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Concatenate two primes is also prime (view source)

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;Task:
Find and show here when the concatenation of two primes &nbsp; ('''p<sub>1</sub>''', &nbsp;'''p<sub>2</sub>''') &nbsp; shown in base ten is also prime, &nbsp; where &nbsp; '''p<sub>1</sub>, &nbsp; p<sub>2</sub> &nbsp;&lt;&nbsp; 100'''.
<br><br>
 
=={{header|11l}}==
{{trans|Nim}}
 
<syntaxhighlight lang="11l">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] concatPrimes
L(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 ‘ ’)</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|Action!}}==
{{libheader|Action! Tool Kit}}
{{libheader|Action! Sieve of Eratosthenes}}
<syntaxhighlight lang="action!">INCLUDE "D2:SORT.ACT" ;from the Action! Tool Kit
INCLUDE "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</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Concatenate_two_primes_is_also_prime.png Screenshot from Atari 8-bit computer]
<pre>
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
</pre>
 
=={{header|Ada}}==
<syntaxhighlight lang="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;</syntaxhighlight>
{{out}}
<pre>
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.
</pre>
 
=={{header|ALGOL 68}}==
{{libheader|ALGOL 68-primes}}
<syntaxhighlight lang="algol68">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</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|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.
<syntaxhighlight lang="algolw">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" )
end
end.</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">primesBelow100: select 1..100 => prime?
allPossibleConcats: permutate.repeat.by:2 primesBelow100
 
concatPrimes: allPossibleConcats | map 'x -> to :integer (to :string x\[0]) ++ (to :string x\[1])
| select => prime?
| sort
| unique
 
print ["Found" size concatPrimes "concatenations of primes below 100:"]
loop split.every: 16 concatPrimes 'x ->
print map x 's -> pad to :string s 4
</syntaxhighlight>
 
{{out}}
 
<pre>Found 128 concatenations of 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</pre>
 
=={{header|AWK}}==
<syntaxhighlight lang="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)
}
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|BASIC}}==
==={{header|BASIC256}}===
<syntaxhighlight lang="basic256">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 = 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 p2
next p1
end
 
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 True
end function</syntaxhighlight>
 
==={{header|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.
<syntaxhighlight lang="freebasic">#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 p2
next p1
</syntaxhighlight>
{{out}}<pre>
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
</pre>
 
==={{header|Yabasic}}===
<syntaxhighlight lang="yabasic">c = 0
for 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 p2
next p1
print
end
 
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 True
end sub</syntaxhighlight>
 
 
=={{header|C}}==
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <locale.h>
 
bool isPrime(int n) {
if (n < 2) return false;
if (n%2 == 0) return n == 2;
if (n%3 == 0) return n == 3;
int d = 5;
while (d*d <= n) {
if (n%d == 0) return false;
d += 2;
if (n%d == 0) return false;
d += 4;
}
return true;
}
 
int compare(const void* a, const void* b) {
int arg1 = *(const int*)a;
int arg2 = *(const int*)b;
if (arg1 < arg2) return -1;
if (arg1 > arg2) return 1;
return 0;
}
 
int main() {
int primes[30] = {2}, results[200];
int i, j, p, q, pq, limit = 100, pc = 1, rc = 0;
for (i = 3; i < limit; i += 2) {
if (isPrime(i)) primes[pc++] = i;
}
for (i = 0; i < pc; ++i) {
p = primes[i];
for (j = 0; j < pc; ++j) {
q = primes[j];
pq = (q < 10) ? p * 10 + q : p * 100 + q;
if (isPrime(pq)) results[rc++] = pq;
}
}
qsort(results, rc, sizeof(int), compare);
setlocale(LC_NUMERIC, "");
printf("Two primes under 100 concatenated together to form another prime:\n");
for (i = 0, j = 0; i < rc; ++i) {
if (i > 0 && results[i] == results[i-1]) continue;
printf("%'6d ", results[i]);
if (++j % 10 == 0) printf("\n");
}
printf("\n\nFound %d such concatenated primes.\n", j);
return 0;
}</syntaxhighlight>
 
{{out}}
<pre>
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.
</pre>
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
 
