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# Strange unique prime triplets

Strange unique prime triplets is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Primes   n,   m,   and   p   are   strange unique primes   if   n,   m,   and   p   are unique and their sum     n + m + p     is also prime. Assume n < m < p.

•   Find all triplets of strange unique primes in which   n,   m,   and   p   are all less than   30.
•   (stretch goal)   Show the count (only) of all the triplets of strange unique primes in which     n, m, and p    are all less than   1,000.

## 11l

Translation of: Python
`F primes_upto(limit)   V is_prime = [0B] * 2 [+] [1B] * (limit - 1)   L(n) 0 .< Int(limit ^ 0.5 + 1.5)      I is_prime[n]         L(i) (n * n .< limit + 1).step(n)            is_prime[i] = 0B   R enumerate(is_prime).filter((i, prime) -> prime).map((i, prime) -> i) F strange_triplets(Int mx = 30)   [(Int, Int, Int)] r   V primes = Array(primes_upto(mx))   V primes3 = Set(primes_upto(3 * mx))   L(n) primes      V i = L.index      L(m) primes[i + 1 ..]         V j = L.index + i + 1         L(p) primes[j + 1 ..]            I n + m + p C primes3               r.append((n, m, p))   R r L(n, m, p) strange_triplets()   print(‘#2: #2+#2+#2 = #.’.format(L.index + 1, n, m, p, n + m + p)) V mx = 1'000print("\nIf n, m, p < #. finds #.".format(mx, strange_triplets(mx).len))`
Output:
``` 1:  3+ 5+11 = 19
2:  3+ 5+23 = 31
3:  3+ 5+29 = 37
4:  3+ 7+13 = 23
5:  3+ 7+19 = 29
6:  3+11+17 = 31
7:  3+11+23 = 37
8:  3+11+29 = 43
9:  3+17+23 = 43
10:  5+ 7+11 = 23
11:  5+ 7+17 = 29
12:  5+ 7+19 = 31
13:  5+ 7+29 = 41
14:  5+11+13 = 29
15:  5+13+19 = 37
16:  5+13+23 = 41
17:  5+13+29 = 47
18:  5+17+19 = 41
19:  5+19+23 = 47
20:  5+19+29 = 53
21:  7+11+13 = 31
22:  7+11+19 = 37
23:  7+11+23 = 41
24:  7+11+29 = 47
25:  7+13+17 = 37
26:  7+13+23 = 43
27:  7+17+19 = 43
28:  7+17+23 = 47
29:  7+17+29 = 53
30:  7+23+29 = 59
31: 11+13+17 = 41
32: 11+13+19 = 43
33: 11+13+23 = 47
34: 11+13+29 = 53
35: 11+17+19 = 47
36: 11+19+23 = 53
37: 11+19+29 = 59
38: 13+17+23 = 53
39: 13+17+29 = 59
40: 13+19+29 = 61
41: 17+19+23 = 59
42: 19+23+29 = 71

If n, m, p < 1000 finds 241580
```

## Action!

`INCLUDE "H6:SIEVE.ACT" PROC Main()  DEFINE MAXPRIME="29"  DEFINE MAX="99"  BYTE ARRAY primes(MAX+1)  BYTE n,m,p,c  INT count=[0]   Put(125) PutE() ;clear the screen  Sieve(primes,MAX+1)  c=0  FOR n=2 TO MAXPRIME-2  DO    IF primes(n) THEN      FOR m=n+1 TO MAXPRIME-1      DO        IF primes(m) THEN          FOR p=m+1 TO MAXPRIME          DO            IF primes(p)=1 AND primes(n+m+p)=1 THEN              PrintF("%I+%I+%I=%I ",n,m,p,n+m+p)              count==+1 c==+1              IF c=3 THEN                c=0 PutE()              FI            FI          OD        FI      OD    FI  OD  PrintF("%EThere are %I prime triplets",count)RETURN`
Output:
```3+5+11=19 3+5+23=31 3+5+29=37
3+7+13=23 3+7+19=29 3+11+17=31
3+11+23=37 3+11+29=43 3+17+23=43
5+7+11=23 5+7+17=29 5+7+19=31
5+7+29=41 5+11+13=29 5+13+19=37
5+13+23=41 5+13+29=47 5+17+19=41
5+19+23=47 5+19+29=53 7+11+13=31
7+11+19=37 7+11+23=41 7+11+29=47
7+13+17=37 7+13+23=43 7+17+19=43
7+17+23=47 7+17+29=53 7+23+29=59
11+13+17=41 11+13+19=43 11+13+23=47
11+13+29=53 11+17+19=47 11+19+23=53
11+19+29=59 13+17+23=53 13+17+29=59
13+19+29=61 17+19+23=59 19+23+29=71

There are 42 prime triplets
```

## ALGOL 68

Translation of: Algol W
which is based on
Translation of: Wren
`BEGIN # find some strange unique primes - triplets of primes n, m, p        #      # where n + m + p is also prime and n =/= m =/= p                     #    # we need to find the strange unique prime triplets below 1000          #    # so the maximum triplet sum could be roughly 3000                      #    INT max number = 1000;    # sieve the primes to the maximum reuired prime #    PR read "primes.incl.a68" PR    []BOOL prime = PRIMESIEVE ( max number * 3 );    # we need to find the strange unique prime triplets below 1000          #    INT s count := 0, c30 := 0;    # 2 cannot be one of the primes as the sum would be even otherwise      #    FOR n FROM 3 BY 2 TO max number - 5 DO        IF prime[ n ] THEN            FOR m FROM n + 2 BY 2 TO max number- 3 DO                IF prime[ m ] THEN                    FOR p FROM m + 2 BY 2 TO max number DO                        IF prime[ p ] THEN                            IF INT s = n + m + p;                               prime[ s ]                            THEN                                # have 3 unique primes whose sum is prime   #                                s count +:= 1;                                IF p <= 30 AND m <= 30 AND n <= 30 THEN                                    c30 +:= 1;                                    print( ( whole( c30, -3 ), ": "                                           , whole( n,   -3 ), " + "                                           , whole( m,   -3 ), " + "                                           , whole( p,   -3 ), " = "                                           , whole( s,   -3 ), newline                                           )                                         )                                FI                            FI                        FI                    OD # p #                FI            OD # m #        FI    OD # n # ;    print( ( "Found ", whole( c30,     -6 ), " strange unique prime triplets up to   30", newline ) );    print( ( "Found ", whole( s count, -6 ), " strange unique prime triplets up to 1000", newline ) )END`
Output:
```  1:   3 +   5 +  11 =  19
2:   3 +   5 +  23 =  31
3:   3 +   5 +  29 =  37
4:   3 +   7 +  13 =  23
5:   3 +   7 +  19 =  29
6:   3 +  11 +  17 =  31
7:   3 +  11 +  23 =  37
8:   3 +  11 +  29 =  43
9:   3 +  17 +  23 =  43
10:   5 +   7 +  11 =  23
11:   5 +   7 +  17 =  29
12:   5 +   7 +  19 =  31
13:   5 +   7 +  29 =  41
14:   5 +  11 +  13 =  29
15:   5 +  13 +  19 =  37
16:   5 +  13 +  23 =  41
17:   5 +  13 +  29 =  47
18:   5 +  17 +  19 =  41
19:   5 +  19 +  23 =  47
20:   5 +  19 +  29 =  53
21:   7 +  11 +  13 =  31
22:   7 +  11 +  19 =  37
23:   7 +  11 +  23 =  41
24:   7 +  11 +  29 =  47
25:   7 +  13 +  17 =  37
26:   7 +  13 +  23 =  43
27:   7 +  17 +  19 =  43
28:   7 +  17 +  23 =  47
29:   7 +  17 +  29 =  53
30:   7 +  23 +  29 =  59
31:  11 +  13 +  17 =  41
32:  11 +  13 +  19 =  43
33:  11 +  13 +  23 =  47
34:  11 +  13 +  29 =  53
35:  11 +  17 +  19 =  47
36:  11 +  19 +  23 =  53
37:  11 +  19 +  29 =  59
38:  13 +  17 +  23 =  53
39:  13 +  17 +  29 =  59
40:  13 +  19 +  29 =  61
41:  17 +  19 +  23 =  59
42:  19 +  23 +  29 =  71
Found     42 strange unique prime triplets up to   30
Found 241580 strange unique prime triplets up to 1000
```

