

lst: select select 2..5500 => prime? 'x 
        -> and? [prime? x+2] [prime? x+6]

loop split.every: 5 lst 'a -> 
    print map a 'item [
        pad join.with:", " 
            to [:string] @[item item+2 item+6] 17
    ]
Output:
         5, 7, 11        11, 13, 17        17, 19, 23        41, 43, 47     101, 103, 107 
    107, 109, 113     191, 193, 197     227, 229, 233     311, 313, 317     347, 349, 353 
    461, 463, 467     641, 643, 647     821, 823, 827     857, 859, 863     881, 883, 887 
 1091, 1093, 1097  1277, 1279, 1283  1301, 1303, 1307  1427, 1429, 1433  1481, 1483, 1487 
 1487, 1489, 1493  1607, 1609, 1613  1871, 1873, 1877  1997, 1999, 2003  2081, 2083, 2087 
 2237, 2239, 2243  2267, 2269, 2273  2657, 2659, 2663  2687, 2689, 2693  3251, 3253, 3257 
 3461, 3463, 3467  3527, 3529, 3533  3671, 3673, 3677  3917, 3919, 3923  4001, 4003, 4007 
 4127, 4129, 4133  4517, 4519, 4523  4637, 4639, 4643  4787, 4789, 4793  4931, 4933, 4937 
 4967, 4969, 4973  5231, 5233, 5237  5477, 5479, 5483

AWK 

# syntax: GAWK -f PRIME_TRIPLETS.AWK
BEGIN {
    start = 1
    stop = 5499
    for (i=start; i<=stop; i++) {
      if (is_prime(i+6) && is_prime(i+2) && is_prime(i)) {
        printf("%d %d %d\n",i,i+2,i+6)
        count++
      }
    }
    printf("Prime Triplets %d-%d: %d\n",start,stop,count)
    exit(0)
}
function is_prime(x,  i) {
    if (x <= 1) {
      return(0)
    }
    for (i=2; i<=int(sqrt(x)); i++) {
      if (x % i == 0) {
        return(0)
      }
    }
    return(1)
}
Output:
5 7 11
11 13 17
17 19 23
41 43 47
101 103 107
107 109 113
191 193 197
227 229 233
311 313 317
347 349 353
461 463 467
641 643 647
821 823 827
857 859 863
881 883 887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483
Prime Triplets 1-5499: 43


BASIC

BASIC256 

function isPrime(v)
	if v < 2 then return False
	if v mod 2 = 0 then return v = 2
	if v mod 3 = 0 then return v = 3
	d = 5
	while d * d <= v
		if v mod d = 0 then return False else d += 2
	end while
	return True
end function

for p = 3 to 5499 step 2
	if not isPrime(p+6) then continue for
	if not isPrime(p+2) then continue for
	if not isPrime(p) then continue for
	print "["; p; " "; p+2; " "; p+6; "]"
next p
end

PureBasic 

Procedure isPrime(v.i)
  If     v <= 1    : ProcedureReturn #False
  ElseIf v < 4     : ProcedureReturn #True
  ElseIf v % 2 = 0 : ProcedureReturn #False
  ElseIf v < 9     : ProcedureReturn #True
  ElseIf v % 3 = 0 : ProcedureReturn #False
  Else
    Protected r = Round(Sqr(v), #PB_Round_Down)
    Protected f = 5
    While f <= r
      If v % f = 0 Or v % (f + 2) = 0
        ProcedureReturn #False
      EndIf
      f + 6
    Wend
  EndIf
  ProcedureReturn #True
EndProcedure

OpenConsole()
For p.i = 3 To 5499 Step 2
  If Not isPrime(p+6) 
    Continue
  EndIf
  If Not isPrime(p+2) 
    Continue
  EndIf
  If Not isPrime(p) 
    Continue
  EndIf        
  PrintN("["+ Str(p) + " " + Str(p+2) + " " + Str(p+6) + "]")
Next p
PrintN(#CRLF$ + "--- terminado, pulsa RETURN---"): Input()
CloseConsole()

Yabasic 

sub isPrime(v)
    if v < 2 then return False : fi
    if mod(v, 2) = 0 then return v = 2 : fi
    if mod(v, 3) = 0 then return v = 3 : fi
    d = 5
    while d * d <= v
        if mod(v, d) = 0 then return False else d = d + 2 : fi
    wend
    return True
end sub

for p = 3 to 5499 step 2
    if not isPrime(p+6) continue
    if not isPrime(p+2) continue
    if not isPrime(p) continue
    print "[", p using "####", p+2 using "####", p+6 using "####", "]"
next p
end

Delphi

Works with: Delphi version 6.0
Library: SysUtils,StdCtrls


function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
     begin
     I:=5;
     Stop:=Trunc(sqrt(N+0.0));
     Result:=False;
     while I<=Stop do
           begin
           if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
           Inc(I,6);
           end;
     Result:=True;
     end;
end;