 
<syntaxhighlight lang="Delphi">
 
function Compare(P1,P2: pointer): integer;
{Compare for quick sort}
begin
Result:=Integer(P1)-Integer(P2);
end;
 
procedure ConcatonatePrimes(Memo: TMemo);
{Show concatonated pairs of primes that are also prime}
var List: TList;
var I,P1,P2,ConCat: integer;
var Sieve: TPrimeSieve;
const Max =100;
var S: string;
 
function ConcatNums(I1,I2: integer): integer;
begin
Result:=StrToInt(IntToStr(I1)+IntToStr(I2));
end;
 
begin
{Create sieve to for fast prime generation}
Sieve:=TPrimeSieve.Create;
try
List:=TList.Create;
try
{Sieve first 1,000 primes}
Sieve.Intialize(1000);
 
{Generate all combinations of primes}
{ P1 and P2, from 2 to 100}
P1:=2;
while P1<Max do
begin
P2:=2;
while P2<Max do
begin
{Concatonates the two primes}
ConCat:=ConcatNums(P1,P2);
{Test if it is prime and only store unique primes}
if IsPrime(ConCat) then
if List.IndexOf(Pointer(ConCat))<0 then
List.Add(Pointer(ConCat));
P2:=Sieve.NextPrime(P2);
end;
P1:=Sieve.NextPrime(P1);
end;
{Sort list in numerical order}
List.Sort(Compare);
{Display the result}
Memo.Lines.Add('Concatonated Primes Found: '+IntToStr(List.Count));
for I:=0 to List.Count-1 do
begin
S:=S+Format('%5d',[integer(List[I])]);
if (I mod 10)=9 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
finally List.Free; end;
finally Sieve.Free; end;
end;
 
 
</syntaxhighlight>
{{out}}
<pre>
Concatonated Primes Found: 128
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
Elapsed Time: 3.990 ms.
 
</pre>
 
 
=={{header|EasyLang}}==
<syntaxhighlight>
proc sort . d[] .
for i = 1 to len d[] - 1
for j = i + 1 to len d[]
if d[j] < d[i]
swap d[j] d[i]
.
.
.
.
func isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
for i = 2 to 99
if isprim i = 1
prims[] &= i
.
.
for p1 in prims[]
for p2 in prims[]
h$ = p1 & p2
h = number h$
if isprim h = 1
r[] &= h
.
.
.
sort r[]
print r[]
</syntaxhighlight>
 
=={{header|Factor}}==
{{works with|Factor|0.99 2021-06-02}}
<syntaxhighlight lang="factor">USING: formatting grouping io kernel math.parser math.primes
present prettyprint sequences sets sorting ;
 
"Concatenated-pair primes from primes < 100:" print nl
99 primes-upto [ present ] map dup [ append dec> ] cartesian-map
concat [ prime? ] filter members natural-sort [ length ] keep
8 group simple-table. "\nFound %d concatenated primes.\n" printf</syntaxhighlight>
{{out}}
<pre>
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.
</pre>
 
=={{header|Go}}==
{{libheader|Go-rcu}}
<langsyntaxhighlight lang="go">package main
 
import (
Line 47 ⟶ 750:
}
fmt.Println("\n\nFound", len(results), "such concatenated primes.")
}</langsyntaxhighlight>
 
{{out}}
Line 67 ⟶ 770:
 
Found 128 such concatenated primes.
</pre>
 
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Control.Applicative
import Data.List ( sort )
import Data.List.Split ( chunksOf )
 
isPrime :: Int -> Bool
isPrime 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</syntaxhighlight>
{{out}}
<pre>
[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]
</pre>
 
=={{header|J}}==
<syntaxhighlight lang="j"> concat=. (] + (* 10 ^ #@":))"1 0
 
_12 ]\ /:~ (#~ 1&p:) , concat~ i.&.(p:inv) 100
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</syntaxhighlight>
 
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
 
'''Preliminaries'''
<syntaxhighlight lang="jq">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-printing
def 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] + .;
</syntaxhighlight>
'''The task'''
<syntaxhighlight lang="jq"># Emit [p1,p2] where p1 < p2 < . and the concatenation is prime
def 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(" "))</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="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)
</syntaxhighlight>{{out}}
<pre>
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
</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Select[Catenate /* FromDigits /@ Map[IntegerDigits, Tuples[Prime[Range[PrimePi[100]]], 2], {2}], PrimeQ] // Union</syntaxhighlight>
{{out}}
<pre>{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}</pre>
 
