user
Task

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

See also
:   * The OEIS entry:   A022004 - Initial members of prime triples (p, p+2, p+6)
    * The Wikipedia entry:   Prime triplet
    * The MathWorld entry:   Prime Triplet
    * The RosettaCode task for just (p,p+4):   Cousin primes
    * The RosettaCode task for other patterns of primes:   Successive prime differences
assistant
Adapted from Cousin primes

### Filter

Favoring brevity over efficiency due to the small range of n, the most concise solution is:

```
say grep *.all.is-prime, map { $_, $_+2, $_+6 }, 2..5500;

```

Output:

```
((5 7 11) (11 13 17) (17 19 23) (41 43 47) (101 103 107) (107 109 113) (191 193 197) (227 229 233) (311 313 317) (347 349 353) (461 463 467) (641 643 647) (821 823 827) (857 859 863) (881 883 887) (1091 1093 1097) (1277 1279 1283) (1301 1303 1307) (1427 1429 1433) (1481 1483 1487) (1487 1489 1493) (1607 1609 1613) (1871 1873 1877) (1997 1999 2003) (2081 2083 2087) (2237 2239 2243) (2267 2269 2273) (2657 2659 2663) (2687 2689 2693) (3251 3253 3257) (3461 3463 3467) (3527 3529 3533) (3671 3673 3677) (3917 3919 3923) (4001 4003 4007) (4127 4129 4133) (4517 4519 4523) (4637 4639 4643) (4787 4789 4793) (4931 4933 4937) (4967 4969 4973) (5231 5233 5237) (5477 5479 5483))

```

### Infinite List

A more efficient and versatile approach is to generate an infinite list of triple primes, using this info from https://oeis.org/A022004 :

:   All terms are congruent to 5 (mod 6).

```
constant @triples = (5, *+6 … *).map: -> \n { $_ if .all.is-prime given (n, n+2, n+6) }

my $count = @triples.first: :k, *.[0] >= 5500;

say .fmt('%4d') for @triples.head($count);

```

Output:

```
   5    7   11
  11   13   17
  17   19   23
  41   43   47
 101  103  107
 107  109  113
 191  193  197
 227  229  233
 311  313  317
 347  349  353
 461  463  467
 641  643  647
 821  823  827
 857  859  863
 881  883  887
1091 1093 1097
1277 1279 1283
1301 1303 1307
1427 1429 1433
1481 1483 1487
1487 1489 1493
1607 1609 1613
1871 1873 1877
1997 1999 2003
2081 2083 2087
2237 2239 2243
2267 2269 2273
2657 2659 2663
2687 2689 2693
3251 3253 3257
3461 3463 3467
3527 3529 3533
3671 3673 3677
3917 3919 3923
4001 4003 4007
4127 4129 4133
4517 4519 4523
4637 4639 4643
4787 4789 4793
4931 4933 4937
4967 4969 4973
5231 5233 5237
5477 5479 5483
```