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# Concatenate two primes is also prime

Concatenate two primes is also prime 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

Find and show here when the concatenation of two primes   (p1,  p2)   shown in base ten is also prime,   where   p1,   p2  <  100.

## 11l

Translation of: Nim
`F is_prime(a)   I a == 2      R 1B   I a < 2 | a % 2 == 0      R 0B   L(i) (3 .. Int(sqrt(a))).step(2)      I a % i == 0         R 0B   R 1B V primes = (2..99).filter(n -> is_prime(n)) Set[Int] concatPrimesL(p1) primes   L(p2) primes      V n = p2 + p1 * (I p2 < 10 {10} E 100)      I is_prime(n)         concatPrimes.add(n) print(‘Found ’concatPrimes.len‘ primes which are a concatenation of two primes below 100:’)L(n) sorted(Array(concatPrimes))   print(‘#4’.format(n), end' I (L.index + 1) % 16 == 0 {"\n"} E ‘ ’)`
Output:
```Found 128 primes which are a concatenation of two primes below 100:
23   37   53   73  113  137  173  193  197  211  223  229  233  241  271  283
293  311  313  317  331  337  347  353  359  367  373  379  383  389  397  433
523  541  547  571  593  613  617  673  677  719  733  743  761  773  797  977
1117 1123 1129 1153 1171 1319 1361 1367 1373 1723 1741 1747 1753 1759 1783 1789
1913 1931 1973 1979 1997 2311 2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159 4337 4373 4397 4723 4729 4759
4783 4789 5323 5347 5923 5953 6113 6131 6143 6173 6197 6719 6737 6761 6779 7129
7159 7331 7919 7937 8311 8317 8329 8353 8389 8923 8929 8941 8971 9719 9743 9767
```

## Action!

`INCLUDE "D2:SORT.ACT" ;from the Action! Tool KitINCLUDE "H6:SIEVE.ACT" PROC Main()  DEFINE MAX="9999"  BYTE ARRAY primes(MAX+1)  BYTE i,j  INT ij,count  INT ARRAY res(130)   Put(125) PutE() ;clear the screen  Sieve(primes,MAX+1)  count=0  FOR i=2 TO 99  DO    IF primes(i) THEN      FOR j=2 TO 99      DO        IF primes(j) THEN          ij=i          IF j<10 THEN            ij==*10          ELSE            ij==*100          FI          ij==+j          IF primes(ij) THEN            res(count)=ij            count==+1          FI        FI      OD    FI  OD   SortI(res,count,0)  FOR i=0 TO count-1  DO    PrintI(res(i)) Put(32)  OD  PrintF("%E%EThere are %I primes",count)RETURN`
Output:
```23 37 53 73 113 137 173 193 197 211 223 229 233 241 271 283 293 311 313 313
317 317 331 337 347 353 359 367 373 373 379 383 389 397 433 523 541 547 571
593 613 617 673 677 719 733 743 761 773 797 797 977 1117 1123 1129 1153 1171
1319 1361 1367 1373 1723 1741 1747 1753 1759 1783 1789 1913 1931 1973 1979
1997 2311 2341 2347 2371 2383 2389 2917 2953 2971 3119 3137 3167 3719 3761
3767 3779 3797 4111 4129 4153 4159 4337 4373 4397 4723 4729 4759 4783 4789
5323 5347 5923 5953 6113 6131 6143 6173 6197 6719 6737 6761 6779 7129 7159
7331 7919 7937 8311 8317 8329 8353 8389 8923 8929 8941 8971 9719 9743 9767

There are 132 primes
```

## Ada

`with Ada.Text_Io;with Ada.Integer_Text_Io;with Ada.Strings.Fixed; procedure Concat_Is_Prime is    Columns : constant := 10;    subtype Full_Range is Integer range 2 .. 9_999;   subtype Low_Range  is Full_Range range Full_Range'First .. 99;    function Concat (Left, Right : Low_Range) return Full_Range is      use Ada.Strings;   begin      return Full_Range'Value (Fixed.Trim (Left'Image, Both) &                                  Fixed.Trim (Right'Image, Both));   end Concat;    use Ada.Text_Io, Ada.Integer_Text_Io;    Is_Prime        : array (Full_Range) of Boolean := (others => True);   Is_Concat_Prime : array (Full_Range) of Boolean := (others => False);   Count           : Natural := 0; begin   for A in Full_Range loop      if Is_Prime (A) then         for B in 2 .. Integer'Last loop            exit when A * B not in Full_Range;            Is_Prime (A * B) := False;         end loop;      end if;   end loop;    for P1 in Low_Range loop      for P2 in Low_Range loop         if           Is_Prime (P1) and Is_Prime (P2) and Is_Prime (Concat (P1, P2))         then            Is_Concat_Prime (Concat (P1, P2)) := True;         end if;      end loop;   end loop;    for A in Is_Concat_Prime'Range loop      if Is_Concat_Prime (A) then         Put (A, Width => 6);         Count := Count + 1;         if Count mod Columns = 0 then            New_Line;         end if;      end if;   end loop;   New_Line;    Put ("There are ");   Put (Natural'Image (Count));   Put (" concat primes.");   New_Line;end Concat_Is_Prime;`
Output:
```    23    37    53    73   113   137   173   193   197   211
223   229   233   241   271   283   293   311   313   317
331   337   347   353   359   367   373   379   383   389
397   433   523   541   547   571   593   613   617   673
677   719   733   743   761   773   797   977  1117  1123
1129  1153  1171  1319  1361  1367  1373  1723  1741  1747
1753  1759  1783  1789  1913  1931  1973  1979  1997  2311
2341  2347  2371  2383  2389  2917  2953  2971  3119  3137
3167  3719  3761  3767  3779  3797  4111  4129  4153  4159
4337  4373  4397  4723  4729  4759  4783  4789  5323  5347
5923  5953  6113  6131  6143  6173  6197  6719  6737  6761
6779  7129  7159  7331  7919  7937  8311  8317  8329  8353
8389  8923  8929  8941  8971  9719  9743  9767
There are  128 concat primes.
```

