# Triplet of three numbers

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Triplet of three numbers 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.

Numbers   n   such that the three numbers   n-1,   n+3,   and   n+5   are all prime,   where   n < 6,000.

## 11l

Translation of: Python
```V n = 6000
V p = [0B] * 6000

L(i) 2 .< Int(round(sqrt(n)))
I !p[i]
L(j) (i * 2 .< n).step(i)
p[j] = 1B

L(i) 3 .< n
I (p[i - 1] | p[i + 3] | p[i + 5])
L.continue
E
print(f:‘{i:4}: {i - 1:4} {i + 3:4} {i + 5:4}’)```
Output:
```   8:    7   11   13
14:   13   17   19
38:   37   41   43
68:   67   71   73
98:   97  101  103
104:  103  107  109
194:  193  197  199
224:  223  227  229
278:  277  281  283
308:  307  311  313
458:  457  461  463
614:  613  617  619
824:  823  827  829
854:  853  857  859
878:  877  881  883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743
```

## Action!

```INCLUDE "H6:SIEVE.ACT"

PROC Main()
DEFINE MAX="5999"
BYTE ARRAY primes(MAX+1)
INT i,count=[0]

Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
FOR i=3 TO MAX-5
DO
IF primes(i-1)=1 AND primes(i+3)=1 AND primes(i+5)=1 THEN
PrintF("(%I,%I,%I) ",i-1,i+3,i+5)
count==+1
FI
OD
PrintF("%E%EThere are %I triplets",count)
RETURN```
Output:
```(7,11,13) (13,17,19) (37,41,43) (67,71,73) (97,101,103) (103,107,109) (193,197,199) (223,227,229) (277,281,283)
(307,311,313) (457,461,463) (613,617,619) (823,827,829) (853,857,859) (877,881,883) (1087,1091,1093)
(1297,1301,1303) (1423,1427,1429) (1447,1451,1453) (1483,1487,1489) (1663,1667,1669) (1693,1697,1699)
(1783,1787,1789) (1867,1871,1873) (1873,1877,1879) (1993,1997,1999) (2083,2087,2089) (2137,2141,2143)
(2377,2381,2383) (2683,2687,2689) (2707,2711,2713) (2797,2801,2803) (3163,3167,3169) (3253,3257,3259)
(3457,3461,3463) (3463,3467,3469) (3847,3851,3853) (4153,4157,4159) (4513,4517,4519) (4783,4787,4789)
(5227,5231,5233) (5413,5417,5419) (5437,5441,5443) (5647,5651,5653) (5653,5657,5659) (5737,5741,5743)

There are 46 triplets
```

```with Ada.Text_Io;

procedure Triplets is

Limit : constant := 5999;
Prime : array (1 .. Limit + 5) of Boolean := (others => True);

procedure Fill_Primes is
begin
Prime (1) := False;
for N in 2 .. Limit loop
if Prime (N) then
for I in 2 .. Positive'Last loop
exit when I * N not in Prime'Range;
Prime (I * N) := False;
end loop;
end if;
end loop;
end Fill_Primes;

function Is_Triplet (N : Natural) return Boolean is
begin
return
Prime (N - 1) and then
Prime (N + 3) and then
Prime (N + 5);
end Is_Triplet;

package Natural_Io is new Ada.Text_Io.Integer_Io (Natural);
begin
Natural_Io.Default_Width := 5;
Fill_Primes;

for N in 2 .. Limit loop
if Is_Triplet (N) then
Put (N, Width => 4);
Put (":");
Put (N - 1);
Put (N + 3);
Put (N + 5);
New_Line;
end if;
end loop;
end Triplets;
```
Output:
```   8:    7   11   13
14:   13   17   19
38:   37   41   43
68:   67   71   73
98:   97  101  103
104:  103  107  109
194:  193  197  199
224:  223  227  229
278:  277  281  283
308:  307  311  313
458:  457  461  463
614:  613  617  619
824:  823  827  829
854:  853  857  859
878:  877  881  883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743
```

## ALGOL 68

```BEGIN # find numbers n where n-1, n+3 and n+5 are prime                    #
# sieve the primes up to the maximum number for the task #
[]BOOL prime = PRIMESIEVE 6000;
# returns a string represention of n #
OP TOSTRING = ( INT n )STRING: whole( n, 0 );
# look for suitable numbers #
# 2 is clearly not a member of the required numbers, so we start at 3 #
INT n count := 0;
FOR n FROM 3 TO UPB prime - 5 DO
IF prime[ n - 1 ] AND prime[ n + 3 ] AND prime[ n + 5 ] THEN
print( ( " (", TOSTRING n, " | ", TOSTRING ( n - 1 ), ", ", TOSTRING ( n + 3 ), ", ", TOSTRING ( n + 5 ), ")" ) );
n count +:= 1;
IF n count MOD 4 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline, "Found ", TOSTRING n count, " triplets", newline ) )
END```
Output:
``` (8 | 7, 11, 13) (14 | 13, 17, 19) (38 | 37, 41, 43) (68 | 67, 71, 73)
(98 | 97, 101, 103) (104 | 103, 107, 109) (194 | 193, 197, 199) (224 | 223, 227, 229)
(278 | 277, 281, 283) (308 | 307, 311, 313) (458 | 457, 461, 463) (614 | 613, 617, 619)
(824 | 823, 827, 829) (854 | 853, 857, 859) (878 | 877, 881, 883) (1088 | 1087, 1091, 1093)
(1298 | 1297, 1301, 1303) (1424 | 1423, 1427, 1429) (1448 | 1447, 1451, 1453) (1484 | 1483, 1487, 1489)
(1664 | 1663, 1667, 1669) (1694 | 1693, 1697, 1699) (1784 | 1783, 1787, 1789) (1868 | 1867, 1871, 1873)
(1874 | 1873, 1877, 1879) (1994 | 1993, 1997, 1999) (2084 | 2083, 2087, 2089) (2138 | 2137, 2141, 2143)
(2378 | 2377, 2381, 2383) (2684 | 2683, 2687, 2689) (2708 | 2707, 2711, 2713) (2798 | 2797, 2801, 2803)
(3164 | 3163, 3167, 3169) (3254 | 3253, 3257, 3259) (3458 | 3457, 3461, 3463) (3464 | 3463, 3467, 3469)
(3848 | 3847, 3851, 3853) (4154 | 4153, 4157, 4159) (4514 | 4513, 4517, 4519) (4784 | 4783, 4787, 4789)
(5228 | 5227, 5231, 5233) (5414 | 5413, 5417, 5419) (5438 | 5437, 5441, 5443) (5648 | 5647, 5651, 5653)
(5654 | 5653, 5657, 5659) (5738 | 5737, 5741, 5743)
Found 46 triplets
```

## Arturo

```lst: select 3..6000 'x
-> all? @[prime? x-1 prime? x+3 prime? x+5]

loop split.every: 10 lst 'a ->
print map a => [pad to :string & 5]
```
Output:
```    8    14    38    68    98   104   194   224   278   308
458   614   824   854   878  1088  1298  1424  1448  1484
1664  1694  1784  1868  1874  1994  2084  2138  2378  2684
2708  2798  3164  3254  3458  3464  3848  4154  4514  4784
5228  5414  5438  5648  5654  5738```

## AWK

```# syntax: GAWK -f TRIPLET_OF_THREE_NUMBERS.AWK
BEGIN {
start = 1
stop = 6000
print("   N   N-1  N+3  N+5")
print("----- ---- ---- ----")
for (i=start; i<=stop; i++) {
if (is_prime(i-1) && is_prime(i+3) && is_prime(i+5)) {
printf("%4d: %4d %4d %4d\n",i,i-1,i+3,i+5)
count++
}
}
printf("Triplet of three numbers %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:
```   N   N-1  N+3  N+5
----- ---- ---- ----
8:    7   11   13
14:   13   17   19
38:   37   41   43
68:   67   71   73
98:   97  101  103
104:  103  107  109
194:  193  197  199
224:  223  227  229
278:  277  281  283
308:  307  311  313
458:  457  461  463
614:  613  617  619
824:  823  827  829
854:  853  857  859
878:  877  881  883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743
Triplet of three numbers 1-6000: 46
```

## BASIC