procedure ShowTriple026Prime(Memo: TMemo);
var N,Sum,Cnt: integer;
var NS,S: string;
begin
Cnt:=0;
S:='';
for N:=1 to 5500-1 do
 if IsPrime(N) then
  if IsPrime(N+2) and IsPrime(N+6) then
	begin
	Inc(Cnt);
	S:=S+Format('%6d%6d%6d',[N,N+2,N+6]);
	S:=S+CRLF;
	end;
Memo.Lines.Add('     P   P+2   P+6');
Memo.Lines.Add('------------------');
Memo.Lines.Add(S);
Memo.Lines.Add('Count = '+IntToStr(Cnt));
end;
Output:
     P   P+2   P+6
------------------
     5     7    11
    11    13    17
    17    19    23
    41    43    47
   101   103   107
   107   109   113
   191   193   197
   227   229   233
   311   313   317
   347   349   353
   461   463   467
   641   643   647
   821   823   827
   857   859   863
   881   883   887
  1091  1093  1097
  1277  1279  1283
  1301  1303  1307
  1427  1429  1433
  1481  1483  1487
  1487  1489  1493
  1607  1609  1613
  1871  1873  1877
  1997  1999  2003
  2081  2083  2087
  2237  2239  2243
  2267  2269  2273
  2657  2659  2663
  2687  2689  2693
  3251  3253  3257
  3461  3463  3467
  3527  3529  3533
  3671  3673  3677
  3917  3919  3923
  4001  4003  4007
  4127  4129  4133
  4517  4519  4523
  4637  4639  4643
  4787  4789  4793
  4931  4933  4937
  4967  4969  4973
  5231  5233  5237
  5477  5479  5483

Count = 43
Elapsed Time: 13.263 ms.


EasyLang 

fastfunc isprim num .
   i = 2
   while i <= sqrt num
      if num mod i = 0
         return 0
      .
      i += 1
   .
   return 1
.
for i = 2 to 5499
   if isprim i = 1 and isprim (i + 2) = 1 and isprim (i + 6) = 1
      write "(" & i & " " & i + 2 & " " & i + 6 & ") "
   .
.
Output:
(5 7 11) (11 13 17) (17 19 23) (41 43 47) (101 103 107) (107 109 113) (191 193 197) (227 229 233) (311 313 317) (347 349 353) (461 463 467) (641 643 647) (821 823 827) (857 859 863) (881 883 887) (1091 1093 1097) (1277 1279 1283) (1301 1303 1307) (1427 1429 1433) (1481 1483 1487) (1487 1489 1493) (1607 1609 1613) (1871 1873 1877) (1997 1999 2003) (2081 2083 2087) (2237 2239 2243) (2267 2269 2273) (2657 2659 2663) (2687 2689 2693) (3251 3253 3257) (3461 3463 3467) (3527 3529 3533) (3671 3673 3677) (3917 3919 3923) (4001 4003 4007) (4127 4129 4133) (4517 4519 4523) (4637 4639 4643) (4787 4789 4793) (4931 4933 4937) (4967 4969 4973) (5231 5233 5237) (5477 5479 5483)

Factor

Works with: Factor version 0.98
USING: arrays kernel lists lists.lazy math math.primes
math.primes.lists prettyprint sequences ;

lprimes                                ! An infinite lazy list of primes
[ dup 2 + dup 4 + 3array ] lmap-lazy   ! Map primes to their triplets (e.g. 2 -> { 2 4 8 })
[ [ prime? ] all? ] lfilter            ! Select triplets which contain only primes
[ first 5500 < ] lwhile                ! Make the list end eventually...
[ . ] leach                            ! Print each item in the list
Output:
{ 5 7 11 }
{ 11 13 17 }
{ 17 19 23 }
{ 41 43 47 }
{ 101 103 107 }
{ 107 109 113 }
{ 191 193 197 }
{ 227 229 233 }
{ 311 313 317 }
{ 347 349 353 }
{ 461 463 467 }
{ 641 643 647 }
{ 821 823 827 }
{ 857 859 863 }
{ 881 883 887 }
{ 1091 1093 1097 }
{ 1277 1279 1283 }
{ 1301 1303 1307 }
{ 1427 1429 1433 }
{ 1481 1483 1487 }
{ 1487 1489 1493 }
{ 1607 1609 1613 }
{ 1871 1873 1877 }
{ 1997 1999 2003 }
{ 2081 2083 2087 }
{ 2237 2239 2243 }
{ 2267 2269 2273 }
{ 2657 2659 2663 }
{ 2687 2689 2693 }
{ 3251 3253 3257 }
{ 3461 3463 3467 }
{ 3527 3529 3533 }
{ 3671 3673 3677 }
{ 3917 3919 3923 }
{ 4001 4003 4007 }
{ 4127 4129 4133 }
{ 4517 4519 4523 }
{ 4637 4639 4643 }
{ 4787 4789 4793 }
{ 4931 4933 4937 }
{ 4967 4969 4973 }
{ 5231 5233 5237 }
{ 5477 5479 5483 }

Fermat 

for i=3,5499,2 do if Isprime(i)=1 and Isprime(i+2)=1 and Isprime(i+6)=1 then !!(i,i+2,i+6) fi od

FreeBASIC 

#include "isprime.bas"
for p as uinteger = 3 to 5499 step 2
     if not isprime(p+6) then continue for
     if not isprime(p+2) then continue for
     if not isprime(p) then continue for
     print using "[#### #### ####] ";p;p+2;p+6;
next p
Output:


[   5    7   11] [  11   13   17] [  17   19   23] [  41   43   47] [ 101  103  107] [ 107  109  113] [ 191  193  197] [ 227  229  233] [ 311  313  317] [ 347  349  353] [ 461  463  467] [ 641  643  647] [ 821  823  827] [ 857  859  863] [ 881  883  887] [1091 1093 1097] [1277 1279 1283] [1301 1303 1307] [1427 1429 1433] [1481 1483 1487] [1487 1489 1493] [1607 1609 1613] [1871 1873 1877] [1997 1999 2003] [2081 2083 2087] [2237 2239 2243] [2267 2269 2273] [2657 2659 2663] [2687 2689 2693] [3251 3253 3257] [3461 3463 3467] [3527 3529 3533] [3671 3673 3677] [3917 3919 3923] [4001 4003 4007] [4127 4129 4133] [4517 4519 4523] [4637 4639 4643] [4787 4789 4793] [4931 4933 4937] [4967 4969 4973] [5231 5233 5237] [5477 5479 5483]