## ALGOL 68

`BEGIN  # find primes whose decimal representation is the concatenation of 2 primes #    INT max low prime = 99;  # for the task, only need component primes up to 99   #    INT max prime     = max low prime * max low prime;    # sieve the primes to max prime #    PR read "primes.incl.a68" PR    []BOOL prime = PRIMESIEVE max prime;    # construct a list of the primes up to the maximum low prime to consider #    []INT low prime = EXTRACTPRIMESUPTO max low prime FROMPRIMESIEVE prime;    # find the primes that can be concatenated to form another prime #    [ 1 : max prime ]BOOL concat prime; FOR i TO UPB concat prime DO concat prime[ i ] := FALSE OD;    # note that all possible concatenated primes have at least 2 digits, so the final digit can't be 2 #    #      ( or 5 but we don't check that here ) #    FOR i TO UPB low prime WHILE low prime[ i ] <= max low prime DO        INT p1 = low prime[ i ];        FOR j FROM 2 TO UPB low prime WHILE low prime[ j ] <= max low prime DO            INT p2 = low prime[ j ];            INT pc = ( p1 * IF p2 < 10 THEN 10 ELSE 100 FI ) + p2;            concat prime[ pc ] := prime[ pc ]        OD    OD;    # show the concatenated primes #    INT c count := 0;    FOR n TO UPB concat prime DO        IF concat prime[ n ] THEN            print( ( whole( n, -5 ) ) );            IF ( c count +:= 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI        FI    OD;    print( ( newline, newline, "Found ", whole( c count, 0 ), " concat primes", newline ) )END`
Output:
```   23   37   53   73  113  137  173  193  197  211
223  229  233  241  271  283  293  311  313  317
331  337  347  353  359  367  373  379  383  389
397  433  523  541  547  571  593  613  617  673
677  719  733  743  761  773  797  977 1117 1123
1129 1153 1171 1319 1361 1367 1373 1723 1741 1747
1753 1759 1783 1789 1913 1931 1973 1979 1997 2311
2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159
4337 4373 4397 4723 4729 4759 4783 4789 5323 5347
5923 5953 6113 6131 6143 6173 6197 6719 6737 6761
6779 7129 7159 7331 7919 7937 8311 8317 8329 8353
8389 8923 8929 8941 8971 9719 9743 9767

Found 128 concat primes
```

## ALGOL W

The Algol W for loop allows the loop counter values to be specified as a list - as there are only 25 primes below 100, this feature is used here to save looking through the sieve for the low primes.

`begin % find primes whose decimal representation is the concatenation of 2 primes %    integer MAX_PRIME;    MAX_PRIME := 99 * 99;    begin        logical array isPrime     ( 1 :: MAX_PRIME );        logical array concatPrime ( 1 :: MAX_PRIME );        integer cCount;        % sieve the primes to MAX_PRIME                                           %        isPrime( 1 ) := false; isPrime( 2 ) := true;        for i := 3 step 2 until MAX_PRIME do isPrime( i ) := true;        for i := 4 step 2 until MAX_PRIME do isPrime( i ) := false;        for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin            integer ii; ii := i + i;            if isPrime( i ) then for pr := i * i step ii until MAX_PRIME do isPrime( pr ) := false        end for_i ;        % find the concatenated primes, note their final digit can't be 2 or 5    %        for i := 1 until MAX_PRIME do concatPrime( i ) := false;        cCount := 0;        for     p1 :=  2,  3,  5,  7, 11, 13, 17, 19, 23, 29, 31, 37                    , 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 do begin            for p2 :=      3,      7, 11, 13, 17, 19, 23, 29, 31, 37                    , 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 do begin                integer pc;                pc := ( p1 * ( if p2 < 10 then 10 else 100 ) ) + p2;                concatPrime( pc ) := isPrime( pc )            end for_p2        end for_p1;        % print the concatenated primes                                           %        cCount := 0;        for i := 1 until MAX_PRIME do begin            if concatPrime( i ) then begin                writeon( i_w := 5, s_w := 0, i );                cCount := cCount + 1;                if cCount rem 10 = 0 then write()            end if_concatPrime_i        end for_i;        write();write( i_w := 1, s_w := 0, "Found ", cCount, " concat primes" )    endend.`
Output:
```   23   37   53   73  113  137  173  193  197  211
223  229  233  241  271  283  293  311  313  317
331  337  347  353  359  367  373  379  383  389
397  433  523  541  547  571  593  613  617  673
677  719  733  743  761  773  797  977 1117 1123
1129 1153 1171 1319 1361 1367 1373 1723 1741 1747
1753 1759 1783 1789 1913 1931 1973 1979 1997 2311
2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159
4337 4373 4397 4723 4729 4759 4783 4789 5323 5347
5923 5953 6113 6131 6143 6173 6197 6719 6737 6761
6779 7129 7159 7331 7919 7937 8311 8317 8329 8353
8389 8923 8929 8941 8971 9719 9743 9767

Found 128 concat primes
```

