# Prime triplets

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.

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

## 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!

```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:
```(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 [
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

```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;
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;`

```# 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

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,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

### 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;

```
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

```/*REXX program finds prime triplets:  P, P+2, P+6  are primes, and  P < some specified N*/
parse arg hi cols .                              /*obtain optional argument from the CL.*/
if   hi=='' |   hi==","  then   hi= 5500         /*Not specified?  Then use the default.*/
if cols=='' | cols==","  then cols=    4         /* "      "         "   "   "     "    */
call genP hi + 6                                 /*build semaphore array for low primes.*/
do p=1  while @.p<hi
end  /*p*/;           lim= p-1              /*set  LIM   to the  Pth  prime.       */
w= 30                                            /*width of a prime triplet in a column.*/
__= ' ';       @trip= ' prime triplets:  p, p+2, p+6  are primes,  and p  < '   commas(hi)
if cols>0 then say ' index │'center(@trip,   1 + cols*(w+1)     )
if cols>0 then say '───────┼'center(""   ,   1 + cols*(w+1), '─')
Tprimes= 0;                idx= 1                /*initialize # prime triplets  & index.*/
\$=                                               /*a list of  prime triplets  (so far). */
do j=1  to  lim                             /*look for prime triplets within range.*/
p2= @.j + 2;  if \!.p2  then iterate        /*is  P2  prime?    No, then skip it.  */
p6= p2  + 4;  if \!.p6  then iterate        /* "  P6    "        "    "    "   "   */
Tprimes= Tprimes + 1                        /*bump the number of  prime triplets.  */
if cols==0              then iterate        /*Build the list  (to be shown later)? */
@@@= commas(@.j)__ commas(p2)__ commas(p6)  /*add commas & blanks to prime triplet.*/
\$= \$ left( '('@@@")",  w)                   /*add a prime triplet ──► the  \$  list.*/
if Tprimes//cols\==0    then iterate        /*have we populated a line of output?  */
say center(idx, 7)'│' strip(substr(\$, 2), 'T');    \$=   /*show what we have so far.*/
idx= idx + cols                             /*bump the  index  count for the output*/
end   /*j*/

if \$\==''  then say center(idx, 7)"│" strip(substr(\$, 2), 'T')  /*possible show residual*/
if cols>0 then say '───────┴'center(""                         ,  1 + cols*(w+1), '─')
say
say 'Found '       commas(Tprimes)      @trip
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?;  do jc=length(?)-3  to 1  by -3; ?=insert(',', ?, jc); end;  return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: !.= 0;            parse arg limit          /*placeholders for primes (semaphores).*/
@.1=2;  @.2=3;  @.3=5;  @.4=7;  @.5=11     /*define some low primes.              */
!.2=1;  !.3=1;  !.5=1;  !.7=1;  !.11=1     /*   "     "   "    "     flags.       */
#=5;     s.#= @.# **2    /*number of primes so far;     prime². */
/* [↓]  generate more  primes  ≤  high.*/
do j=@.#+2  by 2  to limit               /*find odd primes from here on.        */
parse var j '' -1 _; if     _==5  then iterate  /*J divisible by 5?  (right dig)*/
if j// 3==0  then iterate  /*"     "      " 3?             */
if j// 7==0  then iterate  /*"     "      " 7?             */
/* [↑]  the above  3  lines saves time.*/
do k=5  while s.k<=j              /* [↓]  divide by the known odd primes.*/
if j // @.k == 0  then iterate j  /*Is  J ÷ X?  Then not prime.     ___  */
end   /*k*/                       /* [↑]  only process numbers  ≤  √ J   */
#= #+1;    @.#= j;    s.#= j*j;   !.j= 1 /*bump # of Ps; assign next P;  P²; P# */
end          /*j*/;   return
```
output   when using the default inputs:
``` index │                                  prime triplets:  p, p+2, p+6  are primes,  and p  <  5,500
───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
1   │ (5  7  11)                     (11  13  17)                   (17  19  23)                   (41  43  47)
5   │ (101  103  107)                (107  109  113)                (191  193  197)                (227  229  233)
9   │ (311  313  317)                (347  349  353)                (461  463  467)                (641  643  647)
13   │ (821  823  827)                (857  859  863)                (881  883  887)                (1,091  1,093  1,097)
17   │ (1,277  1,279  1,283)          (1,301  1,303  1,307)          (1,427  1,429  1,433)          (1,481  1,483  1,487)
21   │ (1,487  1,489  1,493)          (1,607  1,609  1,613)          (1,871  1,873  1,877)          (1,997  1,999  2,003)
25   │ (2,081  2,083  2,087)          (2,237  2,239  2,243)          (2,267  2,269  2,273)          (2,657  2,659  2,663)
29   │ (2,687  2,689  2,693)          (3,251  3,253  3,257)          (3,461  3,463  3,467)          (3,527  3,529  3,533)
33   │ (3,671  3,673  3,677)          (3,917  3,919  3,923)          (4,001  4,003  4,007)          (4,127  4,129  4,133)
37   │ (4,517  4,519  4,523)          (4,637  4,639  4,643)          (4,787  4,789  4,793)          (4,931  4,933  4,937)
41   │ (4,967  4,969  4,973)          (5,231  5,233  5,237)          (5,477  5,479  5,483)
───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  43  prime triplets:  p, p+2, p+6  are primes,  and p  <  5,500
```

## 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
```
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.
```