Triplet of three numbers

From Rosetta Code
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.
Task

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


ALGOL 68

<lang algol68>BEGIN # find numbers n where n-1, n+3 and n+5 are prime # 

   INT max number = 6000;
   # sieve the primes up to max number #
   [ 1 : max number ]BOOL prime;
   prime[ 1 ] := FALSE; prime[ 2 ] := TRUE;
   FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE  OD;
   FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
   FOR i FROM 3 BY 2 TO ENTIER sqrt( max number ) DO
       IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI
   OD;
   # 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 max number - 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</lang>

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

<lang rebol>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]</lang>
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

<lang AWK>

  1. 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)

} </lang>

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

<lang 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</lang>

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

<lang BASIC256> 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 </lang>

Output:
Similar a la entrada de FreeBASIC.

BCPL

<lang 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)

$)</lang>

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

<lang c>#include <stdio.h>

  1. include <stdlib.h>
  2. include <string.h>
  3. include <math.h>
  1. 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;

}</lang>

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

<lang cpp>#include <iostream>

  1. 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;

}</lang>

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? <lang csharp>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); } }</lang>
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.

Cowgol

<lang 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;</lang>

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

F#

This task uses Extensible Prime Generator (F#) <lang fsharp> // 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 "" </lang>

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

<lang factor>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</lang>

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

<lang forth>: 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</lang>

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

<lang 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 </lang> 

    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

<lang go>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))

}</lang>

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

<lang j>triplet=: (1 *./@p: _1 3 5+])"0 echo (0 _1 3 5+])"0 (triplet#]) i.6000 exit </lang>

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

Julia

<lang 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))

</lang>

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]

MAD

<lang MAD> 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 </lang>
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

<lang Nim>import strformat

const 

 N = 5999
 Max = 6003  # 5998 + 5.
  1. 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}."</lang>

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

<lang perl>#!/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 ) };</lang>
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:

(assumes you can add {-1,3,5} to each number in your head easily enough) 

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

PL/M

<lang plm>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;
   DECLARE (I, J) 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 (', $');
   DECLARE N ADDRESS;
   CALL PRINT$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;

DECLARE I ADDRESS; CALL SIEVE(.MEMORY, LIMIT+5); DO I=2 TO LIMIT; 

   IF IS$TRIPLE(.MEMORY, I) THEN CALL PRINT$TRIPLE(I);

END; CALL EXIT; EOF</lang>

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

<lang python>

  1. !/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)

</lang> 

Similar a la entrada de FreeBASIC.


Quackery

<lang 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</lang>
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.

<lang perl6>say "{.[0]+1}: ",$_ for grep *.all.is-prime, ^6000 .race.map: { $_-1, $_+3, $_+5 };</lang>

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

<lang 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.  */
    p3= j + 3;  if \!.p3  then iterate          /* "  P3   "    "         "    "   "   */
    p5= j + 5;  if \!.p5  then iterate          /* "  P5   "    "         "    "   "   */
    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  to hip                 /*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      /*" ÷  " 3?                */
                             if j// 7==0  then iterate      /*" ÷  " 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</lang>
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

<lang 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 </lang>

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...

Seed7

<lang 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;</lang>
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

<lang ruby>^6000 -> grep {|n| [-1, 3, 5].all {|k| n + k -> is_prime } }.say</lang>

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

<lang basic> 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 </lang>

Output:
Similar a la entrada de FreeBASIC.


Wren

Library: Wren-math
Library: Wren-fmt

<lang ecmascript>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.")</lang>

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.
Retrieved from "https://rosettacode.org/wiki/Triplet_of_three_numbers?oldid=312168"