## AWK

` # syntax: GAWK -f CONCATENATE_TWO_PRIMES_IS_ALSO_PRIME.AWK## sorting:#   PROCINFO["sorted_in"] is used by GAWK#   SORTTYPE is used by Thompson Automation's TAWK#BEGIN {    start = 1    stop = 99    for (i=start; i<=stop; i++) {      if (is_prime(i)) {        for (j=start; j<=stop; j++) {          if (is_prime(j)) {            if (is_prime(i j)) {              arr[i j] = ""            }          }        }      }    }    PROCINFO["sorted_in"] = "@ind_num_asc" ; SORTTYPE = 1    for (i in arr) {      printf("%5d%1s",i,++count%10?"":"\n")    }    printf("\nConcatenate two primes is also prime %d-%d: %d\n",start,stop,count)    exit(0)}function is_prime(x,  i) {    if (x <= 1) {      return(0)    }    for (i=2; i<=int(sqrt(x)); i++) {      if (x % i == 0) {        return(0)      }    }    return(1)} `
Output:
```   23    37    53    73   113   137   173   193   197   211
223   229   233   241   271   283   293   311   313   317
331   337   347   353   359   367   373   379   383   389
397   433   523   541   547   571   593   613   617   673
677   719   733   743   761   773   797   977  1117  1123
1129  1153  1171  1319  1361  1367  1373  1723  1741  1747
1753  1759  1783  1789  1913  1931  1973  1979  1997  2311
2341  2347  2371  2383  2389  2917  2953  2971  3119  3137
3167  3719  3761  3767  3779  3797  4111  4129  4153  4159
4337  4373  4397  4723  4729  4759  4783  4789  5323  5347
5923  5953  6113  6131  6143  6173  6197  6719  6737  6761
6779  7129  7159  7331  7919  7937  8311  8317  8329  8353
8389  8923  8929  8941  8971  9719  9743  9767
Concatenate two primes is also prime 1-99: 128
```

## BASIC

### BASIC256

`c = 0for p1 = 2 to 99	if not isPrime(p1) then continue for	for p2 = 2 to 99		if not isPrime(p2) then continue for		cat = rjust(string(p1),2) + rjust(string(p2),2)		if isPrime(cat) then			c += 1			print p1; "|"; p2; "  ";			if c mod 10 = 0 then print		end if	next p2next p1end function isPrime(v)	if v < 2 then return False	if v mod 2 = 0 then return v = 2	if v mod 3 = 0 then return v = 3	d = 5	while d * d <= v		if v mod d = 0 then return False else d += 2	end while	return Trueend function`

### FreeBASIC

This solution focuses more on the primes p1, p2 than on the concatenated prime. Thus, there can be multiple solutions. For example, 373 can be formed from 37 and 3 or from 3 and 73 and will be listed twice.

`#include "isprime.bas"dim as integer p1, p2, cat, c = 0 for p1 = 2 to 99    if not isprime(p1) then continue for    for p2 = 2 to 99        if not isprime(p2) then continue for        cat = val( str(p1) + str(p2) )    ' =^..^=        if isprime(cat) then             c+=1            print using "##|##  ";p1;p2;            if c mod 10 = 0 then print        end if    next p2next p1 `
Output:
```
2| 3   2|11   2|23   2|29   2|41   2|71   2|83   3| 7   3|11   3|13
3|17   3|31   3|37   3|47   3|53   3|59   3|67   3|73   3|79   3|83
3|89   3|97   5| 3   5|23   5|41   5|47   5|71   7| 3   7|19   7|43
7|61   7|73   7|97  11| 3  11|17  11|23  11|29  11|53  11|71  13| 7
13|19  13|61  13|67  13|73  17| 3  17|23  17|41  17|47  17|53  17|59
17|83  17|89  19| 3  19| 7  19|13  19|31  19|73  19|79  19|97  23| 3
23|11  23|41  23|47  23|71  23|83  23|89  29| 3  29|17  29|53  29|71
31| 3  31| 7  31|19  31|37  31|67  37| 3  37|19  37|61  37|67  37|79
37|97  41|11  41|29  41|53  41|59  43| 3  43|37  43|73  43|97  47|23
47|29  47|59  47|83  47|89  53|23  53|47  59| 3  59|23  59|53  61| 3
61| 7  61|13  61|31  61|43  61|73  61|97  67| 3  67| 7  67|19  67|37
67|61  67|79  71|29  71|59  73| 3  73|31  79| 7  79|19  79|37  83|11
83|17  83|29  83|53  83|89  89|23  89|29  89|41  89|71  97| 7  97|19
97|43  97|67

```

### Yabasic

`c = 0for p1 = 2 to 99    if not isPrime(p1) then continue : fi    for p2 = 2 to 99        if not isPrime(p2) then continue : fi        cat = val(str\$(p1) + str\$(p2))        if isPrime(cat) then             c = c + 1			a\$ = str\$(p1,"##")			b\$ = str\$(p2,"##")			print a\$, "|", b\$, "  ";            if mod(c, 10) = 0 then print : fi        end if    next p2next p1printend sub isPrime(v)    if v < 2 then return False : fi    if mod(v, 2) = 0 then return v = 2 : fi    if mod(v, 3) = 0 then return v = 3 : fi    d = 5    while d * d <= v        if mod(v, d) = 0 then return False else d = d + 2 : fi    wend    return Trueend sub`