## ALGOL W

Based on
Translation of: Wren
`begin % find some strange unique primes - triplets of primes n, m, p %      % where n + m + p is also prime and n =/= m =/= p              %    % sets p( 1 :: n ) to a sieve of primes up to n %    procedure Eratosthenes ( logical array p( * ) ; integer value n ) ;    begin        p( 1 ) := false; p( 2 ) := true;        for i := 3 step 2 until n do p( i ) := true;        for i := 4 step 2 until n do p( i ) := false;        for i := 3 step 2 until truncate( sqrt( n ) ) do begin            integer ii; ii := i + i;            if p( i ) then for pr := i * i step ii until n do p( pr ) := false        end for_i ;    end Eratosthenes ;    % we need to find the strange unique prime triplets below 1000 %    integer MAX_PRIME;    MAX_PRIME := 1000;    begin        % the sum of the triplets could be (roughly) 3 x the largest prime %        logical array p ( 1 :: MAX_PRIME * 3 );        integer sCount, c30;        % construct a sieve of primes up to MAX_PRIME * 3                  %        Eratosthenes( p, MAX_PRIME * 3 );        % count the strange prime triplets whose members are < 1000 and    %        % whose sum is prime                                               %        sCount := c30 := 0;        % 2 cannot be one of the primes as the sum would be even otherwise %        for n := 3 step 2 until MAX_PRIME - 5 do begin            if p( n ) then begin                for m := n + 2 step 2 until MAX_PRIME - 3 do begin                    if p( m ) then begin                        for l := m + 2 step 2 until MAX_PRIME do begin                            if p( l ) then begin                                integer s;                                s := n + m + l;                                if p( s ) then begin                                    sCount := sCount + 1;                                    if l <= 30 and m <= 30 and n <= 30 then begin                                        c30 := c30 + 1;                                        write( i_w := 3, s_w := 0, c30, ": ", n, " + ", m, " + ", l, " = ", s )                                    end if_l_m_n_le_30                                end if_p_s                            end if_p_l                        end for_l                    end if_p_m                end for_m            end if_p_n        end for_n ;        write( i_w := 3, s_w := 0, "Found ", c30,    " strange unique prime triplets up to   30" );        write( i_w := 3, s_w := 0, "Found ", sCount, " strange unique prime triplets up to 1000" );    endend.`
Output:
```  1:   3 +   5 +  11 =  19
2:   3 +   5 +  23 =  31
3:   3 +   5 +  29 =  37
4:   3 +   7 +  13 =  23
5:   3 +   7 +  19 =  29
6:   3 +  11 +  17 =  31
7:   3 +  11 +  23 =  37
8:   3 +  11 +  29 =  43
9:   3 +  17 +  23 =  43
10:   5 +   7 +  11 =  23
11:   5 +   7 +  17 =  29
12:   5 +   7 +  19 =  31
13:   5 +   7 +  29 =  41
14:   5 +  11 +  13 =  29
15:   5 +  13 +  19 =  37
16:   5 +  13 +  23 =  41
17:   5 +  13 +  29 =  47
18:   5 +  17 +  19 =  41
19:   5 +  19 +  23 =  47
20:   5 +  19 +  29 =  53
21:   7 +  11 +  13 =  31
22:   7 +  11 +  19 =  37
23:   7 +  11 +  23 =  41
24:   7 +  11 +  29 =  47
25:   7 +  13 +  17 =  37
26:   7 +  13 +  23 =  43
27:   7 +  17 +  19 =  43
28:   7 +  17 +  23 =  47
29:   7 +  17 +  29 =  53
30:   7 +  23 +  29 =  59
31:  11 +  13 +  17 =  41
32:  11 +  13 +  19 =  43
33:  11 +  13 +  23 =  47
34:  11 +  13 +  29 =  53
35:  11 +  17 +  19 =  47
36:  11 +  19 +  23 =  53
37:  11 +  19 +  29 =  59
38:  13 +  17 +  23 =  53
39:  13 +  17 +  29 =  59
40:  13 +  19 +  29 =  61
41:  17 +  19 +  23 =  59
42:  19 +  23 +  29 =  71
Found  42 strange unique prime triplets up to   30
Found 241580 strange unique prime triplets up to 1000
```

## AWK

` # syntax: GAWK -f STRANGE_UNIQUE_PRIME_TRIPLETS.AWK# converted from GoBEGIN {    main(29,1)    main(999,0)    exit(0)}function main(n,show,  count,i,j,k,s) {    for (i=3; i<=n-4; i+=2) {      if (is_prime(i)) {        for (j=i+2; j<=n-2; j+=2) {          if (is_prime(j)) {            for (k=j+2; k<=n; k+=2) {              if (is_prime(k)) {                s = i + j + k                if (is_prime(s)) {                  count++                  if (show == 1) {                    printf("%2d + %2d + %2d = %d\n",i,j,k,s)                  }                }              }            }          }        }      }    }    printf("Unique prime triples 2-%d which sum to a prime: %'d\n\n",n,count)}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:
``` 3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71
Unique prime triples 2-29 which sum to a prime: 42

Unique prime triples 2-999 which sum to a prime: 241,580
```

## C

`#include <stdbool.h>#include <stdio.h>#include <string.h> #define LIMIT 3000 void init_sieve(unsigned char sieve[], int limit) {    int i, j;     for (i = 0; i < limit; i++) {        sieve[i] = 1;    }    sieve[0] = 0;    sieve[1] = 0;     for (i = 2; i < limit; i++) {        if (sieve[i]) {            for (j = i + i; j < limit; j += i) {                sieve[j] = 0;            }        }    }} void strange_unique_prime_triplets(unsigned char sieve[], int limit, bool verbose) {    int count = 0, sum;    int i, j, k, n, p;    int pi, pj, pk;     n = 0;    for (i = 0; i < limit; i++) {        if (sieve[i]) {            n++;        }    }     if (verbose) {        printf("Strange unique prime triplets < %d:\n", limit);    }     for (i = 0; i + 2 < n; i++) {        pi = 2;        p = i;        while (p > 0) {            pi++;            if (sieve[pi]) {                p--;            }        }         for (j = i + 1; j + 1 < n; j++) {            pj = pi;            p = j - i;            while (p > 0) {                pj++;                if (sieve[pj]) {                    p--;                }            }             for (k = j + 1; k < n; k++) {                pk = pj;                p = k - j;                while (p > 0) {                    pk++;                    if (sieve[pk]) {                        p--;                    }                }                 sum = pi + pj + pk;                if (sum < LIMIT && sieve[sum]) {                    count++;                    if (verbose) {                        printf("%2d + %2d + %2d = %d\n", pi, pj, pk, sum);                    }                }            }        }    }     printf("Count of strange unique prime triplets < %d is %d.\n\n", limit, count);} int main() {    unsigned char sieve[LIMIT];     init_sieve(sieve, LIMIT);     strange_unique_prime_triplets(sieve, 30, true);    strange_unique_prime_triplets(sieve, 1000, false);     return 0;}`
Output:
```Strange unique prime triplets < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71
Count of strange unique prime triplets < 30 is 42.

Count of strange unique prime triplets < 1000 is 241580.```

## C#

Just for fun, <30 sorted by sum, instead of order generated. One might think one should include the sieve generation time, but it is orders of magnitude smaller than the permute/sum time for these relatively low numbers.

`using System; using System.Collections.Generic; using static System.Console; using System.Linq; using DT = System.DateTime; class Program { static void Main(string[] args) { string s;  foreach (int lmt in new int[]{ 90, 300, 3000, 30000, 111000 }) {    var pr = PG.Primes(lmt).Skip(1).ToList(); DT st = DT.Now;    int d, f = 0; var r = new List<string>();    int i = -1, m, h = (m = lmt / 3), j, k, pra, prab;    while (i < 0) i = pr.IndexOf(h--); k = (j = i - 1) - 1;    for (int a = 0; a <= k; a++) { pra = pr[a];    for (int b = a + 1; b <= j; b++) { prab = pra + pr[b];     for (int c = b + 1; c <= i; c++) {      if (PG.flags[d = prab + pr[c]]) continue; f++;      if (lmt < 100) r.Add(string.Format("{3,5} = {0,2} + {1,2} + {2,2}", pra, pr[b], pr[c], d)); } } }    s = "s.u.p.t.s under "; r.Sort(); if (r.Count > 0) WriteLine("{0}{1}:\n{2}", s, m, string.Join("\n", r));    if (lmt > 100) WriteLine("Count of {0}{1,6:n0}: {2,13:n0}  {3} sec", s, m, f, (DT.Now - st).ToString().Substring(6)); } } } class PG { public static bool[] flags;  public static IEnumerable<int> Primes(int lim) {  flags = new bool[lim + 1]; int j = 2;  for (int d = 3, sq = 4; sq <= lim; j++, sq += d += 2)    if (!flags[j]) { yield return j;      for (int k = sq; k <= lim; k += j) flags[k] = true; }  for (; j <= lim; j++) if (!flags[j]) yield return j; } }`
Output:

Timings from tio.run