FutureBasic 

local fn IsPrime( n as NSUInteger ) as BOOL
  BOOL       isPrime = YES
  NSUInteger i
  
  if n < 2        then exit fn = NO
  if n = 2        then exit fn = YES
  if n mod 2 == 0 then exit fn = NO
  for i = 3 to int(n^.5) step 2
    if n mod i == 0 then exit fn = NO
  next
end fn = isPrime

local fn PrimeTriplets( limit as NSUInteger )
  NSUInteger p, i = 1
  
  printf @"---------------------"
  printf @"Index   P   P+2   P+6"
  printf @"---------------------"
  for p = 3 to limit step 2
    if fn IsPrime( p+6 ) == NO then continue
    if fn IsPrime( p+2 ) == NO then continue
    if fn IsPrime( p   ) == NO then continue
    printf @"%2lu. %5lu %5lu %5lu", i, p, p+2, p+6
    i++
  next
end fn

fn PrimeTriplets( 5500 )

HandleEvents
Output:
---------------------
Index   P   P+2   P+6
---------------------
 1.     5     7    11
 2.    11    13    17
 3.    17    19    23
 4.    41    43    47
 5.   101   103   107
 6.   107   109   113
 7.   191   193   197
 8.   227   229   233
 9.   311   313   317
10.   347   349   353
11.   461   463   467
12.   641   643   647
13.   821   823   827
14.   857   859   863
15.   881   883   887
16.  1091  1093  1097
17.  1277  1279  1283
18.  1301  1303  1307
19.  1427  1429  1433
20.  1481  1483  1487
21.  1487  1489  1493
22.  1607  1609  1613
23.  1871  1873  1877
24.  1997  1999  2003
25.  2081  2083  2087
26.  2237  2239  2243
27.  2267  2269  2273
28.  2657  2659  2663
29.  2687  2689  2693
30.  3251  3253  3257
31.  3461  3463  3467
32.  3527  3529  3533
33.  3671  3673  3677
34.  3917  3919  3923
35.  4001  4003  4007
36.  4127  4129  4133
37.  4517  4519  4523
38.  4637  4639  4643
39.  4787  4789  4793
40.  4931  4933  4937
41.  4967  4969  4973
42.  5231  5233  5237
43.  5477  5479  5483

Go

Translation of: Wren
Library: Go-rcu
package main

import (
    "fmt"
    "rcu"
)

func main() {
    c := rcu.PrimeSieve(5505, false)
    var triples [][3]int
    fmt.Println("Prime triplets: p, p + 2, p + 6 where p < 5,500:")
    for i := 3; i < 5500; i += 2 {
        if !c[i] && !c[i+2] && !c[i+6] {
            triples = append(triples, [3]int{i, i + 2, i + 6})
        }
    }
    for _, triple := range triples {
        var t [3]string
        for i := 0; i < 3; i++ {
            t[i] = rcu.Commatize(triple[i])
        }
        fmt.Printf("%5s  %5s  %5s\n", t[0], t[1], t[2])
    }
    fmt.Println("\nFound", len(triples), "such prime triplets.")
}
Output:
Same as Wren entry.

GW-BASIC 

10 FOR A = 3 TO 5499 STEP 2
20 P = A
30 GOSUB 1000
40 IF Z = 0 THEN GOTO 500
50 P = A + 2
60 GOSUB 1000
70 IF Z = 0 THEN GOTO 500
80 P = A + 6
90 GOSUB 1000
100 IF Z = 1 THEN PRINT A,A+2,A+6
500 NEXT A
510 END
1000 Z = 1 : I = 2
1010 IF P MOD I = 0 THEN Z = 0 : RETURN
1020 I = I + 1
1030 IF I*I > P THEN RETURN
1040 GOTO 1010

J 

0 2 6 +/~ ((# }:)~ 2 4 E. 2 -~/\ ]) i.&.(p:inv) 5500

Shorter, but slower: 

0 2 6 +/~ I. (#: 81) E. 1 p: i. 5500
Output:
   5    7   11
  11   13   17
  17   19   23
  41   43   47
 101  103  107
 107  109  113
 191  193  197
 227  229  233
 311  313  317
 347  349  353
 461  463  467
 641  643  647
 821  823  827
 857  859  863
 881  883  887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483

jq

Works with: jq

Works with gojq, the Go implementation of jq

The implementation of `is_prime` at Erdős-primes#jq can be used here and is therefore not repeated.

The `prime_triplets` defined here generates an unbounded stream of prime triples, which is harnessed by the generic function `emit_until` defined as follows: 

def emit_until(cond; stream): label $out | stream | if cond then break $out else . end;

The Task: 

# Output: [p,p+2,p+6] where p is prime
def prime_triplets:
  def pt: .[2] == .[1] + 4 and .[1] == .[0] + 2;
  def next: .[1:] + [first( range(.[2] + 2; infinite;2) | select(is_prime))];
  # prime the foreach with the first triplet
  foreach range(7; infinite; 2) as $i ([2,3,5]; next; select(pt) ) ;

emit_until(.[0] >= 5500; prime_triplets)
Output:
[5,7,11]
[11,13,17]
[17,19,23]
[41,43,47]
[101,103,107]
[107,109,113]
[191,193,197]
[227,229,233]
[311,313,317]
[347,349,353]
[461,463,467]
[641,643,647]
[821,823,827]
[857,859,863]
[881,883,887]
[1091,1093,1097]
[1277,1279,1283]
[1301,1303,1307]
[1427,1429,1433]
[1481,1483,1487]
[1487,1489,1493]
[1607,1609,1613]
[1871,1873,1877]
[1997,1999,2003]
[2081,2083,2087]
[2237,2239,2243]
[2267,2269,2273]
[2657,2659,2663]
[2687,2689,2693]
[3251,3253,3257]
[3461,3463,3467]
[3527,3529,3533]
[3671,3673,3677]
[3917,3919,3923]
[4001,4003,4007]
[4127,4129,4133]
[4517,4519,4523]
[4637,4639,4643]
[4787,4789,4793]
[4931,4933,4937]
[4967,4969,4973]
[5231,5233,5237]
[5477,5479,5483]