## Factor

Works with: Factor version 0.99 2021-06-02
`USING: formatting grouping io kernel math.parser math.primespresent prettyprint sequences sets sorting ; "Concatenated-pair primes from primes < 100:" print nl99 primes-upto [ present ] map dup [ append dec> ] cartesian-mapconcat [ prime? ] filter members natural-sort [ length ] keep8 group simple-table. "\nFound %d concatenated primes.\n" printf`
Output:
```Concatenated-pair primes from primes < 100:

23   37   53   73   113  137  173  193
197  211  223  229  233  241  271  283
293  311  313  317  331  337  347  353
359  367  373  379  383  389  397  433
523  541  547  571  593  613  617  673
677  719  733  743  761  773  797  977
1117 1123 1129 1153 1171 1319 1361 1367
1373 1723 1741 1747 1753 1759 1783 1789
1913 1931 1973 1979 1997 2311 2341 2347
2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129
4153 4159 4337 4373 4397 4723 4729 4759
4783 4789 5323 5347 5923 5953 6113 6131
6143 6173 6197 6719 6737 6761 6779 7129
7159 7331 7919 7937 8311 8317 8329 8353
8389 8923 8929 8941 8971 9719 9743 9767

Found 128 concatenated primes.
```

## Go

Library: Go-rcu
`package main import (    "fmt"    "rcu"    "sort") func main() {    const LIMIT = 99    primes := rcu.Primes(LIMIT)    rmap := make(map[int]bool)    for _, p := range primes {        for _, q := range primes {            var pq int            if q < 10 {                pq = p*10 + q            } else {                pq = p*100 + q            }            if rcu.IsPrime(pq) {                rmap[pq] = true            }        }    }    results := make([]int, len(rmap))    i := 0    for k := range rmap {        results[i] = k        i++    }    sort.Ints(results)    fmt.Println("Two primes under 100 concatenated together to form another prime:")    for i, p := range results {        fmt.Printf("%5s ", rcu.Commatize(p))        if (i+1)%10 == 0 {            fmt.Println()        }    }    fmt.Println("\n\nFound", len(results), "such concatenated primes.")}`
Output:
```Two primes under 100 concatenated together to form another prime:
23    37    53    73   113   137   173   193   197   211
223   229   233   241   271   283   293   311   313   317
331   337   347   353   359   367   373   379   383   389
397   433   523   541   547   571   593   613   617   673
677   719   733   743   761   773   797   977 1,117 1,123
1,129 1,153 1,171 1,319 1,361 1,367 1,373 1,723 1,741 1,747
1,753 1,759 1,783 1,789 1,913 1,931 1,973 1,979 1,997 2,311
2,341 2,347 2,371 2,383 2,389 2,917 2,953 2,971 3,119 3,137
3,167 3,719 3,761 3,767 3,779 3,797 4,111 4,129 4,153 4,159
4,337 4,373 4,397 4,723 4,729 4,759 4,783 4,789 5,323 5,347
5,923 5,953 6,113 6,131 6,143 6,173 6,197 6,719 6,737 6,761
6,779 7,129 7,159 7,331 7,919 7,937 8,311 8,317 8,329 8,353
8,389 8,923 8,929 8,941 8,971 9,719 9,743 9,767

Found 128 such concatenated primes.
```