```s.u.p.t.s under 30:
19 =  3 +  5 + 11
23 =  3 +  7 + 13
23 =  5 +  7 + 11
29 =  3 +  7 + 19
29 =  5 +  7 + 17
29 =  5 + 11 + 13
31 =  3 +  5 + 23
31 =  3 + 11 + 17
31 =  5 +  7 + 19
31 =  7 + 11 + 13
37 =  3 +  5 + 29
37 =  3 + 11 + 23
37 =  5 + 13 + 19
37 =  7 + 11 + 19
37 =  7 + 13 + 17
41 =  5 +  7 + 29
41 =  5 + 13 + 23
41 =  5 + 17 + 19
41 =  7 + 11 + 23
41 = 11 + 13 + 17
43 =  3 + 11 + 29
43 =  3 + 17 + 23
43 =  7 + 13 + 23
43 =  7 + 17 + 19
43 = 11 + 13 + 19
47 =  5 + 13 + 29
47 =  5 + 19 + 23
47 =  7 + 11 + 29
47 =  7 + 17 + 23
47 = 11 + 13 + 23
47 = 11 + 17 + 19
53 =  5 + 19 + 29
53 =  7 + 17 + 29
53 = 11 + 13 + 29
53 = 11 + 19 + 23
53 = 13 + 17 + 23
59 =  7 + 23 + 29
59 = 11 + 19 + 29
59 = 13 + 17 + 29
59 = 17 + 19 + 23
61 = 13 + 19 + 29
71 = 19 + 23 + 29
Count of s.u.p.t.s under    100:           891  00.0000243 sec
Count of s.u.p.t.s under  1,000:       241,580  00.0054753 sec
Count of s.u.p.t.s under 10,000:    74,588,542  01.8159964 sec
Count of s.u.p.t.s under 37,000: 2,141,379,201  55.0369689 sec
```

## C++

`#include <iomanip>#include <iostream>#include <vector> std::vector<bool> prime_sieve(size_t limit) {    std::vector<bool> sieve(limit, true);    if (limit > 0)        sieve[0] = false;    if (limit > 1)        sieve[1] = false;    for (size_t i = 4; i < limit; i += 2)        sieve[i] = false;    for (size_t p = 3; ; p += 2) {        size_t q = p * p;        if (q >= limit)            break;        if (sieve[p]) {            size_t inc = 2 * p;            for (; q < limit; q += inc)                sieve[q] = false;        }    }    return sieve;} void strange_unique_prime_triplets(int limit, bool verbose) {    std::vector<bool> sieve = prime_sieve(limit * 3);    std::vector<int> primes;    for (int p = 3; p < limit; p += 2) {        if (sieve[p])            primes.push_back(p);    }    size_t n = primes.size();    size_t count = 0;    if (verbose)        std::cout << "Strange unique prime triplets < " << limit << ":\n";    for (size_t i = 0; i + 2 < n; ++i) {        for (size_t j = i + 1; j + 1 < n; ++j) {            for (size_t k = j + 1; k < n; ++k) {                int sum = primes[i] + primes[j] + primes[k];                if (sieve[sum]) {                    ++count;                    if (verbose) {                        std::cout << std::setw(2) << primes[i] << " + "                                  << std::setw(2) << primes[j] << " + "                                  << std::setw(2) << primes[k] << " = " << sum                                  << '\n';                    }                }            }        }    }    std::cout << "\nCount of strange unique prime triplets < " << limit              << " is " << count << ".\n";} int main() {    strange_unique_prime_triplets(30, true);    strange_unique_prime_triplets(1000, false);    return 0;}`
Output:
```Strange unique prime triplets < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71

Count of strange unique prime triplets < 30 is 42.

Count of strange unique prime triplets < 1000 is 241580.
```

## Delphi

Translation of: Go
` program Strange_primes; {\$APPTYPE CONSOLE} uses  System.SysUtils; function IsPrime(n: Integer): Boolean;begin  if n < 2 then    exit(false);   if n mod 2 = 0 then    exit(n = 2);   if n mod 3 = 0 then    exit(n = 3);   var d := 5;  while d * d <= n do  begin    if n mod d = 0 then      exit(false);     inc(d, 2);     if n mod d = 0 then      exit(false);     inc(d, 4);  end;  Result := true;end; function Commatize(value: Integer): string;begin  Result := FloatToStrF(value, ffNumber, 10, 0);end; function StrangePrimes(n: Integer; countOnly: Boolean): Integer;begin  var c := 0;  var f := '%2d: %2d + %2d + %2d = %2d'#10;  var s: Integer := 0;   var i := 3;  while i <= n - 4 do  begin    if IsPrime(i) then    begin      var j := i + 2;      while j <= n - 2 do      begin        if IsPrime(j) then        begin          var k := j + 2;          while k <= n do          begin            if IsPrime(k) then            begin              s := i + j + k;              if IsPrime(s) then              begin                inc(c);                if not countOnly then                  write(format(f, [c, i, j, k, s]));              end;            end;            inc(k, 2);          end;        end;        inc(j, 2);      end;    end;    inc(i, 2);  end;  Result := c;end; begin  Writeln('Unique prime triples under 30 which sum to a prime:');  strangePrimes(29, false);  var cs := commatize(strangePrimes(999, true));  writeln('There are ', cs, ' unique prime triples under 1,000 which sum to a prime.');  readln;end.`

## F#

This task uses Extensible Prime Generator (F#).

` // Strange unique prime triplets. Nigel Galloway: March 12th., 2021let sP n=let N=primes32()|>Seq.takeWhile((>)n)|>Array.ofSeq         seq{for n in 0..N.Length-1 do for i in n+1..N.Length-1 do for g in i+1..N.Length-1->(N.[n],N.[i],N.[g])}|>Seq.filter(fun(n,i,g)->isPrime(n+i+g))sP 30|>Seq.iteri(fun n(i,g,l)->printfn "%2d: %2d+%2d+%2d=%2d")printfn "%d" (Seq.length(sP 1000))printfn "%d" (Seq.length(sP 10000)) `
Output:
```241580
74588542
```

## Factor

`USING: formatting io kernel math math.combinatorics math.primessequences tools.memory.private ; : .triplet ( seq -- ) "%2d+%2d+%2d = %d\n" vprintf ; : strange ( n -- )    primes-upto 3    [ dup sum dup prime? [ suffix .triplet ] [ 2drop ] if ]    each-combination ; : count-strange ( n -- count )    0 swap primes-upto 3    [ sum prime? [ 1 + ] when ] each-combination ; 30 strange1,000 count-strange commas nl"Found %s strange prime triplets with n, m, p < 1,000.\n" printf`
Output:
``` 3+ 5+11 = 19
3+ 5+23 = 31
3+ 5+29 = 37
3+ 7+13 = 23
3+ 7+19 = 29
3+11+17 = 31
3+11+23 = 37
3+11+29 = 43
3+17+23 = 43
5+ 7+11 = 23
5+ 7+17 = 29
5+ 7+19 = 31
5+ 7+29 = 41
5+11+13 = 29
5+13+19 = 37
5+13+23 = 41
5+13+29 = 47
5+17+19 = 41
5+19+23 = 47
5+19+29 = 53
7+11+13 = 31
7+11+19 = 37
7+11+23 = 41
7+11+29 = 47
7+13+17 = 37
7+13+23 = 43
7+17+19 = 43
7+17+23 = 47
7+17+29 = 53
7+23+29 = 59
11+13+17 = 41
11+13+19 = 43
11+13+23 = 47
11+13+29 = 53
11+17+19 = 47
11+19+23 = 53
11+19+29 = 59
13+17+23 = 53
13+17+29 = 59
13+19+29 = 61
17+19+23 = 59
19+23+29 = 71

Found 241,580 strange prime triplets with n, m, p < 1,000.
```

## Fermat

`Function IsSUPT(n,m,p) =     if Isprime(n) and Isprime(m) and Isprime(p) and Isprime(n+m+p) then 1 else 0 fi. for n=3 to 19 do     for m=n+2 to 23 do         for p=m+2 to 29 do             if IsSUPT(n,m,p) then !!(n,m,p) fi;        od;    od;od`

I'll leave the stretch goal for someone else.

## FreeBASIC

Use the function at Primality by trial division#FreeBASIC as an include; I can't be bothered reproducing it here.

`#include"isprime.bas" dim as uinteger c = 0 for p as uinteger = 3 to 997    if not isprime(p) then continue for    for m as uinteger = p + 1 to 998        if not isprime(m) then continue for        for n as uinteger = m + 1 to 999            if not isprime(n) then continue for            if isprime(p + n + m) then                c = c + 1                if n < 30 then print p;" + ";m;" + ";n;" = "; p + m + n            end if        next n    next mnext p print "There are ";c;" triples below 1000."`
Output:
```3 + 5 + 11 = 19
3 + 5 + 23 = 31
3 + 5 + 29 = 37
3 + 7 + 13 = 23
3 + 7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 + 7 + 11 = 23
5 + 7 + 17 = 29
5 + 7 + 19 = 31
5 + 7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71