Julia 

using Primes

pmask = primesmask(1, 5505)
foreach(n -> println([n, n + 2, n + 6]), filter(n -> pmask[n] && pmask[n + 2] && pmask[n + 6], 1:5500))
Output:
[5, 7, 11]
[11, 13, 17]
[17, 19, 23]
[41, 43, 47]
[101, 103, 107]
[107, 109, 113]
[191, 193, 197]
[227, 229, 233]
[311, 313, 317]
[347, 349, 353]
[461, 463, 467]
[641, 643, 647]
[821, 823, 827]
[857, 859, 863]
[881, 883, 887]
[1091, 1093, 1097]
[1277, 1279, 1283]
[1301, 1303, 1307]
[1427, 1429, 1433]
[1481, 1483, 1487]
[1487, 1489, 1493]
[1607, 1609, 1613]
[1871, 1873, 1877]
[1997, 1999, 2003]
[2081, 2083, 2087]
[2237, 2239, 2243]
[2267, 2269, 2273]
[2657, 2659, 2663]
[2687, 2689, 2693]
[3251, 3253, 3257]
[3461, 3463, 3467]
[3527, 3529, 3533]
[3671, 3673, 3677]
[3917, 3919, 3923]
[4001, 4003, 4007]
[4127, 4129, 4133]
[4517, 4519, 4523]
[4637, 4639, 4643]
[4787, 4789, 4793]
[4931, 4933, 4937]
[4967, 4969, 4973]
[5231, 5233, 5237]
[5477, 5479, 5483]

Lua 

do -- find primes p where p+2 and p+6 are also prime
    local MAX_PRIME = 5500
    local pList = {}
    do -- set pList to a list of primes up to MAX_PRIME
        -- sieve the odd primes to n and construct the list
        local p = {}
        for i = 3, MAX_PRIME, 2 do p[ i ] = true end
        for i = 3, math.floor( math.sqrt( MAX_PRIME ) ), 2 do
            if p[ i ] then
                for s = i * i, MAX_PRIME, i + i do p[ s ] = false end
            end
        end
        pList[ 1 ] = 2
        for i = 3, MAX_PRIME, 2 do
            if p[ i ] then pList[ #pList + 1 ] = i end
        end
    end
    local function fmt ( n ) return string.format( "%4d", n ) end
    io.write( "Prime triplets under ", MAX_PRIME, ":", "\n" )
    local tCount = 0
    for i = 1, #pList - 2 do
        local p1, p2, p3 = pList[ i ], pList[ i + 1 ], pList[ i + 2 ]
        if  p2 - p1 == 2 and p3 - p2 == 4 then
            tCount = tCount + 1
            io.write( "[ ", fmt( p1 ), " ", fmt( p2 ), " ", fmt( p3 ), " ]"
                    , ( tCount % 5 == 0 and "\n" or " " )
                    ) 
        end
    end
    io.write( "\n", "Found ", tCount, " prime triplets\n" )
end
Output:
Prime triplets under 5500:
[    5    7   11 ] [   11   13   17 ] [   17   19   23 ] [   41   43   47 ] [  101  103  107 ]
[  107  109  113 ] [  191  193  197 ] [  227  229  233 ] [  311  313  317 ] [  347  349  353 ]
[  461  463  467 ] [  641  643  647 ] [  821  823  827 ] [  857  859  863 ] [  881  883  887 ]
[ 1091 1093 1097 ] [ 1277 1279 1283 ] [ 1301 1303 1307 ] [ 1427 1429 1433 ] [ 1481 1483 1487 ]
[ 1487 1489 1493 ] [ 1607 1609 1613 ] [ 1871 1873 1877 ] [ 1997 1999 2003 ] [ 2081 2083 2087 ]
[ 2237 2239 2243 ] [ 2267 2269 2273 ] [ 2657 2659 2663 ] [ 2687 2689 2693 ] [ 3251 3253 3257 ]
[ 3461 3463 3467 ] [ 3527 3529 3533 ] [ 3671 3673 3677 ] [ 3917 3919 3923 ] [ 4001 4003 4007 ]
[ 4127 4129 4133 ] [ 4517 4519 4523 ] [ 4637 4639 4643 ] [ 4787 4789 4793 ] [ 4931 4933 4937 ]
[ 4967 4969 4973 ] [ 5231 5233 5237 ] [ 5477 5479 5483 ]
Found 43 prime triplets

Mathematica / Wolfram Language 

Cases[Partition[Most@NestWhileList[NextPrime, 2, # < 5500 &], 3, 
   1], _?(Differences[#] == {2, 4} &)] // TableForm
Output:


5   	7   	11
11  	13  	17
17  	19  	23
41  	43  	47
101 	103 	107
107 	109 	113
191 	193 	197
227 	229 	233
311 	313 	317
347 	349 	353
461 	463 	467
641 	643 	647
821 	823 	827
857 	859 	863
881 	883 	887
1091	1093	1097
1277	1279	1283
1301	1303	1307
1427	1429	1433
1481	1483	1487
1487	1489	1493
1607	1609	1613
1871	1873	1877
1997	1999	2003
2081	2083	2087
2237	2239	2243
2267	2269	2273
2657	2659	2663
2687	2689	2693
3251	3253	3257
3461	3463	3467
3527	3529	3533
3671	3673	3677
3917	3919	3923
4001	4003	4007
4127	4129	4133
4517	4519	4523
4637	4639	4643
4787	4789	4793
4931	4933	4937
4967	4969	4973
5231	5233	5237
5477	5479	5483

newLISP 

(define (prime? n) (= 1 (length (factor n))))

(for (n 3 5500)
  (let (trip (list n (+ 2 n) (+ 6 n)))
    (if (for-all prime? trip) (println trip))))



Nim 

import strformat

const
  N = 5500 - 1
  Max = N + 6

# Sieve of Erathosthenes: false (default) is composite.
var composite: array[3..Max, bool]   # Ignore 2 as all primes should be odd.
var n = 3
while true:
  let n2 = n * n
  if n2 > Max: break
  if not composite[n]:
    for k in countup(n2, Max, 2 * n):
      composite[k] = true
  inc n, 2

template isPrime(n: int): bool = not composite[n]

echo "   p  p+2  p+6"
var count = 0
for n in countup(3, N, 2):
  if n.isPrime and (n + 2).isPrime and (n + 6).isPrime:
    echo &"{n:4} {n+2:4} {n+6:4}"
    inc count

echo &"\nFound {count} primes triplets for p < {N+1}."
Output:
   p  p+2  p+6
   5    7   11
  11   13   17
  17   19   23
  41   43   47
 101  103  107
 107  109  113
 191  193  197
 227  229  233
 311  313  317
 347  349  353
 461  463  467
 641  643  647
 821  823  827
 857  859  863
 881  883  887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483

Found 43 primes triplets for p < 5500.

PARI/GP 

for(i=1,5499,if(isprime(i)&&isprime(i+2)&&isprime(i+6),print(i," ",i+2," ",i+6)))

Perl

Library: ntheory
#!/usr/bin/perl

use strict;
use warnings;
use ntheory qw( is_prime twin_primes );

is_prime($_ + 6) and printf "%5d" x 3 . "\n", $_, $_ + 2, $_ + 6
  for @{ twin_primes( 5500 ) };
Output:
    5    7   11
   11   13   17
   17   19   23
   41   43   47
  101  103  107
  107  109  113
  191  193  197
  227  229  233
  311  313  317
  347  349  353
  461  463  467
  641  643  647
  821  823  827
  857  859  863
  881  883  887
 1091 1093 1097
 1277 1279 1283
 1301 1303 1307
 1427 1429 1433
 1481 1483 1487
 1487 1489 1493
 1607 1609 1613
 1871 1873 1877
 1997 1999 2003
 2081 2083 2087
 2237 2239 2243
 2267 2269 2273
 2657 2659 2663
 2687 2689 2693
 3251 3253 3257
 3461 3463 3467
 3527 3529 3533
 3671 3673 3677
 3917 3919 3923
 4001 4003 4007
 4127 4129 4133
 4517 4519 4523
 4637 4639 4643
 4787 4789 4793
 4931 4933 4937
 4967 4969 4973
 5231 5233 5237
 5477 5479 5483

Phix 

function pt(integer p) return is_prime(p+2) and is_prime(p+6) end function
sequence res = filter(get_primes_le(5500),pt)
         res = apply(true,sq_add,{res,{{0,2,6}}})
         res = apply(true,sprintf,{{"(%d %d %d)"},res})
printf(1,"Found %d prime triplets: %s\n",{length(res),join(shorten(res,"",2),", ")})
Output:
Found 43 prime triplets: (5 7 11), (11 13 17), ..., (5231 5233 5237), (5477 5479 5483)


PL/0

PL/0 can only output 1 numeric value per line (and doesn't handle character data at all), so to avoid confusing output, only the first prime of each triplet is shown here. 

var   n, a, prime;
procedure isnprime;
    var p;
    begin
        prime := 1;
        if n < 2 then prime := 0;
        if n > 2 then begin
            prime := 0;
            if odd( n ) then prime := 1;
            p := 3;
            while p * p <= n * prime do begin
               if n - ( ( n / p ) * p ) = 0 then prime := 0;
               p := p + 2;
            end
        end
    end;
begin
    a := 1;
    while a < 5495 do begin
        a := a + 2;
        n := a;
        call isnprime;
        if prime = 1 then begin
            n := a + 2;
            call isnprime;
            if prime = 1 then begin
                n := a + 6;
                call isnprime;
                if prime = 1 then ! a
            end
        end
    end
end.
Output:
          5
         11
         17
         41
        101
        107
        191
        227
        311
        347
        461
        641
        821
        857
        881
       1091
       1277
       1301
       1427
       1481
       1487
       1607
       1871
       1997
       2081
       2237
       2267
       2657
       2687
       3251
       3461
       3527
       3671
       3917
       4001
       4127
       4517
       4637
       4787
       4931
       4967
       5231
       5477

Python 

#!/usr/bin/python

def isPrime(n):
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False        
    return True

if __name__ == '__main__':
    for p in range(3, 5499, 2):
        if not isPrime(p+6):
            continue
        if not isPrime(p+2):
            continue
        if not isPrime(p):
            continue
        print(f'[{p} {p+2} {p+6}]')

Quackery

eratosthenes and isprime are defined at Sieve of Eratosthenes#Quackery. 