## Haskell

`import Control.Applicativeimport Data.List ( sort ) import Data.List.Split ( chunksOf ) isPrime :: Int -> BoolisPrime n    |n == 2 = True   |n == 1 = False   |otherwise = null \$ filter (\i -> mod n i == 0 ) [2 .. root]   where      root :: Int      root = floor \$ sqrt \$ fromIntegral n solution :: [Int]solution = sort \$ filter isPrime \$ map read ( (++) <\$> numberlist <*> numberlist )  where   numberlist :: [String]   numberlist = map show \$ filter isPrime [1 .. 99] main :: IO ( ) main = do  mapM_ print \$ chunksOf 15 solution`
Output:
```[23,37,53,73,113,137,173,193,197,211,223,229,233,241,271]
[283,293,311,313,313,317,317,331,337,347,353,359,367,373,373]
[379,383,389,397,433,523,541,547,571,593,613,617,673,677,719]
[733,743,761,773,797,797,977,1117,1123,1129,1153,1171,1319,1361,1367]
[1373,1723,1741,1747,1753,1759,1783,1789,1913,1931,1973,1979,1997,2311,2341]
[2347,2371,2383,2389,2917,2953,2971,3119,3137,3167,3719,3761,3767,3779,3797]
[4111,4129,4153,4159,4337,4373,4397,4723,4729,4759,4783,4789,5323,5347,5923]
[5953,6113,6131,6143,6173,6197,6719,6737,6761,6779,7129,7159,7331,7919,7937]
[8311,8317,8329,8353,8389,8923,8929,8941,8971,9719,9743,9767]
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

Preliminaries

`def is_prime:  . as \$n  | if (\$n < 2)         then false    elif (\$n % 2 == 0)  then \$n == 2    elif (\$n % 3 == 0)  then \$n == 3    elif (\$n % 5 == 0)  then \$n == 5    elif (\$n % 7 == 0)  then \$n == 7    elif (\$n % 11 == 0) then \$n == 11    elif (\$n % 13 == 0) then \$n == 13    elif (\$n % 17 == 0) then \$n == 17    elif (\$n % 19 == 0) then \$n == 19    else {i:23}    | until( (.i * .i) > \$n or (\$n % .i == 0); .i += 2)    | .i * .i > \$n    end; # Emit an array of primes less than `.`def primes:  if . < 2 then []  else    [2] + [range(3; .; 2) | select(is_prime)]  end; # Pretty-printingdef nwise(\$n):  def n: if length <= \$n then . else .[0:\$n] , (.[\$n:] | n) end;  n; def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .; `

The task

`# Emit [p1,p2] where p1 < p2 < . and the concatenation is primedef concatenative_primes:  primes  | range(0;length) as \$i  | range(\$i+1;length) as \$j  | [.[\$i], .[\$j]], [.[\$j], .[\$i]]  | select( map(tostring) | add | tonumber | is_prime); [100 | concatenative_primes | join("||")]| (nwise(10) | map(lpad(6)) | join(" "))`
Output:
```  2||3  2||11  2||23  2||29  2||41  2||71  2||83   5||3   3||7   7||3
3||11  11||3  3||13  3||17  17||3  19||3  23||3  29||3  3||31  31||3
3||37  37||3  43||3  3||47  3||53  3||59  59||3  61||3  3||67  67||3
3||73  73||3  3||79  3||83  3||89  3||97  5||23  5||41  5||47  5||71
13||7  7||19  19||7  31||7  7||43  7||61  61||7  67||7  7||73  79||7
7||97  97||7 11||17 11||23 23||11 11||29 41||11 11||53 11||71 83||11
13||19 19||13 13||61 61||13 13||67 13||73 17||23 29||17 17||41 17||47
17||53 17||59 17||83 83||17 17||89 19||31 31||19 37||19 67||19 19||73
19||79 79||19 19||97 97||19 23||41 23||47 47||23 53||23 59||23 23||71
23||83 23||89 89||23 41||29 47||29 29||53 29||71 71||29 83||29 89||29
31||37 61||31 31||67 73||31 43||37 37||61 37||67 67||37 37||79 79||37
37||97 41||53 41||59 89||41 61||43 43||73 43||97 97||43 53||47 47||59
47||83 47||89 59||53 83||53 71||59 67||61 61||73 61||97 67||79 97||67
```

## Julia

`using Primes function catprimes()    found, pri = Int[], primes(100)    for x in pri, y in pri        n = x + y * (x < 10 ? 10 : 100)        isprime(n) && push!(found, n)    end    return sort!(unique(found))end foreach(p -> print(lpad(last(p), 5), first(p) % 16 == 0 ? "\n" : ""),    catprimes() |> enumerate) `
Output:
```   23   37   53   73  113  137  173  193  197  211  223  229  233  241  271  283
293  311  313  317  331  337  347  353  359  367  373  379  383  389  397  433
523  541  547  571  593  613  617  673  677  719  733  743  761  773  797  977
1117 1123 1129 1153 1171 1319 1361 1367 1373 1723 1741 1747 1753 1759 1783 1789
1913 1931 1973 1979 1997 2311 2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159 4337 4373 4397 4723 4729 4759
4783 4789 5323 5347 5923 5953 6113 6131 6143 6173 6197 6719 6737 6761 6779 7129
7159 7331 7919 7937 8311 8317 8329 8353 8389 8923 8929 8941 8971 9719 9743 9767
```

## Mathematica/Wolfram Language

`Select[Catenate /* FromDigits /@ Map[IntegerDigits, Tuples[Prime[Range[PrimePi[100]]], 2], {2}], PrimeQ] // Union`
Output:
`{23, 37, 53, 73, 113, 137, 173, 193, 197, 211, 223, 229, 233, 241, 271, 283, 293, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 433, 523, 541, 547, 571, 593, 613, 617, 673, 677, 719, 733, 743, 761, 773, 797, 977, 1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1913, 1931, 1973, 1979, 1997, 2311, 2341, 2347, 2371, 2383, 2389, 2917, 2953, 2971, 3119, 3137, 3167, 3719, 3761, 3767, 3779, 3797, 4111, 4129, 4153, 4159, 4337, 4373, 4397, 4723, 4729, 4759, 4783, 4789, 5323, 5347, 5923, 5953, 6113, 6131, 6143, 6173, 6197, 6719, 6737, 6761, 6779, 7129, 7159, 7331, 7919, 7937, 8311, 8317, 8329, 8353, 8389, 8923, 8929, 8941, 8971, 9719, 9743, 9767}`

## Nim

`import strutils, sugar func isPrime(n: Positive): bool =  if n == 1: return false  if (n and 1) == 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    if n mod (d + 2) == 0: return false    inc d, 6  result = true # List of primes.const Primes = collect(newSeq, for n in 2..<100: (if n.isPrime: n)) var concatPrimes: set[0..9999]    # Using a set to eliminate duplicates and avoid sort.for p1 in Primes:  for p2 in Primes:    let n = p2 + p1 * (if p2 < 10: 10 else: 100)    if n.isPrime:      concatPrimes.incl n echo "Found \$# primes which are a concatenation of two primes below 100:".format(concatPrimes.len)var i = 1for n in concatPrimes:  stdout.write (\$n).align(4), if i mod 16 == 0: '\n' else: ' '  inc i`
Output:
```Found 128 primes which are a concatenation of two primes below 100:
23   37   53   73  113  137  173  193  197  211  223  229  233  241  271  283
293  311  313  317  331  337  347  353  359  367  373  379  383  389  397  433
523  541  547  571  593  613  617  673  677  719  733  743  761  773  797  977
1117 1123 1129 1153 1171 1319 1361 1367 1373 1723 1741 1747 1753 1759 1783 1789
1913 1931 1973 1979 1997 2311 2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159 4337 4373 4397 4723 4729 4759
4783 4789 5323 5347 5923 5953 6113 6131 6143 6173 6197 6719 6737 6761 6779 7129
7159 7331 7919 7937 8311 8317 8329 8353 8389 8923 8929 8941 8971 9719 9743 9767```

