Triplet of three numbers

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 < 6000

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

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 + 1, n + 5]), filter(makesprimetriplet, 2:6005))

</lang>

Output:

 N       Prime Triplet
--------------------------
8     [7, 9, 13]
14    [13, 15, 19]
38    [37, 39, 43]
68    [67, 69, 73]
98    [97, 99, 103]
104   [103, 105, 109]
194   [193, 195, 199]
224   [223, 225, 229]
278   [277, 279, 283]
308   [307, 309, 313]
458   [457, 459, 463]
614   [613, 615, 619]
824   [823, 825, 829]
854   [853, 855, 859]
878   [877, 879, 883]
1088  [1087, 1089, 1093]
1298  [1297, 1299, 1303]
1424  [1423, 1425, 1429]
1448  [1447, 1449, 1453]
1484  [1483, 1485, 1489]
1664  [1663, 1665, 1669]
1694  [1693, 1695, 1699]
1784  [1783, 1785, 1789]
1868  [1867, 1869, 1873]
1874  [1873, 1875, 1879]
1994  [1993, 1995, 1999]
2084  [2083, 2085, 2089]
2138  [2137, 2139, 2143]
2378  [2377, 2379, 2383]
2684  [2683, 2685, 2689]
2708  [2707, 2709, 2713]
2798  [2797, 2799, 2803]
3164  [3163, 3165, 3169]
3254  [3253, 3255, 3259]
3458  [3457, 3459, 3463]
3464  [3463, 3465, 3469]
3848  [3847, 3849, 3853]
4154  [4153, 4155, 4159]
4514  [4513, 4515, 4519]
4784  [4783, 4785, 4789]
5228  [5227, 5229, 5233]
5414  [5413, 5415, 5419]
5438  [5437, 5439, 5443]
5648  [5647, 5649, 5653]
5654  [5653, 5655, 5659]
5738  [5737, 5739, 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}

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)

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 + " primes" + 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 primes
done...

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.