There are 241580 triples below 1000.```

## Forth

Works with: Gforth
`: prime? ( n -- ? ) here + [email protected] 0= ;: notprime! ( n -- ) here + 1 swap c! ; : prime_sieve ( n -- )  here over erase  0 notprime!  1 notprime!  dup 4 > if    dup 4 do i notprime! 2 +loop  then  3  begin    2dup dup * >  while    dup prime? if      2dup dup * do        i notprime!      dup 2* +loop    then    2 +  repeat  2drop ; : print_strange_unique_prime_triplets ( n -- )  dup 8 < if drop exit then  dup 3 * prime_sieve  dup 4 - 3 do    i prime? if      dup 2 - i 2 + do        i prime? if          dup i 2 + do            i prime? if              i j k + + dup prime? if                k 2 .r ."  + " j 2 .r ."  + " i 2 .r ."  = " 2 .r cr              else                drop              then            then          2 +loop        then      2 +loop    then  2 +loop drop ; : count_strange_unique_prime_triplets ( n -- n )  dup 8 < if drop 0 exit then  dup 3 * prime_sieve  0 swap  dup 4 - 3 do    i prime? if      dup 2 - i 2 + do        i prime? if          dup i 2 + do            i prime? if              i j k + + prime? if                swap 1+ swap              then            then          2 +loop        then      2 +loop    then  2 +loop drop ; ." Strange unique prime triplets < 30:" cr30 print_strange_unique_prime_triplets ." Count of strange unique prime triplets < 1000: "1000 count_strange_unique_prime_triplets . crbye`
Output:
```Strange unique prime triplets < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71
Count of strange unique prime triplets < 1000: 241580
```

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

## Go

### Basic

Translation of: Wren
`package main import "fmt" func isPrime(n int) bool {    switch {    case n < 2:        return false    case n%2 == 0:        return n == 2    case n%3 == 0:        return n == 3    default:        d := 5        for d*d <= n {            if n%d == 0 {                return false            }            d += 2            if n%d == 0 {                return false            }            d += 4        }        return true    }} func commatize(n int) string {    s := fmt.Sprintf("%d", n)    if n < 0 {        s = s[1:]    }    le := len(s)    for i := le - 3; i >= 1; i -= 3 {        s = s[0:i] + "," + s[i:]    }    if n >= 0 {        return s    }    return "-" + s} func strangePrimes(n int, countOnly bool) int {    c := 0    f := "%2d: %2d + %2d + %2d = %2d\n"    var s int     for i := 3; i <= n-4; i += 2 {        if isPrime(i) {            for j := i + 2; j <= n-2; j += 2 {                if isPrime(j) {                    for k := j + 2; k <= n; k += 2 {                        if isPrime(k) {                            s = i + j + k                            if isPrime(s) {                                c++                                if !countOnly {                                    fmt.Printf(f, c, i, j, k, s)                                }                            }                        }                    }                }            }        }    }    return c} func main() {    fmt.Println("Unique prime triples under 30 which sum to a prime:")    strangePrimes(29, false)    cs := commatize(strangePrimes(999, true))    fmt.Printf("\nThere are %s unique prime triples under 1,000 which sum to a prime.\n", cs)}`
Output:
```Unique prime triples under 30 which sum to a prime:
1:  3 +  5 + 11 = 19
2:  3 +  5 + 23 = 31
3:  3 +  5 + 29 = 37
4:  3 +  7 + 13 = 23
5:  3 +  7 + 19 = 29
6:  3 + 11 + 17 = 31
7:  3 + 11 + 23 = 37
8:  3 + 11 + 29 = 43
9:  3 + 17 + 23 = 43
10:  5 +  7 + 11 = 23
11:  5 +  7 + 17 = 29
12:  5 +  7 + 19 = 31
13:  5 +  7 + 29 = 41
14:  5 + 11 + 13 = 29
15:  5 + 13 + 19 = 37
16:  5 + 13 + 23 = 41
17:  5 + 13 + 29 = 47
18:  5 + 17 + 19 = 41
19:  5 + 19 + 23 = 47
20:  5 + 19 + 29 = 53
21:  7 + 11 + 13 = 31
22:  7 + 11 + 19 = 37
23:  7 + 11 + 23 = 41
24:  7 + 11 + 29 = 47
25:  7 + 13 + 17 = 37
26:  7 + 13 + 23 = 43
27:  7 + 17 + 19 = 43
28:  7 + 17 + 23 = 47
29:  7 + 17 + 29 = 53
30:  7 + 23 + 29 = 59
31: 11 + 13 + 17 = 41
32: 11 + 13 + 19 = 43
33: 11 + 13 + 23 = 47
34: 11 + 13 + 29 = 53
35: 11 + 17 + 19 = 47
36: 11 + 19 + 23 = 53
37: 11 + 19 + 29 = 59
38: 13 + 17 + 23 = 53
39: 13 + 17 + 29 = 59
40: 13 + 19 + 29 = 61
41: 17 + 19 + 23 = 59
42: 19 + 23 + 29 = 71

There are 241,580 unique prime triples under 1,000 which sum to a prime.
```

### Faster

Translation of: Wren
`package main import "fmt" var sieved []boolvar p = []int{2} func sieve(limit int) []bool {    limit++    // True denotes composite, false denotes prime.    c := make([]bool, limit) // all false by default    c[0] = true    c[1] = true    // no need to bother with even numbers over 2 for this task    p := 3 // Start from 3.    for {        p2 := p * p        if p2 >= limit {            break        }        for i := p2; i < limit; i += 2 * p {            c[i] = true        }        for {            p += 2            if !c[p] {                break            }        }    }    return c} func commatize(n int) string {    s := fmt.Sprintf("%d", n)    if n < 0 {        s = s[1:]    }    le := len(s)    for i := le - 3; i >= 1; i -= 3 {        s = s[0:i] + "," + s[i:]    }    if n >= 0 {        return s    }    return "-" + s} func strangePrimes(n int, countOnly bool) int {    c := 0    f := "%2d: %2d + %2d + %2d = %2d\n"    var r, s int    m := 0    for ; m < len(p) && p[m] <= n; m++ {     }    for i := 1; i < m-2; i++ {        for j := i + 1; j < m-1; j++ {            r = p[i] + p[j]            for k := j + 1; k < m; k++ {                s = r + p[k]                if !sieved[s] {                    c++                    if !countOnly {                        fmt.Printf(f, c, p[i], p[j], p[k], s)                    }                }            }        }    }    return c} func main() {    const max = 1000    sieved = sieve(3*max)    for i := 3; i <= max; i += 2 {        if !sieved[i] {            p = append(p, i)        }    }    fmt.Println("Unique prime triples under 30 which sum to a prime:")    strangePrimes(29, false)    cs := commatize(strangePrimes(999, true))    fmt.Printf("\nThere are %s unique prime triples under 1,000 which sum to a prime.\n", cs)}`
Output:

Same as 'basic' version.

## Java

`import java.util.*; public class StrangeUniquePrimeTriplets {    public static void main(String[] args) {        strangeUniquePrimeTriplets(30, true);        strangeUniquePrimeTriplets(1000, false);    }     private static void strangeUniquePrimeTriplets(int limit, boolean verbose) {        boolean[] sieve = primeSieve(limit * 3);        List<Integer> primeList = new ArrayList<>();        for (int p = 3; p < limit; p += 2) {            if (sieve[p])                primeList.add(p);        }        int n = primeList.size();        // Convert object list to primitive array for performance        int[] primes = new int[n];        for (int i = 0; i < n; ++i)            primes[i] = primeList.get(i);        int count = 0;        if (verbose)            System.out.printf("Strange unique prime triplets < %d:\n", limit);        for (int i = 0; i + 2 < n; ++i) {            for (int j = i + 1; j + 1 < n; ++j) {                int s = primes[i] + primes[j];                for (int k = j + 1; k < n; ++k) {                    int sum = s + primes[k];                    if (sieve[sum]) {                        ++count;                        if (verbose)                            System.out.printf("%2d + %2d + %2d = %2d\n", primes[i], primes[j], primes[k], sum);                    }                }            }        }        System.out.printf("\nCount of strange unique prime triplets < %d is %d.\n", limit, count);    }     private static boolean[] primeSieve(int limit) {        boolean[] sieve = new boolean[limit];        Arrays.fill(sieve, true);        if (limit > 0)            sieve[0] = false;        if (limit > 1)            sieve[1] = false;        for (int i = 4; i < limit; i += 2)            sieve[i] = false;        for (int p = 3; ; p += 2) {            int q = p * p;            if (q >= limit)                break;            if (sieve[p]) {                int inc = 2 * p;                for (; q < limit; q += inc)                    sieve[q] = false;            }        }        return sieve;    }}`
Output:
```Strange unique prime triplets < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71

Count of strange unique prime triplets < 30 is 42.

Count of strange unique prime triplets < 1000 is 241580.
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

See e.g. Erdős-primes#jq for a suitable implementation of `is_prime`.

`def count(s): reduce s as \$x (null; .+1); def task(\$n):  [2, (range(3;\$n;2)|select(is_prime))]   | . as \$p  | range(0; length) as \$i  | range(\$i+1; length) as \$j  | range(\$j+1; length) as \$k  | [.[\$i], .[\$j], .[\$k]]   | select( add| is_prime) ; task(30),"\nStretch goal: \(count(task(1000)))"`
Output:
```[3,5,11]
[3,5,23]
[3,5,29]
[3,7,13]
[3,7,19]
[3,11,17]
[3,11,23]
[3,11,29]
[3,17,23]
[5,7,11]
[5,7,17]
[5,7,19]
[5,7,29]
[5,11,13]
[5,13,19]
[5,13,23]
[5,13,29]
[5,17,19]
[5,19,23]
[5,19,29]
[7,11,13]
[7,11,19]
[7,11,23]
[7,11,29]
[7,13,17]
[7,13,23]
[7,17,19]
[7,17,23]
[7,17,29]
[7,23,29]
[11,13,17]
[11,13,19]
[11,13,23]
[11,13,29]
[11,17,19]
[11,19,23]
[11,19,29]
[13,17,23]
[13,17,29]
[13,19,29]
[17,19,23]
[19,23,29]