```10 DEFINT A-Z: N=6000
20 DIM P(N+5)
30 FOR I=2 TO SQR(N)
40 IF NOT P(I) THEN FOR J=I*2 TO N STEP I: P(J)=1: NEXT
50 NEXT
60 FOR I=3 TO N
70 IF P(I-1) OR P(I+3) OR P(I+5) GOTO 90
80 PRINT USING "####,: ####, ####, ####,";I;I-1;I+3;I+5
90 NEXT
```
Output:
```    8:     7    11    13
14:    13    17    19
38:    37    41    43
68:    67    71    73
98:    97   101   103
104:   103   107   109
194:   193   197   199
224:   223   227   229
278:   277   281   283
308:   307   311   313
458:   457   461   463
614:   613   617   619
824:   823   827   829
854:   853   857   859
878:   877   881   883
1,088: 1,087 1,091 1,093
1,298: 1,297 1,301 1,303
1,424: 1,423 1,427 1,429
1,448: 1,447 1,451 1,453
1,484: 1,483 1,487 1,489
1,664: 1,663 1,667 1,669
1,694: 1,693 1,697 1,699
1,784: 1,783 1,787 1,789
1,868: 1,867 1,871 1,873
1,874: 1,873 1,877 1,879
1,994: 1,993 1,997 1,999
2,084: 2,083 2,087 2,089
2,138: 2,137 2,141 2,143
2,378: 2,377 2,381 2,383
2,684: 2,683 2,687 2,689
2,708: 2,707 2,711 2,713
2,798: 2,797 2,801 2,803
3,164: 3,163 3,167 3,169
3,254: 3,253 3,257 3,259
3,458: 3,457 3,461 3,463
3,464: 3,463 3,467 3,469
3,848: 3,847 3,851 3,853
4,154: 4,153 4,157 4,159
4,514: 4,513 4,517 4,519
4,784: 4,783 4,787 4,789
5,228: 5,227 5,231 5,233
5,414: 5,413 5,417 5,419
5,438: 5,437 5,441 5,443
5,648: 5,647 5,651 5,653
5,654: 5,653 5,657 5,659
5,738: 5,737 5,741 5,743```

## BASIC256

Translation of: FreeBASIC
```N = 6000
dim p(N+6)

for i = 2 to sqr(N)
if not p[i] then
for j = i*2 to N step i
p[j] = 1
next j
end if
next i

for i = 3 to N
if (p[i-1] or p[i+3] or p[i+5]) then
# en BASIC256 no exite un comando CONTINUE
else
print i; ": "; i-1; "  "; i+3; "  "; i+5
end if
next i
end```
Output:
```Similar a la entrada de FreeBASIC.
```

## BCPL

```get "libhdr"
manifest \$( limit = 6000 \$)

let sieve(p, n) be
\$(  p!0 := false
p!1 := false
for i=2 to n do p!i := true
for i=2 to n/2
if p!i
\$(  let j = i*2
while j <= n
\$(  p!j := false
j := j+i
\$)
\$)
\$)

let triplet(p, n) = n>=2 & p!(n-1) & p!(n+3) & p!(n+5)

let start() be
\$(  let prime = getvec(limit)
sieve(prime, limit)
for i=2 to limit
if triplet(prime, i) do
writef("%I4: %I4, %I4, %I4*N", i, i-1, i+3, i+5)
freevec(prime)
\$)```
Output:
```   8:    7,   11,   13
14:   13,   17,   19
38:   37,   41,   43
68:   67,   71,   73
98:   97,  101,  103
104:  103,  107,  109
194:  193,  197,  199
224:  223,  227,  229
278:  277,  281,  283
308:  307,  311,  313
458:  457,  461,  463
614:  613,  617,  619
824:  823,  827,  829
854:  853,  857,  859
878:  877,  881,  883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## C

```#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

#define LIMIT 6000

char *primes(unsigned int limit) {
char *p = malloc(limit + 1);
int i, j, sqr = sqrt(limit);

p[0] = p[1] = 0;
memset(p+2, 1, limit-1);
for (i=2; i<=sqr; i++)
if (p[i])
for (j=i*2; j<=limit; j+=i)
p[j] = 0;

return p;
}

int triplet(const char *p, unsigned int n) {
return n >= 2 && p[n-1] && p[n+3] && p[n+5];
}

int main() {
char *p = primes(LIMIT+5);
int i;

for (i=2; i<LIMIT; i++)
if (triplet(p, i))
printf("%4d: %4d, %4d, %4d\n", i, i-1, i+3, i+5);

free(p);
return 0;
}
```
Output:
```   8:    7,   11,   13
14:   13,   17,   19
38:   37,   41,   43
68:   67,   71,   73
98:   97,  101,  103
104:  103,  107,  109
194:  193,  197,  199
224:  223,  227,  229
278:  277,  281,  283
308:  307,  311,  313
458:  457,  461,  463
614:  613,  617,  619
824:  823,  827,  829
854:  853,  857,  859
878:  877,  881,  883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## C++

Translation of: C
```#include <iostream>
#include <vector>

constexpr unsigned int LIMIT = 6000;

std::vector<bool> primes(unsigned int limit) {
std::vector<bool> p(limit + 1, true);
unsigned int root = std::sqrt(limit);

p[0] = false;
p[1] = false;

for (size_t i = 2; i <= root; i++) {
if (p[i]) {
for (size_t j = 2 * i; j <= limit; j += i) {
p[j] = false;
}
}
}

return p;
}

bool triplet(const std::vector<bool> &p, unsigned int n) {
return n >= 2 && p[n - 1] && p[n + 3] && p[n + 5];
}

int main() {
std::vector<bool> p = primes(LIMIT);

for (size_t i = 2; i < LIMIT; i++) {
if (triplet(p, i)) {
printf("%4d: %4d, %4d, %4d\n", i, i - 1, i + 3, i + 5);
}
}

return 0;
}
```
Output:
```   8:    7,   11,   13
14:   13,   17,   19
38:   37,   41,   43
68:   67,   71,   73
98:   97,  101,  103
104:  103,  107,  109
194:  193,  197,  199
224:  223,  227,  229
278:  277,  281,  283
308:  307,  311,  313
458:  457,  461,  463
614:  613,  617,  619
824:  823,  827,  829
854:  853,  857,  859
878:  877,  881,  883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## C#

How about some upper limits above 6000?

```using System; using System.Collections.Generic; using System.Linq;
using T3 = System.Tuple<int, int, int>; using static System.Console;
class Program { static void Main() {
WriteLine(" \"N\":  Prime Triplet    Adjacent (to previous)\n" +
" ---- ----------------- -----------------------");
foreach(var lmt in new double[]{6e3, 1e5, 1e6, 1e7, 1e8}) {
var pr = PG.Primes((int)lmt); int l = 0, c = 0; bool a;
foreach (var t in pr) { c += (a = l == t.Item1) ? 1 : 0;
if (lmt < 1e5) WriteLine("{0,4}: {1,-18} {2}",
t.Item1 + 1, t, a ? " *" : ""); l = t.Item3; }
Console.WriteLine ("Up to {0:n0} there are {1:n0} prime triples, " +
"of which {2:n0} were found to be adjacent.", lmt, pr.Count(), c); } } }

class PG { static bool[] f; static bool isPrT(int x, int y, int z) {
if (x < 7) return false; return !f[x] && !f[y] && !f[z]; }
public static IEnumerable<T3> Primes(int l) { f = new bool[l += 6];
int j, lj, llj, lllj; j = lj = llj = lllj = 3;
for (int d = 8, s = 9; s < l; lllj = llj, llj = lj, lj = j, j += 2, s += d += 8)
if (!f[j]) { if (isPrT(lllj, lj, j)) yield return new T3(lllj, lj, j);
for (int k = s, i = j << 1; k < l; k += i) f[k] = true; }
for (; j < l; lllj = llj, llj = lj, lj = j, j += 2)
if (isPrT(lllj, lj, j)) yield return new T3(lllj, lj, j); } }
```
Output:
``` "N":  Prime Triplet    Adjacent (to previous)
---- ----------------- -----------------------
8: (7, 11, 13)
14: (13, 17, 19)        *
38: (37, 41, 43)
68: (67, 71, 73)
98: (97, 101, 103)
104: (103, 107, 109)     *
194: (193, 197, 199)
224: (223, 227, 229)
278: (277, 281, 283)
308: (307, 311, 313)
458: (457, 461, 463)
614: (613, 617, 619)
824: (823, 827, 829)
854: (853, 857, 859)
878: (877, 881, 883)
1088: (1087, 1091, 1093)
1298: (1297, 1301, 1303)
1424: (1423, 1427, 1429)
1448: (1447, 1451, 1453)
1484: (1483, 1487, 1489)
1664: (1663, 1667, 1669)
1694: (1693, 1697, 1699)
1784: (1783, 1787, 1789)
1868: (1867, 1871, 1873)
1874: (1873, 1877, 1879)  *
1994: (1993, 1997, 1999)
2084: (2083, 2087, 2089)
2138: (2137, 2141, 2143)
2378: (2377, 2381, 2383)
2684: (2683, 2687, 2689)
2708: (2707, 2711, 2713)
2798: (2797, 2801, 2803)
3164: (3163, 3167, 3169)
3254: (3253, 3257, 3259)
3458: (3457, 3461, 3463)
3464: (3463, 3467, 3469)  *
3848: (3847, 3851, 3853)
4154: (4153, 4157, 4159)
4514: (4513, 4517, 4519)
4784: (4783, 4787, 4789)
5228: (5227, 5231, 5233)
5414: (5413, 5417, 5419)
5438: (5437, 5441, 5443)
5648: (5647, 5651, 5653)
5654: (5653, 5657, 5659)  *
5738: (5737, 5741, 5743)
Up to 6,000 there are 46 prime triples, of which 5 were found to be adjacent.
Up to 100,000 there are 248 prime triples, of which 11 were found to be adjacent.
Up to 1,000,000 there are 1,444 prime triples, of which 31 were found to be adjacent.
Up to 10,000,000 there are 8,677 prime triples, of which 161 were found to be adjacent.
Up to 100,000,000 there are 55,556 prime triples, of which 686 were found to be adjacent.
```

## CLU