=={{header|Lua}}==
Based on the Algol W sample.
<syntaxhighlight lang="lua">
do -- find primes whose decimal representation is the concatenation of 2 primes < 100
local MAX_PRIME = 99 * 99
-- returns true if n is prime, false otherwise, uses trial division
local function isPrime ( n )
if n < 3 then return n == 2
elseif n % 3 == 0 then return n == 3
elseif n % 2 == 0 then return false
else
local prime = true
local f, f2, toNext = 5, 25, 24
while f2 <= n and prime do
prime = n % f ~= 0
f = f + 2
f2 = toNext
toNext = toNext + 8
end
return prime
end
end
local concatPrime = {}
-- tables of small primes, sp2 will be the final digits so does not include 2 or 5
local sp1 = { 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
}
local sp2 = { 3, 7, 11, 13, 17, 19, 23, 29, 31, 37
, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
}
-- find the concatenated primes
for i = 1, MAX_PRIME do concatPrime[ i ] = false end
for _, p1 in pairs( sp1 ) do
for _, p2 in pairs( sp2 ) do
local pc = ( p1 * ( p2 < 10 and 10 or 100 ) ) + p2
concatPrime[ pc ] = isPrime( pc )
end
end
-- print the concatenated primes
local cCount = 0
for i = 1, MAX_PRIME do
if concatPrime[ i ] then
io.write( string.format( "%5d", i ) )
cCount = cCount + 1
if cCount % 10 == 0 then io.write( "\n" ) end
end
end
io.write( "\n\nFound ", cCount, " concat primes" )
end
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Nim}}==
<langsyntaxhighlight Nimlang="nim">import strutils, sugar
 
func isPrime(n: Positive): bool =
Line 97 ⟶ 1,014:
for n in concatPrimes:
stdout.write ($n).align(4), if i mod 16 == 0: '\n' else: ' '
inc i</langsyntaxhighlight>
 
{{out}}
Line 111 ⟶ 1,028:
 
=={{header|Perl}}==
<langsyntaxhighlight lang="perl">#!/usr/bin/perl
 
use strict; # https://rosettacode.org/wiki/Concatenate_two_primes_is_also_prime
Line 121 ⟶ 1,038:
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;</langsyntaxhighlight>
{{out}}
<pre>
Line 134 ⟶ 1,051:
6719 6737 6761 6779 7129 7159 7331 7919 7937 8311 8317 8329 8353 8389 8923 8929
8941 8971 9719 9743 9767
</pre>
 
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">pq</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;"><</span><span style="color: #000000;">10</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">q</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pq</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">pq</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">unique</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- (see note)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Found %d such primes: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)})</span>
<!--</syntaxhighlight>-->
<small>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.<br>
While the (human-readable) error message (without it) is deep within sort(), the call stack makes it clear where that call should best go.</small>
{{out}}
<pre>
Found 128 such primes: {23,37,53,73,113,"...",8941,8971,9719,9743,9767}
</pre>
 
=={{header|PL/M}}==
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
<syntaxhighlight lang="plm">
100H: /* FIND SOME PAIRS OF PRIMES BETWEEN 1 AND 99 SUCH THAT IF THEIR */
/* DIGITS ARE CONCATENATED, THE RESULT IS ALSO A PRIME */
 
/* CP/M BDOS SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$STRING( .( 0DH, 0AH, '$' ) ); END;
PR$NUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
 