Stretch goal: 241580
```

## Julia

`using Primes function prime_sum_prime_triplets_to(N, verbose=false)    a = primes(3, N)    prime_sieve_set = primesmask(1, N * 3)    len, triplets, n = length(a), Dict{Tuple{Int64,Int64,Int64}, Int}(), 0    for i in eachindex(a), j in i+1:len, k in j+1:len        if prime_sieve_set[a[i] + a[j] + a[k]]            verbose && (triplets[(a[i], a[j], a[k])] = 1)            n += 1        end    end    if verbose        len = (length(string(N)) + 2) * 3        println("\n", rpad("Triplet", len), "Sum\n", "-"^(len+3))        for k in sort(collect(keys(triplets)), lt = (x, y) -> collect(x) < collect(y))            println(rpad(k, len), sum(k))        end    end    println("\n\n\$n unique triplets of 3 primes between 2 and \$N sum to a prime.")    return tripletsend prime_sum_prime_triplets_to(30, true)prime_sum_prime_triplets_to(1000)@time prime_sum_prime_triplets_to(10000)@time prime_sum_prime_triplets_to(100000) `
Output:
```Triplet     Sum
---------------
(3, 5, 11)  19
(3, 5, 23)  31
(3, 5, 29)  37
(3, 7, 13)  23
(3, 7, 19)  29
(3, 11, 17) 31
(3, 11, 23) 37
(3, 11, 29) 43
(3, 17, 23) 43
(5, 7, 11)  23
(5, 7, 17)  29
(5, 7, 19)  31
(5, 7, 29)  41
(5, 11, 13) 29
(5, 13, 19) 37
(5, 13, 23) 41
(5, 13, 29) 47
(5, 17, 19) 41
(5, 19, 23) 47
(5, 19, 29) 53
(7, 11, 13) 31
(7, 11, 19) 37
(7, 11, 23) 41
(7, 11, 29) 47
(7, 13, 17) 37
(7, 13, 23) 43
(7, 17, 19) 43
(7, 17, 23) 47
(7, 17, 29) 53
(7, 23, 29) 59
(11, 13, 17)41
(11, 13, 19)43
(11, 13, 23)47
(11, 13, 29)53
(11, 17, 19)47
(11, 19, 23)53
(11, 19, 29)59
(13, 17, 23)53
(13, 17, 29)59
(13, 19, 29)61
(17, 19, 23)59
(19, 23, 29)71

42 unique triplets of 3 primes between 2 and 30 sum to a prime.

241580 unique triplets of 3 primes between 2 and 1000 sum to a prime.

74588542 unique triplets of 3 primes between 2 and 10000 sum to a prime.
0.509732 seconds (31 allocations: 25.938 KiB)

28694800655 unique triplets of 3 primes between 2 and 100000 sum to a prime.
224.940756 seconds (35 allocations: 218.156 KiB)
```

## Mathematica/Wolfram Language

`p = Prime[[email protected][30]];Select[Subsets[p, {3}], Total/*PrimeQ] p = Prime[[email protected][1000]];Length[Select[Subsets[p, {3}], Total/*PrimeQ]]`
Output:
```{{3,5,11},{3,5,23},{3,5,29},{3,7,13},{3,7,19},{3,11,17},{3,11,23},{3,11,29},{3,17,23},{5,7,11},{5,7,17},{5,7,19},{5,7,29},{5,11,13},{5,13,19},{5,13,23},{5,13,29},{5,17,19},{5,19,23},{5,19,29},{7,11,13},{7,11,19},{7,11,23},{7,11,29},{7,13,17},{7,13,23},{7,17,19},{7,17,23},{7,17,29},{7,23,29},{11,13,17},{11,13,19},{11,13,23},{11,13,29},{11,17,19},{11,19,23},{11,19,29},{13,17,23},{13,17,29},{13,19,29},{17,19,23},{19,23,29}}
241580```

## Nim

`import strformat, strutils, sugar func isPrime(n: Positive): bool =  if n < 2: return false  if n mod 2 == 0: return n == 2  if n mod 3 == 0: return n == 3  var d = 5  while d * d <= n:    if n mod d == 0: return false    inc d, 2    if n mod d == 0: return false    inc d, 4  result = true  iterator triplets(primes: openArray[int]): (int, int, int) =  ## Yield the triplets.  for i in 0..primes.high-2:    let n = primes[i]    for j in (i+1)..primes.high-1:      let m = primes[j]      for k in (j+1)..primes.high:        let p = primes[k]        if (n + m + p).isPrime:          yield (n, m, p)  const Primes30 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]echo "List of strange unique prime triplets for n < m < p < 30:"for (n, m, p) in Primes30.triplets():  echo &"{n:2} + {m:2} + {p:2} = {n+m+p}" echo()const Primes1000 = collect(newSeq):                     for n in 2..999:                       if n.isPrime: nvar count = 0for _ in Primes1000.triplets(): inc countecho "Count of strange unique prime triplets for n < m < p < 1000: ", (\$count).insertSep()`
Output:
```List of strange unique prime triplets for n < m < p < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71

Count of strange unique prime triplets for n < m < p < 1000: 241_580```

## Pascal

Works with: Free Pascal
`program PrimeTriplets;//Free Pascal Compiler version 3.2.1 [2020/11/03] for x86_64fpc  3.2.1{\$IFDEF FPC}  {\$MODE DELPHI}  {\$Optimization ON,ALL}  {\$ELSE}  {\$APPTYPE CONSOLE}  {\$ENDIF}  const  MAXZAHL = 100000;// > 3  MAXSUM  = 3*MAXZAHL;   CountOfPrimes = trunc(MAXZAHL/(ln(MAXZAHL)-1.08))+100; type  tChkprimes = array[0..MAXSUM] of byte;//prime == 1 , nonprime == 0var  Chkprimes:tChkprimes;    primes : array[0..CountOfPrimes]of Uint32;//here starting with 3  count,primeCount:NativeInt; procedure InitPrimes;//sieve of eratothenesvar  i,j : NativeInt;begin  fillchar(Chkprimes,SizeOf(tChkprimes),#1);  i := 2;  j := 2*2;  if j> MAXSUM then      EXIT;  repeat    Chkprimes[j]:= 0;    inc(j,i);  until j> Maxsum;        For i := 3 to MAXSUM do  Begin    if Chkprimes[i] <>0 then    Begin      j := i*i;      if j> MAXSUM then        Break;      repeat        Chkprimes[j]:= 0;        inc(j,2*i);      until j> Maxsum;        end;  end;         j := 0;  For i := 3 to MAXZAHL do    IF Chkprimes[i]<>0 then    Begin      primes[j] := i;      inc(j);    end;    primeCount := j-1;  j :=CountOfPrimes -primeCount;   IF j <0 then   begin    writeln(' Need more space for primes ', -j);    HALT(-243);  end;end; function GetMaxPrimeIdx(lmt:NativeInt):NativeInt;begin  if lmt >= Maxzahl then  Begin    result := primecount;    EXIT;   end;   result := 0;  while (result < primecount) AND (primes[result]<lmt) do    inc(result);  dec(result);  end; procedure Out_Check(lmt:nativeInt);//simplest versionvar  i,j,k,s,pc:   NativeInt;Begin  pc:= GetMaxPrimeIdx(lmt);  count := 0;  For i := 0 to pc do    For j := i+1 to pc do      For k := j+1 to pc do      Begin        s := primes[i]+primes[j]+Primes[k];        //if takes the longest time        if ChkPrimes[s]<> 0 then        begin          inc(count);          writeln(count:3,': ',primes[i],'+',primes[j],'+',primes[k],' = ',s);        end;        end;    writeln;end; procedure Count_Check(pc:nativeInt);// the power of many registers ( 64-Bit )var  cnt : Uint64;  pPrimes : pUint32;  pChkPrimes : ^tChkprimes;  pi,pij,i,j,k:   NativeInt;Begin  cnt := 0;  pPrimes := @primes[0];  pChkPrimes := @Chkprimes[0];  For i := 0 to pc do  Begin    pi := pPrimes[i];    For j := i+1 to pc do    begin      pij := pi+pPrimes[j];      For k := j+1 to pc do        inc(cnt,pChkPrimes^[pij+pPrimes[k]]);    end;    end;    count := cnt;end; procedure Check_Limit(lmt:NativeInt);Begin  If lmt>primes[primecount] then    lmt := MaxZahl;  write('Limit = ',lmt,' count: ');  Count_Check(GetMaxPrimeIdx(lmt));  writeln(count);end; BEGIN  InitPrimes;  Out_Check(30);  Check_Limit(100);  Check_Limit(1000);  Check_Limit(10000);//Check_Limit(MAXZAHL);  END.`
Output:
```  1: 3+5+11 = 19
2: 3+5+23 = 31
3: 3+5+29 = 37
4: 3+7+13 = 23
5: 3+7+19 = 29
6: 3+11+17 = 31
7: 3+11+23 = 37
8: 3+11+29 = 43
9: 3+17+23 = 43
10: 5+7+11 = 23
11: 5+7+17 = 29
12: 5+7+19 = 31
13: 5+7+29 = 41
14: 5+11+13 = 29
15: 5+13+19 = 37
16: 5+13+23 = 41
17: 5+13+29 = 47
18: 5+17+19 = 41
19: 5+19+23 = 47
20: 5+19+29 = 53
21: 7+11+13 = 31
22: 7+11+19 = 37
23: 7+11+23 = 41
24: 7+11+29 = 47
25: 7+13+17 = 37
26: 7+13+23 = 43
27: 7+17+19 = 43
28: 7+17+23 = 47
29: 7+17+29 = 53
30: 7+23+29 = 59
31: 11+13+17 = 41
32: 11+13+19 = 43
33: 11+13+23 = 47
34: 11+13+29 = 53
35: 11+17+19 = 47
36: 11+19+23 = 53
37: 11+19+29 = 59
38: 13+17+23 = 53
39: 13+17+29 = 59
40: 13+19+29 = 61
41: 17+19+23 = 59
42: 19+23+29 = 71