```LIMIT = 6000

isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then return(s) end
x1: int := (x0 + s/x0)/2
while x1 < x0 do
x0 := x1
x1 := (x0 + s/x0)/2
end
return(x0)
end isqrt

sieve = proc (n: int) returns (array[bool])
prime: array[bool] := array[bool]\$fill(2,n-1,true)
for p: int in int\$from_to(2,isqrt(n)) do
if prime[p] then
for c: int in int\$from_to_by(p*p,n,p) do
prime[c] := false
end
end
end
return(prime)
end sieve

triplet = proc (n: int, prime: array[bool]) returns (bool)
return(prime[n-1] & prime[n+3] & prime[n+5])
except when bounds: return(false) end
end triplet

start_up = proc ()
po: stream := stream\$primary_output()
prime: array[bool] := sieve(LIMIT)
for i: int in int\$from_to(2,LIMIT) do
if triplet(i, prime) then
stream\$putright(po, int\$unparse(i), 4)
stream\$puts(po, ": ")
stream\$putright(po, int\$unparse(i-1), 4)
stream\$puts(po, ", ")
stream\$putright(po, int\$unparse(i+3), 4)
stream\$puts(po, ", ")
stream\$putright(po, int\$unparse(i+5), 4)
stream\$putl(po, "")
end
end
end start_up```
Output:
```   8:    7,   11,   13
14:   13,   17,   19
38:   37,   41,   43
68:   67,   71,   73
98:   97,  101,  103
104:  103,  107,  109
194:  193,  197,  199
224:  223,  227,  229
278:  277,  281,  283
308:  307,  311,  313
458:  457,  461,  463
614:  613,  617,  619
824:  823,  827,  829
854:  853,  857,  859
878:  877,  881,  883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## Comal

```0010 lim#:=6000
0020 DIM prime#(lim#)
0030 FOR i#:=2 TO lim# DO prime#(i#):=TRUE
0040 FOR p#:=2 TO INT(SQR(lim#)) DO
0050   FOR c#:=p#^2 TO lim# STEP p# DO prime#(c#):=FALSE
0060 ENDFOR p#
0070 FOR i#:=2 TO lim#-5 DO
0080   IF prime#(i#-1) AND prime#(i#+3) AND prime#(i#+5) THEN
0090     PRINT USING "####: ####, ####, ####":i#,i#-1,i#+3,i#+5
0100   ENDIF
0110 ENDFOR i#
0120 END
```
Output:
```   8:    7,   11,   13
14:   13,   17,   19
38:   37,   41,   43
68:   67,   71,   73
98:   97,  101,  103
104:  103,  107,  109
194:  193,  197,  199
224:  223,  227,  229
278:  277,  281,  283
308:  307,  311,  313
458:  457,  461,  463
614:  613,  617,  619
824:  823,  827,  829
854:  853,  857,  859
878:  877,  881,  883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## Cowgol

```include "cowgol.coh";

const LIMIT := 6000;

var prime: uint8[LIMIT+5];
var i: @indexof prime;
var j: @indexof prime;

prime[0] := 0;
prime[1] := 0;
MemSet(&prime[2], 1, @bytesof prime-2);
i := 2;
while i <= @sizeof prime/2-1 loop
if prime[i] != 0 then
j := i*2;
while j <= @sizeof prime-1 loop
prime[j] := 0;
j := j+i;
end loop;
end if;
i := i+1;
end loop;

i := 2;
while i < LIMIT loop
if prime[i-1] & prime[i+3] & prime[i+5] != 0 then
print_i32(i as uint32);
print(": ");
print_i32(i as uint32-1);
print(", ");
print_i32(i as uint32+3);
print(", ");
print_i32(i as uint32+5);
print_nl();
end if;
i := i + 1;
end loop;```
Output:
```8: 7, 11, 13
14: 13, 17, 19
38: 37, 41, 43
68: 67, 71, 73
98: 97, 101, 103
104: 103, 107, 109
194: 193, 197, 199
224: 223, 227, 229
278: 277, 281, 283
308: 307, 311, 313
458: 457, 461, 463
614: 613, 617, 619
824: 823, 827, 829
854: 853, 857, 859
878: 877, 881, 883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## Delphi

Works with: Delphi version 6.0

Uses the Delphi Prime-Generator Object

```procedure ShowTriplePrimes(Memo: TMemo);
var I: integer;
var Sieve: TPrimeSieve;
begin
Sieve:=TPrimeSieve.Create;
try
Sieve.Intialize(10000);
for I:=1 to 6000-1 do
begin
if Sieve.Flags[I-1] and
Sieve.Flags[I+3] and
Sieve.Flags[I+5] then
begin
end;
end;

finally Sieve.Free; end;
end;
```
Output:
```   8:    7   11   13
14:   13   17   19
38:   37   41   43
68:   67   71   73
98:   97  101  103
104:  103  107  109
194:  193  197  199
224:  223  227  229
278:  277  281  283
308:  307  311  313
458:  457  461  463
614:  613  617  619
824:  823  827  829
854:  853  857  859
878:  877  881  883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743

Elapsed Time: 96.852 ms.
```

## EasyLang

Translation of: BASIC256
```n = 6000
len p[] n + 4
for i = 2 to sqrt len p[]
if p[i] = 0
for j = i * 2 step i to len p[]
p[j] = 1
.
.
.
for i = 3 to n - 1
if p[i - 1] = 0 and p[i + 3] = 0 and p[i + 5] = 0
print i & ": " & i - 1 & " " & i + 3 & " " & i + 5
.
.```

## F#

This task uses Extensible Prime Generator (F#)

```// Prime triplets: Nigel Galloway. May 18th., 2021
primes32()|>Seq.takeWhile((>)6000)|>Seq.filter(fun n->isPrime(n+4)&&isPrime(n+6))|>Seq.iter((+)1>>printf "%d "); printfn ""
```
Output:
```8 14 38 68 98 104 194 224 278 308 458 614 824 854 878 1088 1298 1424 1448 1484 1664 1694 1784 1868 1874 1994 2084 2138 2378 2684 2708 2798 3164 3254 3458 3464 3848 4154 4514 4784 5228 5414 5438 5648 5654 5738
```

## Factor

Works with: Factor version 0.99 2021-02-05
```USING: combinators formatting grouping kernel math math.primes
math.statistics sequences ;

: 4,2-gaps ( upto -- seq )
4 + primes-upto 3 <clumps>
[ differences { 4 2 } sequence= ] filter ;

: triplet. ( 1 n 2 3 -- )
"..., %4d, [%4d], __, __, %4d, __, %4d, ...\n" printf ;

6000 4,2-gaps [ first3 [ dup 1 + ] 2dip triplet. ] each
```
Output:
```...,    7, [   8], __, __,   11, __,   13, ...
...,   13, [  14], __, __,   17, __,   19, ...
...,   37, [  38], __, __,   41, __,   43, ...
...,   67, [  68], __, __,   71, __,   73, ...
...,   97, [  98], __, __,  101, __,  103, ...
...,  103, [ 104], __, __,  107, __,  109, ...
...,  193, [ 194], __, __,  197, __,  199, ...
...,  223, [ 224], __, __,  227, __,  229, ...
...,  277, [ 278], __, __,  281, __,  283, ...
...,  307, [ 308], __, __,  311, __,  313, ...
...,  457, [ 458], __, __,  461, __,  463, ...
...,  613, [ 614], __, __,  617, __,  619, ...
...,  823, [ 824], __, __,  827, __,  829, ...
...,  853, [ 854], __, __,  857, __,  859, ...
...,  877, [ 878], __, __,  881, __,  883, ...
..., 1087, [1088], __, __, 1091, __, 1093, ...
..., 1297, [1298], __, __, 1301, __, 1303, ...
..., 1423, [1424], __, __, 1427, __, 1429, ...
..., 1447, [1448], __, __, 1451, __, 1453, ...
..., 1483, [1484], __, __, 1487, __, 1489, ...
..., 1663, [1664], __, __, 1667, __, 1669, ...
..., 1693, [1694], __, __, 1697, __, 1699, ...
..., 1783, [1784], __, __, 1787, __, 1789, ...
..., 1867, [1868], __, __, 1871, __, 1873, ...
..., 1873, [1874], __, __, 1877, __, 1879, ...
..., 1993, [1994], __, __, 1997, __, 1999, ...
..., 2083, [2084], __, __, 2087, __, 2089, ...
..., 2137, [2138], __, __, 2141, __, 2143, ...
..., 2377, [2378], __, __, 2381, __, 2383, ...
..., 2683, [2684], __, __, 2687, __, 2689, ...
..., 2707, [2708], __, __, 2711, __, 2713, ...
..., 2797, [2798], __, __, 2801, __, 2803, ...
..., 3163, [3164], __, __, 3167, __, 3169, ...
..., 3253, [3254], __, __, 3257, __, 3259, ...
..., 3457, [3458], __, __, 3461, __, 3463, ...
..., 3463, [3464], __, __, 3467, __, 3469, ...
..., 3847, [3848], __, __, 3851, __, 3853, ...
..., 4153, [4154], __, __, 4157, __, 4159, ...
..., 4513, [4514], __, __, 4517, __, 4519, ...
..., 4783, [4784], __, __, 4787, __, 4789, ...
..., 5227, [5228], __, __, 5231, __, 5233, ...
..., 5413, [5414], __, __, 5417, __, 5419, ...
..., 5437, [5438], __, __, 5441, __, 5443, ...
..., 5647, [5648], __, __, 5651, __, 5653, ...
..., 5653, [5654], __, __, 5657, __, 5659, ...
..., 5737, [5738], __, __, 5741, __, 5743, ...
```

## Forth

Works with: Gforth
```: prime? ( n -- ? ) here + c@ 0= ;
: notprime! ( n -- ) here + 1 swap c! ;