  5506 eratosthenes

  [] 5500 4 - times
     [ i^ isprime while
       i^ 2 + isprime while
       i^ 6 + isprime while
       i^ dup 2 + dup 4 +
       join join nested join ]
 dup witheach [ echo cr ]
 cr say "There are "
 size echo say " prime triplets < 5500."
Output:
[ 5 7 11 ]
[ 11 13 17 ]
[ 17 19 23 ]
[ 41 43 47 ]
[ 101 103 107 ]
[ 107 109 113 ]
[ 191 193 197 ]
[ 227 229 233 ]
[ 311 313 317 ]
[ 347 349 353 ]
[ 461 463 467 ]
[ 641 643 647 ]
[ 821 823 827 ]
[ 857 859 863 ]
[ 881 883 887 ]
[ 1091 1093 1097 ]
[ 1277 1279 1283 ]
[ 1301 1303 1307 ]
[ 1427 1429 1433 ]
[ 1481 1483 1487 ]
[ 1487 1489 1493 ]
[ 1607 1609 1613 ]
[ 1871 1873 1877 ]
[ 1997 1999 2003 ]
[ 2081 2083 2087 ]
[ 2237 2239 2243 ]
[ 2267 2269 2273 ]
[ 2657 2659 2663 ]
[ 2687 2689 2693 ]
[ 3251 3253 3257 ]
[ 3461 3463 3467 ]
[ 3527 3529 3533 ]
[ 3671 3673 3677 ]
[ 3917 3919 3923 ]
[ 4001 4003 4007 ]
[ 4127 4129 4133 ]
[ 4517 4519 4523 ]
[ 4637 4639 4643 ]
[ 4787 4789 4793 ]
[ 4931 4933 4937 ]
[ 4967 4969 4973 ]
[ 5231 5233 5237 ]
[ 5477 5479 5483 ]

There are 43 prime triplets < 5500.

Raku

Adapted from Cousin primes

Filter

Favoring brevity over efficiency due to the small range of n, the most concise solution is: 

say grep *.all.is-prime, map { $_, $_+2, $_+6 }, 2..5500;
Output:
((5 7 11) (11 13 17) (17 19 23) (41 43 47) (101 103 107) (107 109 113) (191 193 197) (227 229 233) (311 313 317) (347 349 353) (461 463 467) (641 643 647) (821 823 827) (857 859 863) (881 883 887) (1091 1093 1097) (1277 1279 1283) (1301 1303 1307) (1427 1429 1433) (1481 1483 1487) (1487 1489 1493) (1607 1609 1613) (1871 1873 1877) (1997 1999 2003) (2081 2083 2087) (2237 2239 2243) (2267 2269 2273) (2657 2659 2663) (2687 2689 2693) (3251 3253 3257) (3461 3463 3467) (3527 3529 3533) (3671 3673 3677) (3917 3919 3923) (4001 4003 4007) (4127 4129 4133) (4517 4519 4523) (4637 4639 4643) (4787 4789 4793) (4931 4933 4937) (4967 4969 4973) (5231 5233 5237) (5477 5479 5483))

Infinite List

A more efficient and versatile approach is to generate an infinite list of triple primes, using this info from https://oeis.org/A022004 :

All terms are congruent to 5 (mod 6).
constant @triples = (5, *+6 … *).map: -> \n { $_ if .all.is-prime given (n, n+2, n+6) }

my $count = @triples.first: :k, *.[0] >= 5500;

say .fmt('%4d') for @triples.head($count);
Output:
   5    7   11
  11   13   17
  17   19   23
  41   43   47
 101  103  107
 107  109  113
 191  193  197
 227  229  233
 311  313  317
 347  349  353
 461  463  467
 641  643  647
 821  823  827
 857  859  863
 881  883  887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483

REXX

Modules: How to use
Modules: Source code
As in many other REXX entries, the needed primes are sieved by procedure Primes in Sequences. 

-- 26 Mar 2025
include Settings
numeric digits 10
arg xx
if xx = '' then
   xx = 5500

say 'PRIME TRIPLETS'
say version
say
call GetPrimes xx
call ShowTriplets
exit

GetPrimes:
call Time('r')
arg xx
say 'Analysis for primes up to' xx 'follows'
say
say 'Get primes...'
call Primes xx
say prim.0 'primes found'
say Format(Time('e'),,3) 'seconds'; say
return

ShowTriplets:
call Time('r')
say 'Show triplets...'
p = prim.0; p = prim.p
n = 0; a = prim.1; b = prim.2
do i = 3 to prim.0
   c = prim.i
   if b-a = 2 then do
      if c-a = 6 then do
         n = n+1
         if p > 5500 then
            iterate i
         call Charout, Left('['a b c']',18)
         if n//5 = 0 then
            say
      end
   end
   a = b; b = c
end
say
say n 'triplets found'
say Format(Time('e'),,3) 'seconds'; say
return

include Sequences
include Functions
include Abend
Output:
PRIME TRIPLETS
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024

Analysis for primes up to 5500 follows

Get primes...
725 primes found
0.001 seconds

Show triplets...
[5 7 11]          [11 13 17]        [17 19 23]        [41 43 47]        [101 103 107]
[107 109 113]     [191 193 197]     [227 229 233]     [311 313 317]     [347 349 353]
[461 463 467]     [641 643 647]     [821 823 827]     [857 859 863]     [881 883 887]
[1091 1093 1097]  [1277 1279 1283]  [1301 1303 1307]  [1427 1429 1433]  [1481 1483 1487]
[1487 1489 1493]  [1607 1609 1613]  [1871 1873 1877]  [1997 1999 2003]  [2081 2083 2087]
[2237 2239 2243]  [2267 2269 2273]  [2657 2659 2663]  [2687 2689 2693]  [3251 3253 3257]
[3461 3463 3467]  [3527 3529 3533]  [3671 3673 3677]  [3917 3919 3923]  [4001 4003 4007]
[4127 4129 4133]  [4517 4519 4523]  [4637 4639 4643]  [4787 4789 4793]  [4931 4933 4937]
[4967 4969 4973]  [5231 5233 5237]  [5477 5479 5483]
43 triplets found
0.000 seconds

Analysis for primes up to 1E6 follows

Get primes...
78498 primes found
0.271 seconds

Show triplets...

