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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 = 0L(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 [        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.AWKBEGIN {    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 Trueend 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 pend`

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 #TrueEndProcedure 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 pPrintN(#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 Trueend 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 pend`

Factor

Works with: Factor version 0.98
`USING: arrays kernel lists lists.lazy math math.primesmath.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]

```

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 220 P = A30 GOSUB 100040 IF Z = 0 THEN GOTO 50050 P = A + 260 GOSUB 100070 IF Z = 0 THEN GOTO 50080 P = A + 690 GOSUB 1000100 IF Z = 1 THEN PRINT A,A+2,A+6500 NEXT A510 END1000 Z = 1 : I = 21010 IF P MOD I = 0 THEN Z = 0 : RETURN1020 I = I + 11030 IF I*I > P THEN RETURN1040 GOTO 1010`

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 primedef 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]
```

Mathematica / Wolfram Language

`Cases[Partition[[email protected][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

```

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 = 3while 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 = 0for 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)
```

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}]')`

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; 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

`/*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), '─')saysay 'Found '       commas(Tprimes)      @tripexit 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 [email protected].#+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..." + nlsee "Initial members of prime triples (p, p+2, p+6) are:" + nlsee "p p+2 p+6" + nlrow = 0limit = 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    oknext see "Found " + row + " primes" + nlsee "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...

```

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 10100 REM PRIMALITY BY TRIAL DIVISION    LET Z = 1    LET I = 2110 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 Intimport "/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 = 3while (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 numberint  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.
```