: prime_sieve { n -- }
here n erase
0 notprime!
1 notprime!
n 4 > if
n 4 do i notprime! 2 +loop
then
3
begin
dup dup * n <
while
dup prime? if
n over dup * do
i notprime!
dup 2* +loop
then
2 +
repeat
drop ;

: main { n -- }
."    N    N-1   N+3   N+5" cr
n prime_sieve
0
n 1 do
i 1- prime? if
i 3 + prime? if
i 5 + prime? if
i 4 .r ." :"
i 1-  6 .r
i 3 + 6 .r
i 5 + 6 .r cr
1+
then
then
then
loop
cr ." Count: " . cr ;

6000 main
bye
```
Output:
```   N    N-1   N+3   N+5
8:     7    11    13
14:    13    17    19
38:    37    41    43
68:    67    71    73
98:    97   101   103
104:   103   107   109
194:   193   197   199
224:   223   227   229
278:   277   281   283
308:   307   311   313
458:   457   461   463
614:   613   617   619
824:   823   827   829
854:   853   857   859
878:   877   881   883
1088:  1087  1091  1093
1298:  1297  1301  1303
1424:  1423  1427  1429
1448:  1447  1451  1453
1484:  1483  1487  1489
1664:  1663  1667  1669
1694:  1693  1697  1699
1784:  1783  1787  1789
1868:  1867  1871  1873
1874:  1873  1877  1879
1994:  1993  1997  1999
2084:  2083  2087  2089
2138:  2137  2141  2143
2378:  2377  2381  2383
2684:  2683  2687  2689
2708:  2707  2711  2713
2798:  2797  2801  2803
3164:  3163  3167  3169
3254:  3253  3257  3259
3458:  3457  3461  3463
3464:  3463  3467  3469
3848:  3847  3851  3853
4154:  4153  4157  4159
4514:  4513  4517  4519
4784:  4783  4787  4789
5228:  5227  5231  5233
5414:  5413  5417  5419
5438:  5437  5441  5443
5648:  5647  5651  5653
5654:  5653  5657  5659
5738:  5737  5741  5743

Count: 46
```

## FreeBASIC

```Dim As Integer N = 6000
Dim As Integer p(N)

For i As Integer = 2 To Sqr(N)
If Not p(i) Then
For j As Integer = i * 2 To N Step i
p(j) = 1
Next j
End If
Next i
For i As Integer = 3 To N
If (p(i-1) Or p(i+3) Or p(i+5)) Then
Continue For
Else
Print Using "####,: ####, ####, ####,"; i; i-1; i+3; i+5
End If
Next i
Sleep```
```    8:     7    11    13
14:    13    17    19
38:    37    41    43
68:    67    71    73
98:    97   101   103
104:   103   107   109
194:   193   197   199
224:   223   227   229
278:   277   281   283
308:   307   311   313
458:   457   461   463
614:   613   617   619
824:   823   827   829
854:   853   857   859
878:   877   881   883
1,088: 1,087 1,091 1,093
1,298: 1,297 1,301 1,303
1,424: 1,423 1,427 1,429
1,448: 1,447 1,451 1,453
1,484: 1,483 1,487 1,489
1,664: 1,663 1,667 1,669
1,694: 1,693 1,697 1,699
1,784: 1,783 1,787 1,789
1,868: 1,867 1,871 1,873
1,874: 1,873 1,877 1,879
1,994: 1,993 1,997 1,999
2,084: 2,083 2,087 2,089
2,138: 2,137 2,141 2,143
2,378: 2,377 2,381 2,383
2,684: 2,683 2,687 2,689
2,708: 2,707 2,711 2,713
2,798: 2,797 2,801 2,803
3,164: 3,163 3,167 3,169
3,254: 3,253 3,257 3,259
3,458: 3,457 3,461 3,463
3,464: 3,463 3,467 3,469
3,848: 3,847 3,851 3,853
4,154: 4,153 4,157 4,159
4,514: 4,513 4,517 4,519
4,784: 4,783 4,787 4,789
5,228: 5,227 5,231 5,233
5,414: 5,413 5,417 5,419
5,438: 5,437 5,441 5,443
5,648: 5,647 5,651 5,653
5,654: 5,653 5,657 5,659
5,738: 5,737 5,741 5,743
```

## Go

Translation of: Wren
Library: Go-rcu
```package main

import (
"fmt"
"rcu"
)

func main() {
c := rcu.PrimeSieve(6003, false)
var numbers []int
fmt.Println("Numbers n < 6000 where: n - 1, n + 3, n + 5 are all primes:")
for n := 4; n < 6000; n += 2 {
if !c[n-1] && !c[n+3] && !c[n+5] {
numbers = append(numbers, n)
}
}
for _, n := range numbers {
fmt.Printf("%6s  => ", rcu.Commatize(n))
for _, p := range []int{n - 1, n + 3, n + 5} {
fmt.Printf("%6s ", rcu.Commatize(p))
}
fmt.Println()
}
fmt.Printf("\n%d such numbers found.\n", len(numbers))
}
```
Output:
```Numbers n < 6000 where: n - 1, n + 3, n + 5 are all primes:
8  =>      7     11     13
14  =>     13     17     19
38  =>     37     41     43
68  =>     67     71     73
98  =>     97    101    103
104  =>    103    107    109
194  =>    193    197    199
224  =>    223    227    229
278  =>    277    281    283
308  =>    307    311    313
458  =>    457    461    463
614  =>    613    617    619
824  =>    823    827    829
854  =>    853    857    859
878  =>    877    881    883
1,088  =>  1,087  1,091  1,093
1,298  =>  1,297  1,301  1,303
1,424  =>  1,423  1,427  1,429
1,448  =>  1,447  1,451  1,453
1,484  =>  1,483  1,487  1,489
1,664  =>  1,663  1,667  1,669
1,694  =>  1,693  1,697  1,699
1,784  =>  1,783  1,787  1,789
1,868  =>  1,867  1,871  1,873
1,874  =>  1,873  1,877  1,879
1,994  =>  1,993  1,997  1,999
2,084  =>  2,083  2,087  2,089
2,138  =>  2,137  2,141  2,143
2,378  =>  2,377  2,381  2,383
2,684  =>  2,683  2,687  2,689
2,708  =>  2,707  2,711  2,713
2,798  =>  2,797  2,801  2,803
3,164  =>  3,163  3,167  3,169
3,254  =>  3,253  3,257  3,259
3,458  =>  3,457  3,461  3,463
3,464  =>  3,463  3,467  3,469
3,848  =>  3,847  3,851  3,853
4,154  =>  4,153  4,157  4,159
4,514  =>  4,513  4,517  4,519
4,784  =>  4,783  4,787  4,789
5,228  =>  5,227  5,231  5,233
5,414  =>  5,413  5,417  5,419
5,438  =>  5,437  5,441  5,443
5,648  =>  5,647  5,651  5,653
5,654  =>  5,653  5,657  5,659
5,738  =>  5,737  5,741  5,743

46 such numbers found.
```