## Perl

`#!/usr/bin/perl use strict; # https://rosettacode.org/wiki/Concatenate_two_primes_is_also_primeuse warnings;use ntheory qw( primes is_prime );use List::Util qw( uniq ); my @primes = @{ primes(100) };my @valid = uniq sort { \$a <=> \$b } grep is_prime(\$_),  map { my \$prefix = \$_; map "\$prefix\$_", @primes } @primes;print @valid . " primes found\n\n@valid\n" =~ s/.{79}\K /\n/gr;`
Output:
```128 primes found

23 37 53 73 113 137 173 193 197 211 223 229 233 241 271 283 293 311 313 317 331
337 347 353 359 367 373 379 383 389 397 433 523 541 547 571 593 613 617 673 677
719 733 743 761 773 797 977 1117 1123 1129 1153 1171 1319 1361 1367 1373 1723 1741
1747 1753 1759 1783 1789 1913 1931 1973 1979 1997 2311 2341 2347 2371 2383 2389
2917 2953 2971 3119 3137 3167 3719 3761 3767 3779 3797 4111 4129 4153 4159 4337
4373 4397 4723 4729 4759 4783 4789 5323 5347 5923 5953 6113 6131 6143 6173 6197
6719 6737 6761 6779 7129 7159 7331 7919 7937 8311 8317 8329 8353 8389 8923 8929
8941 8971 9719 9743 9767
```

## Phix

```with javascript_semantics
sequence primes = get_primes_le(100),
result = {}
for i=1 to length(primes) do
integer p = primes[i]
for j=1 to length(primes) do
integer q = primes[j],
pq = p*iff(q<10?10:100)+q
if is_prime(pq) then result &= pq end if
end for
end for
result = unique(deep_copy(result)) -- (see note)
printf(1,"Found %d such primes: %V\n",{length(result),shorten(result,"",5)})
```

Note: The deep_copy() [for pwa/p2js] on such calls to unique() would be unnecessary were result routine-local, due to automatic pbr, but here that variable is file-level.
While the (human-readable) error message (without it) is deep within sort(), the call stack makes it clear where that call should best go.

Output:
```Found 128 such primes: {23,37,53,73,113,"...",8941,8971,9719,9743,9767}
```

## Raku

Inefficient, but for a limit of 100, who cares?