1360 triplets found
0.030 seconds

Analysis for primes up to 1E7 follows

Get primes...
664579 primes found
3.133 seconds

Show triplets...

8384 triplets found
1.075 seconds

Analysis for primes up to 1E8 follows

Get primes...
5761455 primes found
38.423 seconds

Show triplets...

54904 triplets found
144.341 seconds

Ring 

load "stdlib.ring"
see "working..." + nl
see "Initial members of prime triples (p, p+2, p+6) are:" + nl
see "p p+2 p+6" + nl
row = 0
limit = 5500
 
for n = 1 to limit
    if isprime(n) and isprime(n+2) and isprime(n+6)
       row = row + 1
       see "" + n + " " + (n+2) + " " + (n+6) + nl
    ok
next

see "Found " + row + " primes" + nl
see "done..." + nl
Output:
working...
Initial members of prime triples (p, p+2, p+6) are:
p p+2 p+6
5 7 11
11 13 17
17 19 23
41 43 47
101 103 107
107 109 113
191 193 197
227 229 233
311 313 317
347 349 353
461 463 467
641 643 647
821 823 827
857 859 863
881 883 887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483
Found 43 primes
done...

RPL

Works with: HP version 49
« { } 2 3 5
  WHILE OVER 5500 < REPEAT 
    ROT DROP DUP NEXTPRIME 
    3 DUPN 3 →LIST
    IF DUP ΔLIST { 2 4 } == THEN 
      5 ROLL SWAP 1 →LIST + 4 ROLLD
    ELSE DROP END
  END 
  3 DROPN
» 'TASK' STO
Output:
1: { { 5 7 11 } { 11 13 17 } { 17 19 23 } { 41 43 47 } { 101 103 107 } { 107 109 113 } { 191 193 197 } { 227 229 233 } { 311 313 317 } { 347 349 353 } { 461 463 467 } { 641 643 647 } { 821 823 827 } { 857 859 863 } { 881 883 887 } { 1091 1093 1097 } { 1277 1279 1283 } { 1301 1303 1307 } { 1427 1429 1433 } { 1481 1483 1487 } { 1487 1489 1493 } { 1607 1609 1613 } { 1871 1873 1877 } { 1997 1999 2003 } { 2081 2083 2087 } { 2237 2239 2243 } { 2267 2269 2273 } { 2657 2659 2663 } { 2687 2689 2693 } { 3251 3253 3257 } { 3461 3463 3467 } { 3527 3529 3533 } { 3671 3673 3677 } { 3917 3919 3923 } { 4001 4003 4007 } { 4127 4129 4133 } { 4517 4519 4523 } { 4637 4639 4643 } { 4787 4789 4793 } { 4931 4933 4937 } { 4967 4969 4973 } { 5231 5233 5237 } { 5477 5479 5483 } }

Ruby 

puts Prime.each(5500).each_cons(3).filter_map{|p1,p2,p3|[p1,p2,p3].join(" ") if p2-p1 == 2 && p3-p1 == 6}
Output:
5 7 11
11 13 17
17 19 23
41 43 47
101 103 107
107 109 113
191 193 197
227 229 233
311 313 317
347 349 353
461 463 467
641 643 647
821 823 827
857 859 863
881 883 887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483

Sidef 

say "Values of p such that (p, p+2, p+6) are all prime:"
5500.primes.grep{|p| all_prime(p+2, p+6) }.say
Output:
Values of p such that (p, p+2, p+6) are all prime:
[5, 11, 17, 41, 101, 107, 191, 227, 311, 347, 461, 641, 821, 857, 881, 1091, 1277, 1301, 1427, 1481, 1487, 1607, 1871, 1997, 2081, 2237, 2267, 2657, 2687, 3251, 3461, 3527, 3671, 3917, 4001, 4127, 4517, 4637, 4787, 4931, 4967, 5231, 5477]

Tiny BASIC 

    LET A = 1
 10 LET A = A + 2
    IF A > 5499 THEN END
    LET P = A
    GOSUB 100
    IF Z = 0 THEN GOTO 10
    LET P = A + 2
    GOSUB 100
    IF Z = 0 THEN GOTO 10
    LET P = A + 6
    GOSUB 100
    IF Z = 0 THEN GOTO 10
    PRINT A," ",A+2," ",A+6
    GOTO 10
100 REM PRIMALITY BY TRIAL DIVISION
    LET Z = 1
    LET I = 2
110 IF (P/I)*I = P THEN LET Z = 0
    IF Z = 0 THEN RETURN
    LET I = I + 1
    IF I*I <= P THEN GOTO 110
    RETURN