## J

```triplet=: (1 *./@p: _1 3 5+])"0
echo (0 _1 3 5+])"0 (triplet#]) i.6000
exit ''
```
Output:
```   8    7   11   13
14   13   17   19
38   37   41   43
68   67   71   73
98   97  101  103
104  103  107  109
194  193  197  199
224  223  227  229
278  277  281  283
308  307  311  313
458  457  461  463
614  613  617  619
824  823  827  829
854  853  857  859
878  877  881  883
1088 1087 1091 1093
1298 1297 1301 1303
1424 1423 1427 1429
1448 1447 1451 1453
1484 1483 1487 1489
1664 1663 1667 1669
1694 1693 1697 1699
1784 1783 1787 1789
1868 1867 1871 1873
1874 1873 1877 1879
1994 1993 1997 1999
2084 2083 2087 2089
2138 2137 2141 2143
2378 2377 2381 2383
2684 2683 2687 2689
2708 2707 2711 2713
2798 2797 2801 2803
3164 3163 3167 3169
3254 3253 3257 3259
3458 3457 3461 3463
3464 3463 3467 3469
3848 3847 3851 3853
4154 4153 4157 4159
4514 4513 4517 4519
4784 4783 4787 4789
5228 5227 5231 5233
5414 5413 5417 5419
5438 5437 5441 5443
5648 5647 5651 5653
5654 5653 5657 5659
5738 5737 5741 5743```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

```def is_prime:
if  . == 2 then true
else
2 < . and . % 2 == 1 and
(. as \$in
| ((\$in + 1) | sqrt) as \$m
| [false, 3] | until( .[0] or .[1] > \$m; [\$in % .[1] == 0, .[1] + 2])
| .[0]
| not)
end ;

range(3;6000) | select( all( .-1, .+3, .+5; is_prime))```
Output:
```8
14
38
...
5648
5654
5738
```

## Julia

```using Primes

makesprimetriplet(n) = all(isprime, [n - 1, n + 3, n + 5])
println(" N       Prime Triplet\n--------------------------")
foreach(n -> println(rpad(n, 6), [n - 1, n + 3, n + 5]), filter(makesprimetriplet, 2:6005))
```
Output:
``` N       Prime Triplet
--------------------------
8     [7, 11, 13]
14    [13, 17, 19]
38    [37, 41, 43]
68    [67, 71, 73]
98    [97, 101, 103]
104   [103, 107, 109]
194   [193, 196, 199]
224   [223, 227, 229]
278   [277, 281, 283]
308   [307, 311, 313]
458   [457, 461, 463]
614   [613, 617, 619]
824   [823, 827, 829]
854   [853, 857, 859]
878   [877, 881, 883]
1088  [1087, 1091, 1093]
1298  [1297, 1301, 1303]
1424  [1423, 1427, 1429]
1448  [1447, 1451, 1453]
1484  [1483, 1487, 1489]
1664  [1663, 1667, 1669]
1694  [1693, 1697, 1699]
1784  [1783, 1787, 1789]
1868  [1867, 1871, 1873]
1874  [1873, 1877, 1879]
1994  [1993, 1997, 1999]
2084  [2083, 2087, 2089]
2138  [2137, 2141, 2143]
2378  [2377, 2381, 2383]
2684  [2683, 2687, 2689]
2708  [2707, 2711, 2713]
2798  [2797, 2801, 2803]
3164  [3163, 3167, 3169]
3254  [3253, 3257, 3259]
3458  [3457, 3461, 3463]
3464  [3463, 3467, 3469]
3848  [3847, 3851, 3853]
4154  [4153, 4157, 4159]
4514  [4513, 4517, 4519]
4784  [4783, 4787, 4789]
5228  [5227, 5231, 5233]
5414  [5413, 5417, 5419]
5438  [5437, 5441, 5443]
5648  [5647, 5651, 5653]
5654  [5653, 5657, 5659]
5738  [5737, 5741, 5743]
```

## Ksh

```#!/bin/ksh

# numbers n such that n-1, n+3, and n+5 are all prime where: n < 6,000.

#	# Variables:
#
integer MAX_n=6000

#	# Functions:
#

#	# Function _triplet(n, arr) build array of n-1, n+3, n+5
#
function _triplet {
typeset _n ; integer _n=\$1
typeset _arr ; nameref _arr="\$2"

_arr=( \$((_n-1)) \$((_n+3)) \$((_n+5)) )
}

#	# Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
typeset _n ; integer _n=\$1
typeset _i ; integer _i

(( _n < 2 )) && return 0
for (( _i=2 ; _i*_i<=_n ; _i++ )); do
(( ! ( _n % _i ) )) && return 0
done
return 1
}

######
# main #
######

for ((i=2; i<MAX_n; i++)); do
typeset -a arr
_triplet \${i} arr
for ((j=0; j<\${#arr[*]}; j++)); do
_isprime \${arr[j]}
(( ! \$? )) && unset arr && continue 2
done
oldIFS=\${IFS}
IFS=\,
print "\${i}: \${arr[*]}"
IFS=\${oldIFS}
unset arr
done
```
Output:
```
8: 7,11,13
14: 13,17,19
38: 37,41,43
68: 67,71,73
98: 97,101,103
104: 103,107,109
194: 193,197,199
224: 223,227,229
278: 277,281,283
308: 307,311,313
458: 457,461,463
614: 613,617,619
824: 823,827,829
854: 853,857,859
878: 877,881,883
1088: 1087,1091,1093
1298: 1297,1301,1303
1424: 1423,1427,1429
1448: 1447,1451,1453
1484: 1483,1487,1489
1664: 1663,1667,1669
1694: 1693,1697,1699
1784: 1783,1787,1789
1868: 1867,1871,1873
1874: 1873,1877,1879
1994: 1993,1997,1999
2084: 2083,2087,2089
2138: 2137,2141,2143
2378: 2377,2381,2383
2684: 2683,2687,2689
2708: 2707,2711,2713
2798: 2797,2801,2803
3164: 3163,3167,3169
3254: 3253,3257,3259
3458: 3457,3461,3463
3464: 3463,3467,3469
3848: 3847,3851,3853
4154: 4153,4157,4159
4514: 4513,4517,4519
4784: 4783,4787,4789
5228: 5227,5231,5233
5414: 5413,5417,5419
5438: 5437,5441,5443
5648: 5647,5651,5653
5654: 5653,5657,5659

5738: 5737,5741,5743```

```            NORMAL MODE IS INTEGER
BOOLEAN PRIME
DIMENSION PRIME(6005)
LIMIT = 6000

PRIME(0) = 0B
PRIME(1) = 0B
THROUGH SET, FOR I=2, 1, I.G.LIMIT+5
SET         PRIME(I) = 1B
LAST = SQRT.(LIMIT+5)
THROUGH SIEVE, FOR I=2, 1, I.G.LAST
WHENEVER PRIME(I)
THROUGH UNSET, FOR J=I*2, I, J.G.LIMIT+5
UNSET           PRIME(J) = 0B
END OF CONDITIONAL
SIEVE       CONTINUE

THROUGH TEST, FOR I=2, 1, I.G.LIMIT
WHENEVER PRIME(I-1).AND.PRIME(I+3).AND.PRIME(I+5)
PRINT FORMAT FMT, I, I-1, I+3, I+5
END OF CONDITIONAL
TEST        CONTINUE

VECTOR VALUES FMT = \$I4,3H  =,3(I5)*\$
END OF PROGRAM```
Output:
```   8 =    7   11   13
14 =   13   17   19
38 =   37   41   43
68 =   67   71   73
98 =   97  101  103
104 =  103  107  109
194 =  193  197  199
224 =  223  227  229
278 =  277  281  283
308 =  307  311  313
458 =  457  461  463
614 =  613  617  619
824 =  823  827  829
854 =  853  857  859
878 =  877  881  883
1088 = 1087 1091 1093
1298 = 1297 1301 1303
1424 = 1423 1427 1429
1448 = 1447 1451 1453
1484 = 1483 1487 1489
1664 = 1663 1667 1669
1694 = 1693 1697 1699
1784 = 1783 1787 1789
1868 = 1867 1871 1873
1874 = 1873 1877 1879
1994 = 1993 1997 1999
2084 = 2083 2087 2089
2138 = 2137 2141 2143
2378 = 2377 2381 2383
2684 = 2683 2687 2689
2708 = 2707 2711 2713
2798 = 2797 2801 2803
3164 = 3163 3167 3169
3254 = 3253 3257 3259
3458 = 3457 3461 3463
3464 = 3463 3467 3469
3848 = 3847 3851 3853
4154 = 4153 4157 4159
4514 = 4513 4517 4519
4784 = 4783 4787 4789
5228 = 5227 5231 5233
5414 = 5413 5417 5419
5438 = 5437 5441 5443
5648 = 5647 5651 5653
5654 = 5653 5657 5659
5738 = 5737 5741 5743```

## Mathematica/Wolfram Language

```Select[Range[5999], PrimeQ[# - 1] && PrimeQ[# + 3] && PrimeQ[# + 5] &]
```
Output:
`{8, 14, 38, 68, 98, 104, 194, 224, 278, 308, 458, 614, 824, 854, 878, 1088, 1298, 1424, 1448, 1484, 1664, 1694, 1784, 1868, 1874, 1994, 2084, 2138, 2378, 2684, 2708, 2798, 3164, 3254, 3458, 3464, 3848, 4154, 4514, 4784, 5228, 5414, 5438, 5648, 5654, 5738}`

## Maxima