`my @p = ^1e2 .grep: *.is-prime; say display ( @p X~ @p ).grep( *.is-prime ).unique.sort( +* );  sub display (\$list, :\$cols = 10, :\$fmt = '%6d', :\$title = "{+\$list} matching:\n") {    cache \$list;    \$title ~ \$list.batch(\$cols)».fmt(\$fmt).join: "\n"}`
Output:
```128 matching:
23     37     53     73    113    137    173    193    197    211
223    229    233    241    271    283    293    311    313    317
331    337    347    353    359    367    373    379    383    389
397    433    523    541    547    571    593    613    617    673
677    719    733    743    761    773    797    977   1117   1123
1129   1153   1171   1319   1361   1367   1373   1723   1741   1747
1753   1759   1783   1789   1913   1931   1973   1979   1997   2311
2341   2347   2371   2383   2389   2917   2953   2971   3119   3137
3167   3719   3761   3767   3779   3797   4111   4129   4153   4159
4337   4373   4397   4723   4729   4759   4783   4789   5323   5347
5923   5953   6113   6131   6143   6173   6197   6719   6737   6761
6779   7129   7159   7331   7919   7937   8311   8317   8329   8353
8389   8923   8929   8941   8971   9719   9743   9767```

## REXX

`/*REXX pgm finds base ten neighbor primes P1 & P2,  when concatenated,  is also a prime.*/parse arg hip cols .                             /*obtain optional arguments from the CL*/if  hip=='' |  hip==","  then  hip= 100          /*Not specified?  Then use the default.*/if cols=='' | cols==","  then cols=  10          /* "      "         "   "   "     "    */call genP                                        /*build array of semaphores for primes.*/title= ' concatenation of two neighbor primes (P1, P2) in base ten that results in'  ,                                    "a prime, where P1 & P2 are <"           commas(hip)w= 10                                            /*width of a number in any column.     */if cols>0  then say ' index │'center(title,   1 + cols*(w+1)     )if cols>0  then say '───────┼'center(""   ,   1 + cols*(w+1), '─')a.= 0                                            /*array of  "2cat"  primes             */          do    j=1  for ##                      /*search through specified primes.     */             do k=1  for ##;   cat2= @.j || @.k  /*create a concatenated prime (base 10)*/             if !.cat2  then a.cat2= 1           /*flag it as being a  "2cat"  prime.   */             end   /*k*/                         /* [↑]   forgoes the need for sorting. */          end      /*j*/found= 0;                            idx= 1      /*initialize # of primes found;  IDX.  */\$=;       do n=1  by 2  for hip**2%2             /*search for odd  "cat2"  primes.      */          if \a.n  then iterate                  /*search through allowable primes.     */          found= found + 1                       /*bump the number of primes found.     */          if cols<=0            then iterate     /*Build the list  (to be shown later)? */          c= commas(n)                           /*maybe add commas to the number.      */          \$= \$  right(c, max(w, length(c) ) )    /*add a prime  ──►  \$ list, allow big #*/          if found//cols\==0    then iterate     /*have we populated a line of output?  */          say center(idx, 7)'│' substr(\$, 2); \$= /*display what we have so far  (cols). */          idx= idx + cols                        /*bump the  index  count for the output*/          end   /*n*/ if \$\==''  then say center(idx, 7)"│"  substr(\$, 2)  /*possible display residual output.*/if cols>0  then say '───────┴'center(""   ,   1 + cols*(w+1), '─')saysay 'Found '      commas(found)      titleexit 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:        @.1=2; @.2=3; @.3=5; @.4=7;  @.5=11 /*define some low primes.              */      !.=0;  !.2=1; !.3=1; !.5=1; !.7=1;  !.11=1 /*   "     "   "    "     semaphores.  */                           #= 5;  sq.#= @.#**2   /*the square of the highest low prime. */        do [email protected].#+2  by 2  to hip**2-1            /*find odd primes from here on.        */        parse var  j   ''  -1  _;  if    _==5  then iterate  /*J ÷ by 5?  (right digit).*/        if j//3==0  then iterate;  if j//7==0  then iterate  /*" "  " 3?   J ÷ by 7?    */               do k=5  while sq.k<=j             /* [↓]  divide by the known odd primes.*/               if j // @.k == 0  then iterate j  /*Is  J ÷ X?  Then not prime.     ___  */               end   /*k*/                       /* [↑]  only process numbers  ≤  √ J   */        #= #+1;    @.#= j;    sq.#= j*j;  !.j= 1 /*bump # of Ps; assign next P;  P²; P# */        if j<hip  then ##= #                     /*find a shortcut for the 1st DO loop. */        end          /*j*/;               return`
output   when using the default inputs:
``` index │   concatenation of two neighbor primes (P1, P2) in base ten that results in a prime, where P1 & P2 are < 100
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
1   │         23         37         53         73        113        137        173        193        197        211
11   │        223        229        233        241        271        283        293        311        313        317
21   │        331        337        347        353        359        367        373        379        383        389
31   │        397        433        523        541        547        571        593        613        617        673
41   │        677        719        733        743        761        773        797        977      1,117      1,123
51   │      1,129      1,153      1,171      1,319      1,361      1,367      1,373      1,723      1,741      1,747
61   │      1,753      1,759      1,783      1,789      1,913      1,931      1,973      1,979      1,997      2,311
71   │      2,341      2,347      2,371      2,383      2,389      2,917      2,953      2,971      3,119      3,137
81   │      3,167      3,719      3,761      3,767      3,779      3,797      4,111      4,129      4,153      4,159
91   │      4,337      4,373      4,397      4,723      4,729      4,759      4,783      4,789      5,323      5,347
101  │      5,923      5,953      6,113      6,131      6,143      6,173      6,197      6,719      6,737      6,761
111  │      6,779      7,129      7,159      7,331      7,919      7,937      8,311      8,317      8,329      8,353
121  │      8,389      8,923      8,929      8,941      8,971      9,719      9,743      9,767
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  128  concatenation of two neighbor primes (P1, P2) in base ten that results in a prime, where P1 & P2 are < 100
```

## Ring

` load "stdlib.ring"see "working..." + nlsee "Concatenate two primes is also prime:" + nlrow = 0prime = [] for n = 1 to 100    for m = 1 to 100        ps1 = string(n)        ps2 = string(m)        ps12 = ps1 + ps2        ps21 = ps2 + ps1        p1 = number(ps12)        p2 = number(ps21)        if isprime(n) and isprime(m)           if isprime(p1)              pf = find(prime,p1)              if pf < 1                 add(prime,p1)              ok           ok           if isprime(p2)              pf = find(prime,p2)              if pf < 1                 add(prime,p2)              ok           ok        ok    nextnext prime = sort(prime)for n = 1 to len(prime)    row++    see "" + prime[n] + " "    if row%10 = 0       see nl    oknext see nl + "Found " + row + " prime numbers" + nlsee "done..." + nl `
Output:
```working...
Concatenate two primes is also prime:
23 37 53 73 113 137 173 193 197 211
223 229 233 241 271 283 293 311 313 317
331 337 347 353 359 367 373 379 383 389
397 433 523 541 547 571 593 613 617 673
677 719 733 743 761 773 797 977 1117 1123
1129 1153 1171 1319 1361 1367 1373 1723 1741 1747
1753 1759 1783 1789 1913 1931 1973 1979 1997 2311
2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159
4337 4373 4397 4723 4729 4759 4783 4789 5323 5347
5923 5953 6113 6131 6143 6173 6197 6719 6737 6761
6779 7129 7159 7331 7919 7937 8311 8317 8329 8353
8389 8923 8929 8941 8971 9719 9743 9767
Found 128 prime numbers
done...
```

## Ruby

`require "prime" concats =  Prime.each(100).to_a.repeated_permutation(2).filter_map do |pair|  p1p2 = pair.map(&:to_s).join.to_i  p1p2 if p1p2.prime? endconcats = concats.sort.uniq concats.each_slice(10){|slice|puts slice.map{|el| el.to_s.ljust(6)}.join }`
Output:
```23    37    53    73    113   137   173   193   197   211
223   229   233   241   271   283   293   311   313   317
331   337   347   353   359   367   373   379   383   389
397   433   523   541   547   571   593   613   617   673
677   719   733   743   761   773   797   977   1117  1123
1129  1153  1171  1319  1361  1367  1373  1723  1741  1747
1753  1759  1783  1789  1913  1931  1973  1979  1997  2311
2341  2347  2371  2383  2389  2917  2953  2971  3119  3137
3167  3719  3761  3767  3779  3797  4111  4129  4153  4159
4337  4373  4397  4723  4729  4759  4783  4789  5323  5347
5923  5953  6113  6131  6143  6173  6197  6719  6737  6761
6779  7129  7159  7331  7919  7937  8311  8317  8329  8353
8389  8923  8929  8941  8971  9719  9743  9767
```

## Sidef

`var upto = 100var arr  = upto.primesvar base = 10 arr = arr.map {|p|    var d = p.digits(base);    arr.map {|q| [q.digits(base)..., d...].digits2num(base) }.grep { .is_prime }}.flat.uniq.sort say "Concatenated primes from primes p,q <= #{upto}:" arr.each_slice(10, {|*a|    say a.map { '%6s' % _ }.join(' ')}) say "\nFound #{arr.len} such concatenated primes."`
Output:
```Concatenated primes from primes p,q <= 100:
23     37     53     73    113    137    173    193    197    211
223    229    233    241    271    283    293    311    313    317
331    337    347    353    359    367    373    379    383    389
397    433    523    541    547    571    593    613    617    673
677    719    733    743    761    773    797    977   1117   1123
1129   1153   1171   1319   1361   1367   1373   1723   1741   1747
1753   1759   1783   1789   1913   1931   1973   1979   1997   2311
2341   2347   2371   2383   2389   2917   2953   2971   3119   3137
3167   3719   3761   3767   3779   3797   4111   4129   4153   4159
4337   4373   4397   4723   4729   4759   4783   4789   5323   5347
5923   5953   6113   6131   6143   6173   6197   6719   6737   6761
6779   7129   7159   7331   7919   7937   8311   8317   8329   8353
8389   8923   8929   8941   8971   9719   9743   9767