Limit = 100 count: 891
Limit = 1000 count: 241580
Limit = 10000 count: 74588542
//real    0m0,142s
Limit = 100000 count: 28694800655
real    1m5,378s```

## Perl

Library: ntheory
`use strict;use warnings;use List::Util 'sum';use ntheory <primes is_prime>;use Algorithm::Combinatorics 'combinations'; for my \$n (30, 1000) {    printf "Found %d strange unique prime triplets up to \$n.\n",        scalar grep { is_prime(sum @\$_) } combinations(primes(\$n), 3);}`
Output:
```Found 42 strange unique prime triplets up to 30.
Found 241580 strange unique prime triplets up to 1000.```

## Phix

```with javascript_semantics
requires("0.8.4")
function create_sieve(integer limit)
sequence sieve = repeat(true,limit)
sieve[1] = false
for i=4 to limit by 2 do
sieve[i] = false
end for
for p=3 to floor(sqrt(limit)) by 2 do
integer p2 = p*p
if sieve[p2] then
for k=p2 to limit by p*2 do
sieve[k] = false
end for
end if
end for
return sieve
end function

procedure strange_triplets(integer lim, bool bCountOnly=true)
atom t0 = time(), t1 = t0+1
sequence primes = get_primes_le(lim),
sieve = create_sieve(lim*3),
res = {}
atom count = 0
--
-- It is not worth involving 2, ie primes[1],
-- since (2 + any other two primes) is even,
-- also we may as well leave space for {j,k},
-- {k} in the two outer loops.
-- Using a sieve on the inner test is over
-- ten times faster than is_prime(), whereas
-- using a separate table of primes for the
-- two outer loops is about twice as fast as
-- scanning the sieve skipping falsies. Also
-- interestingly, using nm = n+m is twice as
-- fast as nmp = n+m+p.
--
for i=2 to length(primes)-2 do
integer n = primes[i]
for j=i+1 to length(primes)-1 do
integer m = primes[j],
nm = n+m
for k=j+1 to length(primes) do
integer p = primes[k],
nmp = nm+p
if sieve[nmp] then
count += 1
if not bCountOnly then
res = append(res,sprintf("%2d: %2d+%2d+%2d = %d",
{count, n,  m,  p, nmp}))
end if
end if
if platform()!=JS and time()>t1 then
progress("Working... (%,d)\r",{count})
t1 = time()+1
end if
end for
end for
end for
if platform()!=JS then progress("") end if
string r = iff(bCountOnly?sprintf(" (%s)",{elapsed(time()-t0)})
:sprintf(":\n%s",{join(shorten(res,"",3),"\n")}))
printf(1,"%,d strange triplets < %,d found%s\n\n",{count,lim,r})
end procedure

strange_triplets(30,false)
strange_triplets(1000)
strange_triplets(10000)
```
Output:
```42 strange triplets < 30 found:
1:  3+ 5+11 = 19
2:  3+ 5+23 = 31
3:  3+ 5+29 = 37
...
40: 13+19+29 = 61
41: 17+19+23 = 59
42: 19+23+29 = 71

241,580 strange triplets < 1,000 found (0.0s)

74,588,542 strange triplets < 10,000 found (11.4s)
```

## Python

Using sympy.primerange.

`from sympy import primerange def strange_triplets(mx: int = 30) -> None:    primes = list(primerange(0, mx))    primes3 = set(primerange(0, 3 * mx))    for i, n in enumerate(primes):        for j, m in enumerate(primes[i + 1:], i + 1):            for p in primes[j + 1:]:                if n + m + p in primes3:                    yield n, m, p for c, (n, m, p) in enumerate(strange_triplets(), 1):    print(f"{c:2}: {n:2}+{m:2}+{p:2} = {n + m + p}") mx = 1_000print(f"\nIf n, m, p < {mx:_} finds {sum(1 for _ in strange_triplets(mx)):_}")`
Output:
``` 1:  3+ 5+11 = 19
2:  3+ 5+23 = 31
3:  3+ 5+29 = 37
4:  3+ 7+13 = 23
5:  3+ 7+19 = 29
6:  3+11+17 = 31
7:  3+11+23 = 37
8:  3+11+29 = 43
9:  3+17+23 = 43
10:  5+ 7+11 = 23
11:  5+ 7+17 = 29
12:  5+ 7+19 = 31
13:  5+ 7+29 = 41
14:  5+11+13 = 29
15:  5+13+19 = 37
16:  5+13+23 = 41
17:  5+13+29 = 47
18:  5+17+19 = 41
19:  5+19+23 = 47
20:  5+19+29 = 53
21:  7+11+13 = 31
22:  7+11+19 = 37
23:  7+11+23 = 41
24:  7+11+29 = 47
25:  7+13+17 = 37
26:  7+13+23 = 43
27:  7+17+19 = 43
28:  7+17+23 = 47
29:  7+17+29 = 53
30:  7+23+29 = 59
31: 11+13+17 = 41
32: 11+13+19 = 43
33: 11+13+23 = 47
34: 11+13+29 = 53
35: 11+17+19 = 47
36: 11+19+23 = 53
37: 11+19+29 = 59
38: 13+17+23 = 53
39: 13+17+29 = 59
40: 13+19+29 = 61
41: 17+19+23 = 59
42: 19+23+29 = 71

If n, m, p < 1_000 finds 241_580```

## Raku

(formerly Perl 6)

`# 20210312 Raku programming solution for 30, 1000 -> \k {   given (2..k).grep(*.is-prime).combinations(3).grep(*.sum.is-prime) {      say "Found ", +\$_, " strange unique prime triplets up to ", k   }}`
Output:
```Found 42 strange unique prime triplets up to 30
Found 241580 strange unique prime triplets up to 1000
```