```/* Function that find the number and the triple with the property */
triplets(n):=block(
L:makelist([i-1,i+3,i+5],i,1,n),
caching:length(L),
L1:[],
for i from 1 thru caching do if map(primep,L[i])=[true,true,true] then L1:endcons(append([[i]],L[i]),L1),
L1)\$

/* Test case */
triplets(6000);
```
Output:
```[[[8],7,11,13],[[14],13,17,19],[[38],37,41,43],[[68],67,71,73],[[98],97,101,103],[[104],103,107,109],[[194],193,197,199],[[224],223,227,229],[[278],277,281,283],[[308],307,311,313],[[458],457,461,463],[[614],613,617,619],[[824],823,827,829],[[854],853,857,859],[[878],877,881,883],[[1088],1087,1091,1093],[[1298],1297,1301,1303],[[1424],1423,1427,1429],[[1448],1447,1451,1453],[[1484],1483,1487,1489],[[1664],1663,1667,1669],[[1694],1693,1697,1699],[[1784],1783,1787,1789],[[1868],1867,1871,1873],[[1874],1873,1877,1879],[[1994],1993,1997,1999],[[2084],2083,2087,2089],[[2138],2137,2141,2143],[[2378],2377,2381,2383],[[2684],2683,2687,2689],[[2708],2707,2711,2713],[[2798],2797,2801,2803],[[3164],3163,3167,3169],[[3254],3253,3257,3259],[[3458],3457,3461,3463],[[3464],3463,3467,3469],[[3848],3847,3851,3853],[[4154],4153,4157,4159],[[4514],4513,4517,4519],[[4784],4783,4787,4789],[[5228],5227,5231,5233],[[5414],5413,5417,5419],[[5438],5437,5441,5443],[[5648],5647,5651,5653],[[5654],5653,5657,5659],[[5738],5737,5741,5743]]
```

## Nim

```import strformat

const
N = 5999
Max = 6003  # 5998 + 5.

# 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 "   n   n-1  n+3  n+5"
var count = 0
for n in countup(4, N, 2):
if (n - 1).isPrime and (n + 3).isPrime and (n + 5).isPrime:
echo &"{n:4}: {n-1:4} {n+3:4} {n+5:4}"
inc count

echo &"\nFound {count} triplets for n < {N+1}."
```
Output:
```   n   n-1  n+3  n+5
8:    7   11   13
14:   13   17   19
38:   37   41   43
68:   67   71   73
98:   97  101  103
104:  103  107  109
194:  193  197  199
224:  223  227  229
278:  277  281  283
308:  307  311  313
458:  457  461  463
614:  613  617  619
824:  823  827  829
854:  853  857  859
878:  877  881  883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743

Found 46 triplets for n < 6000.```

## Perl

Library: ntheory
```#!/usr/bin/perl

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

is_prime(\$_ - 4) and printf "%5d" x 4 . "\n", \$_ - 3, \$_ - 4, \$_, \$_ + 2
for @{ twin_primes( 6000 ) };
```
Output:
```    8    7   11   13
14   13   17   19
38   37   41   43
68   67   71   73
98   97  101  103
104  103  107  109
194  193  197  199
224  223  227  229
278  277  281  283
308  307  311  313
458  457  461  463
614  613  617  619
824  823  827  829
854  853  857  859
878  877  881  883
1088 1087 1091 1093
1298 1297 1301 1303
1424 1423 1427 1429
1448 1447 1451 1453
1484 1483 1487 1489
1664 1663 1667 1669
1694 1693 1697 1699
1784 1783 1787 1789
1868 1867 1871 1873
1874 1873 1877 1879
1994 1993 1997 1999
2084 2083 2087 2089
2138 2137 2141 2143
2378 2377 2381 2383
2684 2683 2687 2689
2708 2707 2711 2713
2798 2797 2801 2803
3164 3163 3167 3169
3254 3253 3257 3259
3458 3457 3461 3463
3464 3463 3467 3469
3848 3847 3851 3853
4154 4153 4157 4159
4514 4513 4517 4519
4784 4783 4787 4789
5228 5227 5231 5233
5414 5413 5417 5419
5438 5437 5441 5443
5648 5647 5651 5653
5654 5653 5657 5659
5738 5737 5741 5743
```

## Phix

```function trio(integer n) return sum(apply({n-1,n+3,n+5},is_prime))=3 end function
sequence res = filter(tagset(6000),trio)
printf(1,"%d found: %V\n",{length(res),shorten(res,"",5)})
```
Output:

```46 found: {8,14,38,68,98,"...",5414,5438,5648,5654,5738}
```

## PL/M

```100H:
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9, S); END PRINT;

DECLARE LIMIT LITERALLY '6000';

PRINT\$NUMBER: PROCEDURE (N);
DECLARE S (6) BYTE INITIAL ('.....\$');
DECLARE (N, P) ADDRESS, C BASED P BYTE;
P = .S(5);
DIGIT:
P = P-1;
C = N MOD 10 + '0';
N = N/10;
IF N>0 THEN GO TO DIGIT;
CALL PRINT(P);
END PRINT\$NUMBER;

SIEVE: PROCEDURE (PX, N);
DECLARE (PX, N, P BASED PX) ADDRESS;
P(0) = 0;
P(1) = 0;
DO I=2 TO N;
P(I) = 1;
END;
DO I=2 TO N/2;
IF P(I) THEN
DO J=I*2 TO N BY I;
P(J) = 0;
END;
END;
END SIEVE;

IS\$TRIPLE: PROCEDURE (PX, N) BYTE;
DECLARE (PX, N, P BASED PX) ADDRESS;
IF N < 2 THEN RETURN 0;
RETURN P(N-1) AND P(N+3) AND P(N+5);
END IS\$TRIPLE;

PRINT\$TRIPLE: PROCEDURE (N);
DECLARE COMMA DATA (', \$');
CALL PRINT\$NUMBER(N);
CALL PRINT(.': \$');
CALL PRINT\$NUMBER(N-1);
CALL PRINT(.COMMA);
CALL PRINT\$NUMBER(N+3);
CALL PRINT(.COMMA);
CALL PRINT\$NUMBER(N+5);
CALL PRINT(.(13,10,'\$'));
END PRINT\$TRIPLE;

CALL SIEVE(.MEMORY, LIMIT+5);
DO I=2 TO LIMIT;
IF IS\$TRIPLE(.MEMORY, I) THEN CALL PRINT\$TRIPLE(I);
END;
CALL EXIT;
EOF```
Output:
```8: 7, 11, 13
14: 13, 17, 19
38: 37, 41, 43
68: 67, 71, 73
98: 97, 101, 103
104: 103, 107, 109
194: 193, 197, 199
224: 223, 227, 229
278: 277, 281, 283
308: 307, 311, 313
458: 457, 461, 463
614: 613, 617, 619
824: 823, 827, 829
854: 853, 857, 859
878: 877, 881, 883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743```

## Python

Translation of: FreeBASIC
```#!/usr/bin/python3

N = 6000
p = [None] * 6000  #inicializamos la lista

for i in range(2, round(pow(N,0.5))):
if not p[i]:
for j in range(i*2, N, i):
p[j] = 1

for i in range(3, N):
if (p[i-1] or p[i+3] or p[i+5]):
continue
else:
print(i, ': ', i-1,  ' ', i+3,  ' ', i+5)
```
```Similar a la entrada de FreeBASIC.
```

## Quackery

``` [ 1 swap times [ i 1+ * ] ] is !     ( n --> n )

[ dup 2 < iff
[ drop false ] done
dup 1 - ! 1+
swap mod 0 = ]            is prime ( n --> b )

[] 3000 times
[ i^ 2 *
dup 1 - prime iff
[ dup 3 + prime iff
[ dup 5 + prime iff
join else drop ]
else drop ]
else drop ]
echo```
Output:
`[ 8 14 38 68 98 104 194 224 278 308 458 614 824 854 878 1088 1298 1424 1448 1484 1664 1694 1784 1868 1874 1994 2084 2138 2378 2684 2708 2798 3164 3254 3458 3464 3848 4154 4514 4784 5228 5414 5438 5648 5654 5738 ]`

## Raku

A weird combination of Cousin primes and Twin primes that are siblings, but known by their neighbor.... I shall dub these Alabama primes.