Found 128 such concatenated primes.
```

## Wren

Library: Wren-math
Library: Wren-fmt
Library: Wren-seq
`import "/math" for Intimport "/fmt" for Fmtimport "/seq" for Lst var limit = 99var primes = Int.primeSieve(limit)var results = []for (p in primes) {    for (q in primes) {        var pq = (q < 10) ? p*10 + q : p*100 + q        if (Int.isPrime(pq)) results.add(pq)    }}results = Lst.distinct(results)results.sort()System.print("Two primes under 100 concatenated together to form another prime:")for (chunk in Lst.chunks(results, 10)) Fmt.print("\$,6d", chunk)System.print("\nFound %(results.count) such concatenated primes.")`
Output:
```Two primes under 100 concatenated together to form another prime:
23     37     53     73    113    137    173    193    197    211
223    229    233    241    271    283    293    311    313    317
331    337    347    353    359    367    373    379    383    389
397    433    523    541    547    571    593    613    617    673
677    719    733    743    761    773    797    977  1,117  1,123
1,129  1,153  1,171  1,319  1,361  1,367  1,373  1,723  1,741  1,747
1,753  1,759  1,783  1,789  1,913  1,931  1,973  1,979  1,997  2,311
2,341  2,347  2,371  2,383  2,389  2,917  2,953  2,971  3,119  3,137
3,167  3,719  3,761  3,767  3,779  3,797  4,111  4,129  4,153  4,159
4,337  4,373  4,397  4,723  4,729  4,759  4,783  4,789  5,323  5,347
5,923  5,953  6,113  6,131  6,143  6,173  6,197  6,719  6,737  6,761
6,779  7,129  7,159  7,331  7,919  7,937  8,311  8,317  8,329  8,353
8,389  8,923  8,929  8,941  8,971  9,719  9,743  9,767

Found 128 such concatenated primes.
```

## XPL0

`func IsPrime(N);        \Return 'true' if N is a prime numberint  N, I;[if N <= 1 then return false;for I:= 2 to sqrt(N) do    if rem(N/I) = 0 then return false;return true;]; char Set(9999+1);int  P1, P2, P, Count;[for P:= 0 to 9999 do Set(P):= false;for P1:= 0 to 99 do  if IsPrime(P1) then    for P2:= 0 to 99 do      if IsPrime(P2) then        [if P2 >= 10 then              P:= P1*100 + P2        else  P:= P1*10 + P2;        if IsPrime(P) then Set(P):= true;        ];Count:= 0;for P:= 0 to 9999 do    if Set(P) then        [IntOut(0, P);        Count:= Count+1;        if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);        ];CrLf(0);IntOut(0, Count);Text(0, " such concatenated primes found.");]`
Output:
```23      37      53      73      113     137     173     193     197     211
223     229     233     241     271     283     293     311     313     317
331     337     347     353     359     367     373     379     383     389
397     433     523     541     547     571     593     613     617     673
677     719     733     743     761     773     797     977     1117    1123
1129    1153    1171    1319    1361    1367    1373    1723    1741    1747
1753    1759    1783    1789    1913    1931    1973    1979    1997    2311
2341    2347    2371    2383    2389    2917    2953    2971    3119    3137
3167    3719    3761    3767    3779    3797    4111    4129    4153    4159
4337    4373    4397    4723    4729    4759    4783    4789    5323    5347
5923    5953    6113    6131    6143    6173    6197    6719    6737    6761
6779    7129    7159    7331    7919    7937    8311    8317    8329    8353
8389    8923    8929    8941    8971    9719    9743    9767
128 such concatenated primes found.
```