## REXX

`/*REXX program finds/lists triplet strange primes (<HI) where the triplets' sum is prime*/parse arg hi .                                   /*obtain optional argument from the CL.*/if hi=='' | hi==","  then hi= 30                 /*Not specified?  Then use the default.*/tell= hi>0;            hi= abs(hi);  hi= hi - 1  /*use absolute value of  HI for limit. */if tell>0  then say  'list of unique triplet strange primes whose sum is a prime.:'call genP                                        /*build array of semaphores for primes.*/finds= 0                                         /*# of triplet strange primes (so far).*/say   do     m=2+1  by 2  to hi;     if \!.m  then iterate      /*just use the odd primes. */     do   n=m+2  by 2  to hi;     if \!.n  then iterate      /*  "   "   "   "     "    */     mn= m + n                                               /*partial sum (deep loops).*/       do p=n+2  by 2  to hi;     if \!.p  then iterate      /*just use the odd primes. */       sum= mn + p                                           /*compute sum of 3 primes. */       if \!.sum  then iterate                   /*Is the sum prime?   No, then skip it.*/       finds= finds + 1                          /*bump # of triplet  "strange"  primes.*/       if tell  then say right(m, w+9) right(n, w) right(p, w) ' sum to:'  right(sum, w+2)       end   /*p*/     end     /*n*/   end       /*m*/saysay 'Found '      commas(finds)      " unique triplet strange primes  < "   commas(hi+1) ,                                     " which sum to a prime."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;                    w= length(hi)    /*semaphores for primes;  width of #'s.*/      @.1=2;  @.2=3;  @.3=5;  @.4=7;  @.5=11     /*define some low primes.              */      !.2=1;  !.3=1;  !.5=1;  !.7=1;  !.11=1     /*   "     "   "    "     semaphores.  */                        #=5;     s.#= @.# **2    /*number of primes so far;     prime². */                                                 /* [↓]  generate more  primes  ≤  high.*/        do [email protected].#+2  by 2  for hi*3%2             /*find odd primes from here on.        */        parse var j '' -1 _; if     _==5  then iterate  /*J divisible by 5?  (right dig)*/                             if j// 3==0  then iterate  /*"     "      " 3?             */                             if j// 7==0  then iterate  /*"     "      " 7?             */                                                 /* [↑]  the above five lines saves time*/               do k=5  while s.k<=j              /* [↓]  divide by the known odd primes.*/               if j // @.k == 0  then iterate j  /*Is  J ÷ X?  Then not prime.     ___  */               end   /*k*/                       /* [↑]  only process numbers  ≤  √ J   */        #= #+1;    @.#= j;    s.#= j*j;   !.j= 1 /*bump # of Ps; assign next P;  P²; P# */        end          /*j*/;   return`
output   when using the default input:
```list of unique triplet strange primes that sum to a prime:
prime generation took 0.02 seconds.

3  5 11   sum to:    19
3  5 23   sum to:    31
3  5 29   sum to:    37
3  7 13   sum to:    23
3  7 19   sum to:    29
3 11 17   sum to:    31
3 11 23   sum to:    37
3 11 29   sum to:    43
3 17 23   sum to:    43
5  7 11   sum to:    23
5  7 17   sum to:    29
5  7 19   sum to:    31
5  7 29   sum to:    41
5 11 13   sum to:    29
5 13 19   sum to:    37
5 13 23   sum to:    41
5 13 29   sum to:    47
5 17 19   sum to:    41
5 19 23   sum to:    47
5 19 29   sum to:    53
7 11 13   sum to:    31
7 11 19   sum to:    37
7 11 23   sum to:    41
7 11 29   sum to:    47
7 13 17   sum to:    37
7 13 23   sum to:    43
7 17 19   sum to:    43
7 17 23   sum to:    47
7 17 29   sum to:    53
7 23 29   sum to:    59
11 13 17   sum to:    41
11 13 19   sum to:    43
11 13 23   sum to:    47
11 13 29   sum to:    53
11 17 19   sum to:    47
11 19 23   sum to:    53
11 19 29   sum to:    59
13 17 23   sum to:    53
13 17 29   sum to:    59
13 19 29   sum to:    61
17 19 23   sum to:    59
19 23 29   sum to:    71

Found  42  unique triplet strange primes  <  30  which sum to a prime.
```
output   when using the input of:     -1000
```Found  241,580  unique triplet strange primes  <  1,000  which sum to a prime.
```

## Ring

` load "stdlib.ring" num = 0limit = 30 see "working..." + nlsee "the strange primes are:" + nl for n = 1 to limit    for m = n+1 to limit        for p = m+1 to limit            sum = n+m+p            if isprime(sum) and isprime(n) and isprime(m) and isprime(p)               num = num + 1               see "" + num + ": " + n + "+" + m + "+" + p + " = " + sum + nl            ok        next    nextnext see "done..." + nl `
Output:
```working...
the strange primes are:
1: 3+5+11 = 19
2: 3+5+23 = 31
3: 3+5+29 = 37
4: 3+7+13 = 23
5: 3+7+19 = 29
6: 3+11+17 = 31
7: 3+11+23 = 37
8: 3+11+29 = 43
9: 3+17+23 = 43
10: 5+7+11 = 23
11: 5+7+17 = 29
12: 5+7+19 = 31
13: 5+7+29 = 41
14: 5+11+13 = 29
15: 5+13+19 = 37
16: 5+13+23 = 41
17: 5+13+29 = 47
18: 5+17+19 = 41
19: 5+19+23 = 47
20: 5+19+29 = 53
21: 7+11+13 = 31
22: 7+11+19 = 37
23: 7+11+23 = 41
24: 7+11+29 = 47
25: 7+13+17 = 37
26: 7+13+23 = 43
27: 7+17+19 = 43
28: 7+17+23 = 47
29: 7+17+29 = 53
30: 7+23+29 = 59
31: 11+13+17 = 41
32: 11+13+19 = 43
33: 11+13+23 = 47
34: 11+13+29 = 53
35: 11+17+19 = 47
36: 11+19+23 = 53
37: 11+19+29 = 59
38: 13+17+23 = 53
39: 13+17+29 = 59
40: 13+19+29 = 61
41: 17+19+23 = 59
42: 19+23+29 = 71
done...

```

## Rust

`fn prime_sieve(limit: usize) -> Vec<bool> {    let mut sieve = vec![true; limit];    if limit > 0 {        sieve[0] = false;    }    if limit > 1 {        sieve[1] = false;    }    for i in (4..limit).step_by(2) {        sieve[i] = false;    }    let mut p = 3;    loop {        let mut q = p * p;        if q >= limit {            break;        }        if sieve[p] {            let inc = 2 * p;            while q < limit {                sieve[q] = false;                q += inc;            }        }        p += 2;    }    sieve} fn strange_unique_prime_triplets(limit: usize, verbose: bool) {    if limit < 6 {        return;    }    let mut primes = Vec::new();    let sieve = prime_sieve(limit * 3);    for p in (3..limit).step_by(2) {        if sieve[p] {            primes.push(p);        }    }    if verbose {        println!("Strange unique prime triplets < {}:", limit);    }    let mut count = 0;    let n = primes.len();    for i in 0..n - 2 {        for j in i + 1..n - 1 {            for k in j + 1..n {                let sum = primes[i] + primes[j] + primes[k];                if sieve[sum] {                    count += 1;                    if verbose {                        println!(                            "{:2} + {:2} + {:2} = {:2}",                            primes[i], primes[j], primes[k], sum                        );                    }                }            }        }    }    println!(        "Count of strange unique prime triplets < {} is {}.",        limit, count    );} fn main() {    strange_unique_prime_triplets(30, true);    strange_unique_prime_triplets(1000, false);}`
Output:
```Strange unique prime triplets < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71
Count of strange unique prime triplets < 30 is 42.
Count of strange unique prime triplets < 1000 is 241580.
```

## Swift

`import Foundation func primeSieve(limit: Int) -> [Bool] {    guard limit > 0 else {        return []    }    var sieve = Array(repeating: true, count: limit)    sieve[0] = false    if limit > 1 {        sieve[1] = false    }    if limit > 4 {        for i in stride(from: 4, to: limit, by: 2) {            sieve[i] = false        }    }    var p = 3    while true {        var q = p * p        if q >= limit {            break        }        if sieve[p] {            let inc = 2 * p            while q < limit {                sieve[q] = false                q += inc            }        }        p += 2    }    return sieve} func strangeUniquePrimeTriplets(limit: Int, verbose: Bool) {    guard limit > 5 else {        return;    }    let sieve = primeSieve(limit: 3 * limit)    var primes: [Int] = []    for p in stride(from: 3, to: limit, by: 2) {        if sieve[p] {            primes.append(p)        }    }    let n = primes.count    var count = 0    if verbose {        print("Strange unique prime triplets < \(limit):")    }    for i in (0..<n - 2) {        for j in (i + 1..<n - 1) {            for k in (j + 1..<n) {                let sum = primes[i] + primes[j] + primes[k]                if sieve[sum] {                    count += 1                    if verbose {                        print(String(format: "%2d + %2d + %2d = %2d",                                     primes[i], primes[j], primes[k], sum))                    }                }            }        }    }    print("\nCount of strange unique prime triplets < \(limit) is \(count).")} strangeUniquePrimeTriplets(limit: 30, verbose: true)strangeUniquePrimeTriplets(limit: 1000, verbose: false)`
Output:
```Strange unique prime triplets < 30:
3 +  5 + 11 = 19
3 +  5 + 23 = 31
3 +  5 + 29 = 37
3 +  7 + 13 = 23
3 +  7 + 19 = 29
3 + 11 + 17 = 31
3 + 11 + 23 = 37
3 + 11 + 29 = 43
3 + 17 + 23 = 43
5 +  7 + 11 = 23
5 +  7 + 17 = 29
5 +  7 + 19 = 31
5 +  7 + 29 = 41
5 + 11 + 13 = 29
5 + 13 + 19 = 37
5 + 13 + 23 = 41
5 + 13 + 29 = 47
5 + 17 + 19 = 41
5 + 19 + 23 = 47
5 + 19 + 29 = 53
7 + 11 + 13 = 31
7 + 11 + 19 = 37
7 + 11 + 23 = 41
7 + 11 + 29 = 47
7 + 13 + 17 = 37
7 + 13 + 23 = 43
7 + 17 + 19 = 43
7 + 17 + 23 = 47
7 + 17 + 29 = 53
7 + 23 + 29 = 59
11 + 13 + 17 = 41
11 + 13 + 19 = 43
11 + 13 + 23 = 47
11 + 13 + 29 = 53
11 + 17 + 19 = 47
11 + 19 + 23 = 53
11 + 19 + 29 = 59
13 + 17 + 23 = 53
13 + 17 + 29 = 59
13 + 19 + 29 = 61
17 + 19 + 23 = 59
19 + 23 + 29 = 71

Count of strange unique prime triplets < 30 is 42.

Count of strange unique prime triplets < 1000 is 241580.
```