```say "{.[0]+1}: ",\$_ for grep *.all.is-prime, ^6000 .race.map: { \$_-1, \$_+3, \$_+5 };
```
Output:
```8: (7 11 13)
14: (13 17 19)
38: (37 41 43)
68: (67 71 73)
98: (97 101 103)
104: (103 107 109)
194: (193 197 199)
224: (223 227 229)
278: (277 281 283)
308: (307 311 313)
458: (457 461 463)
614: (613 617 619)
824: (823 827 829)
854: (853 857 859)
878: (877 881 883)
1088: (1087 1091 1093)
1298: (1297 1301 1303)
1424: (1423 1427 1429)
1448: (1447 1451 1453)
1484: (1483 1487 1489)
1664: (1663 1667 1669)
1694: (1693 1697 1699)
1784: (1783 1787 1789)
1868: (1867 1871 1873)
1874: (1873 1877 1879)
1994: (1993 1997 1999)
2084: (2083 2087 2089)
2138: (2137 2141 2143)
2378: (2377 2381 2383)
2684: (2683 2687 2689)
2708: (2707 2711 2713)
2798: (2797 2801 2803)
3164: (3163 3167 3169)
3254: (3253 3257 3259)
3458: (3457 3461 3463)
3464: (3463 3467 3469)
3848: (3847 3851 3853)
4154: (4153 4157 4159)
4514: (4513 4517 4519)
4784: (4783 4787 4789)
5228: (5227 5231 5233)
5414: (5413 5417 5419)
5438: (5437 5441 5443)
5648: (5647 5651 5653)
5654: (5653 5657 5659)
5738: (5737 5741 5743)```

## REXX

```/*REXX pgm finds prime triplets:  n-1, n+3, n+5  are primes, and  n < some specified  #.*/
parse arg hi cols .                              /*obtain optional argument from the CL.*/
if   hi=='' |   hi==","  then   hi= 6000         /*Not specified?  Then use the default.*/
if cols=='' | cols==","  then cols=    4         /* "      "         "   "   "     "    */
call genP hi + 5                                 /*build semaphore array for low primes.*/
w= 30                                            /*width of a prime triplet in a column.*/
title= ' prime triplets:  n-1, n+3, n+5  are primes,  and  n  < '     commas(hi)
if cols>0  then say ' index │'center(title,   1 + cols*(w+1)     )
if cols>0  then say '───────┼'center(""   ,   1 + cols*(w+1), '─')
found= 0;                        idx= 1          /*initialize # prime triplets  & index.*/
\$=;                               __= ' '        /*a list of  prime triplets  (so far). */
do j=1  for hi-1                            /*look for prime triplets within range.*/
p1= j - 1;  if \!.p1  then iterate          /*Is  P1  not prime?    Then skip it.  */       /* ◄■■■■■■■ a filter.*/
p3= j + 3;  if \!.p3  then iterate          /* "  P3   "    "         "    "   "   */       /* ◄■■■■■■■ a filter.*/
p5= j + 5;  if \!.p5  then iterate          /* "  P5   "    "         "    "   "   */       /* ◄■■■■■■■ a filter.*/
found= found + 1                            /*bump the number of  prime triplets.  */
if cols<=0            then iterate          /*Build the list  (to be shown later)? */
ttt= commas(p1)__  commas(p3)__  commas(p5) /*add commas & blanks to prime triplet.*/
\$= \$ left( '('ttt")",  w)                   /*add a prime triplet ──► the  \$  list.*/
if found//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(found)       title
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 hip            /*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;    sq.#= @.# ** 2   /*number of primes so far;     prime². */
/* [↓]  generate more  primes  ≤  high.*/
do j=@.#+2  by 2  for max(0, hip%2-@.#%2-1)      /*find odd primes from here on.*/
parse var  j   ''  -1  _;  if    _==5  then iterate  /*J ÷ by 5?  (right digit).*/
if j//3==0  then iterate;  if j//7==0  then iterate  /*" "  " 3?   Is J ÷ by 7? */
do k=5  while sq.k<=j             /* [↓]  divide by the known odd primes.*/
if j//@.k==0  then iterate j      /*Is J÷@.k ?  Then not prime.     ___  */
end   /*k*/                       /* [↑]  only process numbers  ≤  √ J   */
#= #+1;    @.#= j;    sq.#= j*j;  !.j= 1 /*bump # of Ps; assign next P;  P²; P# */
end          /*j*/;               return
```
output   when using the default inputs:
``` index │                                prime triplets:  n-1, n+3, n+5  are primes,  and  n  <  6,000
───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
1   │ (7  11  13)                    (13  17  19)                   (37  41  43)                   (67  71  73)
5   │ (97  101  103)                 (103  107  109)                (193  197  199)                (223  227  229)
9   │ (277  281  283)                (307  311  313)                (457  461  463)                (613  617  619)
13   │ (823  827  829)                (853  857  859)                (877  881  883)                (1,087  1,091  1,093)
17   │ (1,297  1,301  1,303)          (1,423  1,427  1,429)          (1,447  1,451  1,453)          (1,483  1,487  1,489)
21   │ (1,663  1,667  1,669)          (1,693  1,697  1,699)          (1,783  1,787  1,789)          (1,867  1,871  1,873)
25   │ (1,873  1,877  1,879)          (1,993  1,997  1,999)          (2,083  2,087  2,089)          (2,137  2,141  2,143)
29   │ (2,377  2,381  2,383)          (2,683  2,687  2,689)          (2,707  2,711  2,713)          (2,797  2,801  2,803)
33   │ (3,163  3,167  3,169)          (3,253  3,257  3,259)          (3,457  3,461  3,463)          (3,463  3,467  3,469)
37   │ (3,847  3,851  3,853)          (4,153  4,157  4,159)          (4,513  4,517  4,519)          (4,783  4,787  4,789)
41   │ (5,227  5,231  5,233)          (5,413  5,417  5,419)          (5,437  5,441  5,443)          (5,647  5,651  5,653)
45   │ (5,653  5,657  5,659)          (5,737  5,741  5,743)
───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  46  prime triplets:  n-1, n+3, n+5  are primes,  and  n  <  6,000
```

## Ring

```load "stdlib.ring"
see "working..." + nl
see "n  prime triplet" + nl
see "----------------" + nl
row = 0

limit = 6000

for n = 2 to limit-2
bool1 = isprime(n-1)
bool2 = isprime(n+3)
bool3 = isprime(n+5)
bool = bool1 and bool2 and bool3
if bool
row = row + 1
see "" + n + ": (" + (n-1) + " " + (n+3) + " " + (n+5) + ")" + nl
ok
next

see "Found " + row + " prime triplets" + nl
see "done..." + nl```
Output:
```working...
n  prime triplet
----------------
8: (7 11 13)
14: (13 17 19)
38: (37 41 43)
68: (67 71 73)
98: (97 101 103)
104: (103 107 109)
194: (193 197 199)
224: (223 227 229)
278: (277 281 283)
308: (307 311 313)
458: (457 461 463)
614: (613 617 619)
824: (823 827 829)
854: (853 857 859)
878: (877 881 883)
1088: (1087 1091 1093)
1298: (1297 1301 1303)
1424: (1423 1427 1429)
1448: (1447 1451 1453)
1484: (1483 1487 1489)
1664: (1663 1667 1669)
1694: (1693 1697 1699)
1784: (1783 1787 1789)
1868: (1867 1871 1873)
1874: (1873 1877 1879)
1994: (1993 1997 1999)
2084: (2083 2087 2089)
2138: (2137 2141 2143)
2378: (2377 2381 2383)
2684: (2683 2687 2689)
2708: (2707 2711 2713)
2798: (2797 2801 2803)
3164: (3163 3167 3169)
3254: (3253 3257 3259)
3458: (3457 3461 3463)
3464: (3463 3467 3469)
3848: (3847 3851 3853)
4154: (4153 4157 4159)
4514: (4513 4517 4519)
4784: (4783 4787 4789)
5228: (5227 5231 5233)
5414: (5413 5417 5419)
5438: (5437 5441 5443)
5648: (5647 5651 5653)
5654: (5653 5657 5659)
5738: (5737 5741 5743)
Found 46 prime triplets
done...
```

## RPL

`PRIM?` is defined at Primality by trial division:

```≪ { } 1 5
7 6000 FOR j
IF j PRIM? THEN
j SWAP -
IF DUP 2 == ROT 4 == AND THEN
SWAP j 5 - + SWAP END
j END
2 STEP DROP2
```
Output:
```1: { 8 14 38 68 98 104 194 224 278 308 458 614 824 854 878 1088 1298 1424 1448 1484 1664 1694 1784 1868 1874 1994 2084 2138 2378 2684 2708 2798 3164 3254 3458 3464 3848 4154 4514 4784 5228 5414 5438 5648 5654 5738 }
```

Runs in 8 minutes 22 seconds on a basic HP-48G

## Ruby

```require 'prime'

primes = Prime.each(6000)
p primes.each_cons(3).filter_map{|p1, p2, p3| p1 + 1 if p1+4 == p2 && p1+6 == p3}
```
Output:
```[8, 14, 38, 68, 98, 104, 194, 224, 278, 308, 458, 614, 824, 854, 878, 1088, 1298, 1424, 1448, 1484, 1664, 1694, 1784, 1868, 1874, 1994, 2084, 2138, 2378, 2684, 2708, 2798, 3164, 3254, 3458, 3464, 3848, 4154, 4514, 4784, 5228, 5414, 5438, 5648, 5654, 5738]
```

## Seed7