Wren

Library: Wren-math
Library: Wren-fmt
import "./math" for Int
import "./fmt" for Fmt

var c = Int.primeSieve(5505, false)
var triples = []
System.print("Prime triplets: p, p + 2, p + 6 where p < 5,500:")
var i = 3
while (i < 5500) {
    if (!c[i] && !c[i+2] && !c[i+6]) triples.add([i, i+2, i+6])
    i = i + 2
}
for (triple in triples) Fmt.print("$,6d", triple)
System.print("\nFound %(triples.count) such prime triplets.")
Output:
Prime triplets: p, p + 2, p + 6 where p < 5,500:
     5      7     11
    11     13     17
    17     19     23
    41     43     47
   101    103    107
   107    109    113
   191    193    197
   227    229    233
   311    313    317
   347    349    353
   461    463    467
   641    643    647
   821    823    827
   857    859    863
   881    883    887
 1,091  1,093  1,097
 1,277  1,279  1,283
 1,301  1,303  1,307
 1,427  1,429  1,433
 1,481  1,483  1,487
 1,487  1,489  1,493
 1,607  1,609  1,613
 1,871  1,873  1,877
 1,997  1,999  2,003
 2,081  2,083  2,087
 2,237  2,239  2,243
 2,267  2,269  2,273
 2,657  2,659  2,663
 2,687  2,689  2,693
 3,251  3,253  3,257
 3,461  3,463  3,467
 3,527  3,529  3,533
 3,671  3,673  3,677
 3,917  3,919  3,923
 4,001  4,003  4,007
 4,127  4,129  4,133
 4,517  4,519  4,523
 4,637  4,639  4,643
 4,787  4,789  4,793
 4,931  4,933  4,937
 4,967  4,969  4,973
 5,231  5,233  5,237
 5,477  5,479  5,483

Found 43 such prime triplets.

XPL0 

func IsPrime(N);        \Return 'true' if N is a prime number
int  N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
    if rem(N/I) = 0 then return false;
return true;
];

int Count, P;
[ChOut(0, ^ );
Count:= 0;
P:= 3;
repeat  if IsPrime(P) & IsPrime(P+2) & IsPrime(P+6) then
            [IntOut(0, P);  ChOut(0, ^ );
            IntOut(0, P+2);  ChOut(0, ^ );
            IntOut(0, P+6);  ChOut(0, ^ );
            Count:= Count+1;
            if rem(Count/5) then ChOut(0, 9\tab\) else CrLf(0);
            ];
        P:= P+2;
until   P >= 5500;
CrLf(0);
IntOut(0, Count);
Text(0, " prime triplets found below 5500.
");
]
Output:
 5 7 11         11 13 17        17 19 23        41 43 47        101 103 107 
107 109 113     191 193 197     227 229 233     311 313 317     347 349 353 
461 463 467     641 643 647     821 823 827     857 859 863     881 883 887 
1091 1093 1097  1277 1279 1283  1301 1303 1307  1427 1429 1433  1481 1483 1487 
1487 1489 1493  1607 1609 1613  1871 1873 1877  1997 1999 2003  2081 2083 2087 
2237 2239 2243  2267 2269 2273  2657 2659 2663  2687 2689 2693  3251 3253 3257 
3461 3463 3467  3527 3529 3533  3671 3673 3677  3917 3919 3923  4001 4003 4007 
4127 4129 4133  4517 4519 4523  4637 4639 4643  4787 4789 4793  4931 4933 4937 
4967 4969 4973  5231 5233 5237  5477 5479 5483  
43 prime triplets found below 5500.

Zig

Library: Primesieve
const std = @import("std");
const ps = @cImport({
    @cInclude("primesieve.h");
});

pub fn main() !void {
    var t0 = try std.time.Timer.start();

    const stdout = std.io.getStdOut().writer();

    const limit = 5500;
    var triplet_generator = try PrimeTripletGenerator.init(limit);
    defer triplet_generator.deinit();

    try stdout.writeAll("Primesieve prime triplets:\n");
    var count: usize = 0;
    while (try triplet_generator.next()) |triplet| {
        count += 1;
        try stdout.print("{d:4}, {d:4}, {d:4}\n", .{ triplet[0], triplet[1], triplet[2] });
    }
    try stdout.print("\n{d} triplets less than {d}\n\n", .{ count, limit });

    try stdout.print("Processed in {}\n", .{std.fmt.fmtDuration(t0.read())});
}

const PrimeTripletGeneratorError = error{PrimeSieveError};

const PrimeTripletGenerator = struct {
    stop: u64,
    it: ps.primesieve_iterator,
    prime1: u64,
    prime2: u64,

    fn init(stop: u64) !PrimeTripletGenerator {
        var it: ps.primesieve_iterator = undefined;
        ps.primesieve_init(&it);

        var primes: [2]u64 = undefined;
        for (&primes) |*prime| {
            prime.* = ps.primesieve_next_prime(&it);
            if (it.is_error != 0 or prime.* == ps.PRIMESIEVE_ERROR)
                return PrimeTripletGeneratorError.PrimeSieveError;
        }
        return PrimeTripletGenerator{
            .stop = stop,
            .it = it,
            .prime1 = primes[0],
            .prime2 = primes[1],
        };
    }
    fn deinit(self: *PrimeTripletGenerator) void {
        ps.primesieve_free_iterator(&self.it);
    }
    fn next(self: *PrimeTripletGenerator) !?[3]u64 {
        while (true) {
            const prime = ps.primesieve_next_prime(&self.it);
            if (self.it.is_error != 0 or prime == ps.PRIMESIEVE_ERROR)
                return PrimeTripletGeneratorError.PrimeSieveError;
            if (prime >= self.stop)
                return null;
            const prime0 = self.prime1;
            self.prime1 = self.prime2;
            self.prime2 = prime;
            if ((self.prime1 - prime0) == 2 and (prime - prime0) == 6)
                return .{ prime0, self.prime1, prime };
        }
    }
};
Retrieved from "https://rosettacode.org/wiki/Prime_triplets?oldid=378639"
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