## Visual Basic .NET

Translation of: C#
`Imports DT = System.DateTime Module Module1     Iterator Function Primes(lim As Integer) As IEnumerable(Of Integer)        Dim flags(lim) As Boolean         Dim j = 2         Dim d = 3        Dim sq = 4        While sq <= lim            If Not flags(j) Then                Yield j                For k = sq To lim Step j                    flags(k) = True                Next            End If             j += 1            d += 2            sq += d        End While         While j <= lim            If Not flags(j) Then                Yield j            End If            j += 1        End While    End Function     Sub Main()        For Each lmt In {90, 300, 3000, 30000, 111000}            Dim pr = Primes(lmt).Skip(1).ToList()            Dim st = DT.Now            Dim f = 0            Dim r As New List(Of String)            Dim i = -1            Dim m = lmt \ 3            Dim h = m            While i < 0                i = pr.IndexOf(h)                h -= 1            End While            Dim j = i - 1            Dim k = j - 1            For a = 0 To k                Dim pra = pr(a)                For b = a + 1 To j                    Dim prab = pra + pr(b)                    For c = b + 1 To i                        Dim d = prab + pr(c)                        If Not pr.Contains(d) Then                            Continue For                        End If                        f += 1                        If lmt < 100 Then                            r.Add(String.Format("{3,5} = {0,2} + {1,2} + {2,2}", pra, pr(b), pr(c), d))                        End If                    Next                Next            Next            Dim s = "s.u.p.t.s under "            r.Sort()            If r.Count > 0 Then                Console.WriteLine("{0}{1}:" + vbNewLine + "{2}", s, m, String.Join(vbNewLine, r))            End If            If lmt > 100 Then                Console.WriteLine("Count of {0}{1,6:n0}: {2,13:n0}  {3} sec", s, m, f, (DT.Now - st).ToString().Substring(6))            End If        Next    End Sub End Module`
Output:
`Same as C#`

## Wren

### Basic

Library: Wren-math
Library: Wren-trait
Library: Wren-fmt
`import "/math" for Intimport "/trait" for Steppedimport "/fmt" for Fmt var strangePrimes = Fn.new { |n, countOnly|    var c = 0    var s     for (i in Stepped.new(3..n-4, 2)) {        if (Int.isPrime(i)) {            for (j in Stepped.new(i+2..n-2, 2)) {                if (Int.isPrime(j)) {                    for (k in Stepped.new(j+2..n, 2)) {                        if (Int.isPrime(k) && Int.isPrime(s = i + j + k)) {                            c = c + 1                            if (!countOnly) Fmt.print("\$2d: \$2d + \$2d + \$2d = \$2d", c, i, j, k, s)                        }                    }                }            }        }    }    return c} System.print("Unique prime triples under 30 which sum to a prime:")strangePrimes.call(29, false)var c = strangePrimes.call(999, true)Fmt.print("\nThere are \$,d unique prime triples under 1,000 which sum to a prime.", c)`
Output:
```Unique prime triples under 30 which sum to a prime:
1:  3 +  5 + 11 = 19
2:  3 +  5 + 23 = 31
3:  3 +  5 + 29 = 37
4:  3 +  7 + 13 = 23
5:  3 +  7 + 19 = 29
6:  3 + 11 + 17 = 31
7:  3 + 11 + 23 = 37
8:  3 + 11 + 29 = 43
9:  3 + 17 + 23 = 43
10:  5 +  7 + 11 = 23
11:  5 +  7 + 17 = 29
12:  5 +  7 + 19 = 31
13:  5 +  7 + 29 = 41
14:  5 + 11 + 13 = 29
15:  5 + 13 + 19 = 37
16:  5 + 13 + 23 = 41
17:  5 + 13 + 29 = 47
18:  5 + 17 + 19 = 41
19:  5 + 19 + 23 = 47
20:  5 + 19 + 29 = 53
21:  7 + 11 + 13 = 31
22:  7 + 11 + 19 = 37
23:  7 + 11 + 23 = 41
24:  7 + 11 + 29 = 47
25:  7 + 13 + 17 = 37
26:  7 + 13 + 23 = 43
27:  7 + 17 + 19 = 43
28:  7 + 17 + 23 = 47
29:  7 + 17 + 29 = 53
30:  7 + 23 + 29 = 59
31: 11 + 13 + 17 = 41
32: 11 + 13 + 19 = 43
33: 11 + 13 + 23 = 47
34: 11 + 13 + 29 = 53
35: 11 + 17 + 19 = 47
36: 11 + 19 + 23 = 53
37: 11 + 19 + 29 = 59
38: 13 + 17 + 23 = 53
39: 13 + 17 + 29 = 59
40: 13 + 19 + 29 = 61
41: 17 + 19 + 23 = 59
42: 19 + 23 + 29 = 71

There are 241,580 unique prime triples under 1,000 which sum to a prime.
```

### Faster

The following version uses a prime sieve and is about 17 times faster than the 'basic' version.

`import "/math" for Intimport "/fmt" for Fmt var max = 1000var sieved = Int.primeSieve(3*max, false) // includes compositesvar p = Int.primeSieve(max, true)         // primes only var strangePrimes = Fn.new { |n, countOnly|    var c = 0    var m = 0    while (m < p.count && p[m] <= n) m = m + 1    var r    var s    for (i in 1...m-2) {        for (j in i+1...m-1) {            r = p[i] + p[j]            for (k in j+1...m) {                if (!sieved[s = r + p[k]]) {                    c = c + 1                    if (!countOnly) Fmt.print("\$2d: \$2d + \$2d + \$2d = \$2d", c, p[i], p[j], p[k], s)                }            }        }    }    return c} System.print("Unique prime triples under 30 which sum to a prime:")strangePrimes.call(29, false)var c = strangePrimes.call(999, true)Fmt.print("\nThere are \$,d unique prime triples under 1,000 which sum to a prime.", c)`
Output:

Same as 'basic' version.

## XPL0

`func IsPrime(N);        \Return 'true' if N is primeint  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;];      \IsPrime int Primes, Cnt, P, M, N, S;[Primes:= [2, 3, 5, 7, 11, 13, 17, 19, 23, 29];Format(2, 0);Cnt:= 0;for P:= 2 to 9 do    for M:= 1 to P-1 do        for N:= 0 to M-1 do            [S:= Primes(N) + Primes(M) + Primes(P);            if IsPrime(S) then                [Cnt:= Cnt+1;                RlOut(0, float(Cnt));                Text(0, ":  ");                RlOut(0, float(Primes(N)));                Text(0, " + ");                RlOut(0, float(Primes(M)));                Text(0, " + ");                RlOut(0, float(Primes(P)));                Text(0, "  =  ");                RlOut(0, float(S));                CrLf(0);                ];            ];]`
Output:
``` 1:   3 +  5 + 11  =  19
2:   5 +  7 + 11  =  23
3:   3 +  7 + 13  =  23
4:   5 + 11 + 13  =  29
5:   7 + 11 + 13  =  31
6:   5 +  7 + 17  =  29
7:   3 + 11 + 17  =  31
8:   7 + 13 + 17  =  37
9:  11 + 13 + 17  =  41
10:   3 +  7 + 19  =  29
11:   5 +  7 + 19  =  31
12:   7 + 11 + 19  =  37
13:   5 + 13 + 19  =  37
14:  11 + 13 + 19  =  43
15:   5 + 17 + 19  =  41
16:   7 + 17 + 19  =  43
17:  11 + 17 + 19  =  47
18:   3 +  5 + 23  =  31
19:   3 + 11 + 23  =  37
20:   7 + 11 + 23  =  41
21:   5 + 13 + 23  =  41
22:   7 + 13 + 23  =  43
23:  11 + 13 + 23  =  47
24:   3 + 17 + 23  =  43
25:   7 + 17 + 23  =  47
26:  13 + 17 + 23  =  53
27:   5 + 19 + 23  =  47
28:  11 + 19 + 23  =  53
29:  17 + 19 + 23  =  59
30:   3 +  5 + 29  =  37
31:   5 +  7 + 29  =  41
32:   3 + 11 + 29  =  43
33:   7 + 11 + 29  =  47
34:   5 + 13 + 29  =  47
35:  11 + 13 + 29  =  53
36:   7 + 17 + 29  =  53
37:  13 + 17 + 29  =  59
38:   5 + 19 + 29  =  53
39:  11 + 19 + 29  =  59
40:  13 + 19 + 29  =  61
41:   7 + 23 + 29  =  59
42:  19 + 23 + 29  =  71
```