```\$ include "seed7_05.s7i";

const func boolean: isPrime (in integer: number) is func
result
var boolean: prime is FALSE;
local
var integer: upTo is 0;
var integer: testNum is 3;
begin
if number = 2 then
prime := TRUE;
elsif odd(number) and number > 2 then
upTo := sqrt(number);
while number rem testNum <> 0 and testNum <= upTo do
testNum +:= 2;
end while;
prime := testNum > upTo;
end if;
end func;

const proc: main is func
local
var integer: n is 0;
var integer: count is 0;
begin
writeln("   n   n-3  n+3  n+5");
writeln("--------------------");
for n range 2 to 5998 step 2 do
if isPrime(n - 1) and isPrime(n + 3) and isPrime(n + 5) then
writeln(n lpad 4 <& ":" <& n - 1 lpad 5 <& n + 3 lpad 5 <& n + 5 lpad 5);
incr(count);
end if;
end for;
writeln("\nFound " <& count <& " triplets for n < 6000.");
end func;```
Output:
```   n   n-3  n+3  n+5
--------------------
8:    7   11   13
14:   13   17   19
38:   37   41   43
68:   67   71   73
98:   97  101  103
104:  103  107  109
194:  193  197  199
224:  223  227  229
278:  277  281  283
308:  307  311  313
458:  457  461  463
614:  613  617  619
824:  823  827  829
854:  853  857  859
878:  877  881  883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743

Found 46 triplets for n < 6000.
```

## Sidef

```^6000 -> grep {|n| [-1, 3, 5].all {|k| n + k -> is_prime } }.say
```
Output:
```[8, 14, 38, 68, 98, 104, 194, 224, 278, 308, 458, 614, 824, 854, 878, 1088, 1298, 1424, 1448, 1484, 1664, 1694, 1784, 1868, 1874, 1994, 2084, 2138, 2378, 2684, 2708, 2798, 3164, 3254, 3458, 3464, 3848, 4154, 4514, 4784, 5228, 5414, 5438, 5648, 5654, 5738]
```

## True BASIC

Translation of: FreeBASIC
```LET n = 6000

DIM p(0)
MAT REDIM p(n)

FOR i = 2 TO SQR(n)
IF (NOT p(i) <> 0) THEN
FOR j = i*2 TO n STEP i
LET p(j) = 1
NEXT j
END IF
NEXT i

FOR i = 3 TO n
IF (p(i-1) <> 0 OR p(i+3) <> 0 OR p(i+5) <> 0) THEN
! en TB no exite un comando CONTINUE
ELSE
PRINT USING "####: ####  ####  ####": i, i-1, i+3, i+5
END IF
NEXT i
END
```
Output:
```Similar a la entrada de FreeBASIC.
```

## V (Vlang)

Translation of: Python
```import math

const n = 6000

fn main() {
mut p := []bool{len:n, init:false}
for i in 2..int(math.round(math.pow(n,.5))) {
if !p[i] {
for j:=i*2;j<n;j+=i {
p[j] = true
}
}
}
for i in 3..n {
if p[i-1] || p[i+3] || p[i+5] {
continue
}
else {
println('\$i : \${i-1} \${i+3} \${i+5}')
}
}
}```
```Similar to Go
```

## Wren

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

var c = Int.primeSieve(6003, false)
var numbers = []
System.print("Numbers n < 6000 where: n - 1, n + 3, n + 5 are all primes:")
var n = 4
while (n < 6000) {
if (!c[n-1] && !c[n+3] && !c[n+5]) numbers.add(n)
n = n + 2
}
for (n in numbers) Fmt.print("\$,6d  => \$,6d", n, [n-1, n+3, n+5])
System.print("\nFound %(numbers.count) such numbers.")
```
Output:
```Numbers n < 6000 where: n - 1, n + 3, n + 5 are all primes:
8  =>      7     11     13
14  =>     13     17     19
38  =>     37     41     43
68  =>     67     71     73
98  =>     97    101    103
104  =>    103    107    109
194  =>    193    197    199
224  =>    223    227    229
278  =>    277    281    283
308  =>    307    311    313
458  =>    457    461    463
614  =>    613    617    619
824  =>    823    827    829
854  =>    853    857    859
878  =>    877    881    883
1,088  =>  1,087  1,091  1,093
1,298  =>  1,297  1,301  1,303
1,424  =>  1,423  1,427  1,429
1,448  =>  1,447  1,451  1,453
1,484  =>  1,483  1,487  1,489
1,664  =>  1,663  1,667  1,669
1,694  =>  1,693  1,697  1,699
1,784  =>  1,783  1,787  1,789
1,868  =>  1,867  1,871  1,873
1,874  =>  1,873  1,877  1,879
1,994  =>  1,993  1,997  1,999
2,084  =>  2,083  2,087  2,089
2,138  =>  2,137  2,141  2,143
2,378  =>  2,377  2,381  2,383
2,684  =>  2,683  2,687  2,689
2,708  =>  2,707  2,711  2,713
2,798  =>  2,797  2,801  2,803
3,164  =>  3,163  3,167  3,169
3,254  =>  3,253  3,257  3,259
3,458  =>  3,457  3,461  3,463
3,464  =>  3,463  3,467  3,469
3,848  =>  3,847  3,851  3,853
4,154  =>  4,153  4,157  4,159
4,514  =>  4,513  4,517  4,519
4,784  =>  4,783  4,787  4,789
5,228  =>  5,227  5,231  5,233
5,414  =>  5,413  5,417  5,419
5,438  =>  5,437  5,441  5,443
5,648  =>  5,647  5,651  5,653
5,654  =>  5,653  5,657  5,659
5,738  =>  5,737  5,741  5,743

Found 46 such numbers.
```

## XPL0

```func IsPrime(N);        \Return 'true' if N is prime
int  N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];

int Count, N;
[ChOut(0, ^ );
Count:= 0;
for N:= 3 to 6000-1 do
if IsPrime(N-1) & IsPrime(N+3) & IsPrime(N+5) then
[IntOut(0, N-1);  ChOut(0, ^ );
IntOut(0, N+3);  ChOut(0, ^ );
IntOut(0, N+5);  ChOut(0, ^ );
Count:= Count+1;
if rem(Count/5) then ChOut(0, 9\tab\) else CrLf(0);
];
CrLf(0);
IntOut(0, Count);
Text(0, " prime triplets found below 6000.
");
]```
Output:
``` 7 11 13        13 17 19        37 41 43        67 71 73        97 101 103
103 107 109     193 197 199     223 227 229     277 281 283     307 311 313
457 461 463     613 617 619     823 827 829     853 857 859     877 881 883
1087 1091 1093  1297 1301 1303  1423 1427 1429  1447 1451 1453  1483 1487 1489
1663 1667 1669  1693 1697 1699  1783 1787 1789  1867 1871 1873  1873 1877 1879
1993 1997 1999  2083 2087 2089  2137 2141 2143  2377 2381 2383  2683 2687 2689
2707 2711 2713  2797 2801 2803  3163 3167 3169  3253 3257 3259  3457 3461 3463
3463 3467 3469  3847 3851 3853  4153 4157 4159  4513 4517 4519  4783 4787 4789
5227 5231 5233  5413 5417 5419  5437 5441 5443  5647 5651 5653  5653 5657 5659
5737 5741 5743
46 prime triplets found below 6000.
```

## Yabasic

Translation of: Python
```// Rosetta Code problem: http://rosettacode.org/wiki/Triplet_of_three_numbers
// by Galileo, 04/2022

N = 6000
dim p(N)

for i = 2 to int(N ^ 0.5)
if not p(i) then
for j = i*2 to N step i
p(j) = 1
next
endif
next

for i = 3 to N
if not (p(i-1) or p(i+3) or p(i+5)) print i, ": ", i-1,  " ", i+3,  " ", i+5
next```
Output:
```8: 7 11 13
14: 13 17 19
38: 37 41 43
68: 67 71 73
98: 97 101 103
104: 103 107 109
194: 193 197 199
224: 223 227 229
278: 277 281 283
308: 307 311 313
458: 457 461 463
614: 613 617 619
824: 823 827 829
854: 853 857 859
878: 877 881 883
1088: 1087 1091 1093
1298: 1297 1301 1303
1424: 1423 1427 1429
1448: 1447 1451 1453
1484: 1483 1487 1489
1664: 1663 1667 1669
1694: 1693 1697 1699
1784: 1783 1787 1789
1868: 1867 1871 1873
1874: 1873 1877 1879
1994: 1993 1997 1999
2084: 2083 2087 2089
2138: 2137 2141 2143
2378: 2377 2381 2383
2684: 2683 2687 2689
2708: 2707 2711 2713
2798: 2797 2801 2803
3164: 3163 3167 3169
3254: 3253 3257 3259
3458: 3457 3461 3463
3464: 3463 3467 3469
3848: 3847 3851 3853
4154: 4153 4157 4159
4514: 4513 4517 4519
4784: 4783 4787 4789
5228: 5227 5231 5233
5414: 5413 5417 5419
5438: 5437 5441 5443
5648: 5647 5651 5653
5654: 5653 5657 5659
5738: 5737 5741 5743
---Program done, press RETURN---```