/* TASK */
 
DECLARE FALSE LITERALLY '0';
DECLARE TRUE LITERALLY '0FFH';
DECLARE CONCAT$PRIME LITERALLY '0FH';
DECLARE MAX$LOW$PRIME LITERALLY '99';
DECLARE PRIME ( 10$000 )BYTE; /* PRIME SIEVE. A BIT LARGER THN NEEDED */
/* THE FIRST NYBBLE WILL BE SET TO 0 IF */
/* IT IS A CONCATENATED PRIME */
/* THE SIZE OF PRIME SHOULD BE AT LEAST MAX$LOW$PRIME SQUARED */
/* SIEVE THE PRIMES TO MAX$PRIME */
DECLARE ( I, J, COUNT ) ADDRESS;
PRIME( 1 ) = FALSE; PRIME( 2 ) = TRUE;
DO I = 3 TO LAST( PRIME ) BY 2; PRIME( I ) = TRUE; END;
DO I = 4 TO LAST( PRIME ) BY 2; PRIME( I ) = FALSE; END;
DO I = 3 TO MAX$LOW$PRIME + 1;
IF PRIME( I ) THEN DO;
DO J = I * I TO LAST( PRIME ) BY I + I; PRIME( J ) = FALSE; END;
END;
END;
/* FIND THE CONCATEDNATED PRIMES */
COUNT = 0;
DO I = 2 TO MAX$LOW$PRIME;
IF PRIME( I ) THEN DO;
DO J = 2 TO MAX$LOW$PRIME;
IF PRIME( J ) THEN DO;
DECLARE CP ADDRESS;
IF J < 10 THEN CP = I * 10;
ELSE CP = I * 100;
CP = CP + J;
IF PRIME( I ) AND PRIME( J ) AND PRIME( CP ) THEN DO;
/* CP IS A CONCATENATED PRIME - FLAG PRIME( CP ) AS SUCH */
PRIME( CP ) = CONCAT$PRIME;
END;
END;
END;
END;
END;
/* SHOW THE CONCATENATED PRIMES */
/* SINGLE DIGIT NUMBERS CAN'T BE CONCATENATED PRIMES, START AT 10 */
DO I = 3 TO LAST( PRIME ) BY 2;
IF PRIME( I ) = CONCAT$PRIME THEN DO;
/* HAVE A CONCATENATED PRIME */
CALL PR$CHAR( ' ' );
IF I < 1000 THEN DO;
CALL PR$CHAR( ' ' );
IF I < 100 THEN CALL PR$CHAR( ' ' );
END;
CALL PR$NUMBER( I );
IF ( COUNT := COUNT + 1 ) MOD 10 = 0 THEN CALL PR$NL;
END;
END;
 
EOF
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Python}}==
<syntaxhighlight lang="python">from itertools import takewhile
 
def is_prime(x):
return x > 1 and all(x % d for d in takewhile(lambda n: n * n <= x, primes))
 
def init_primes(n):
global primes
primes = [2]
for x in range(3, n + 1, 2):
if is_prime(x): primes.append(x)
 
def concat(x, y):
return 10 ** len(str(y)) * x + y
 
init_primes(99)
print(*sorted(n for x in primes for y in primes if is_prime(n := concat(x, y))))</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|Quackery}}==
 
<code>isprime</code> is defined at [[Primality by trial division#Quackery]].
 
<syntaxhighlight lang="Quackery"> [ [] swap
[ base share /mod
rot join swap
dup 0 = until ]
drop ] is digits ( n --> [ )
 
[ 0 swap witheach
[ swap 10 * + ] ] is digits->n ( [ --> n )
 
[ behead dup dip nested rot
witheach
[ tuck != if
[ dup dip
[ nested join ] ] ]
drop ] is -duplicates ( [ --> [ )
 
[] dup temp put
100 times
[ i^ isprime if
[ i^ digits
nested join ] ]
dup witheach
[ over witheach
[ over join
digits->n
dup isprime iff
[ temp take
join
temp put ]
else drop ]
drop ]
drop
temp take
sort -duplicates
[ dup [] != while
10 split swap
witheach
[ dup 1000 < if sp
dup 100 < if sp
echo sp ]
cr
again ]
drop</syntaxhighlight>
 
{{out}}
 
<pre> 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
</pre>
 
=={{header|Raku}}==
Inefficient, but for a limit of 100, who cares?
<syntaxhighlight lang="raku" perl6line>my @p = ^1e2 .grep: *.is-prime;
 
say display ( @p X~ @p ).grep( *.is-prime ).unique.sort( +* );
Line 145 ⟶ 1,266:
cache $list;
$title ~ $list.batch($cols)».fmt($fmt).join: "\n"
}</langsyntaxhighlight>
{{out}}
<pre>128 matching:
Line 163 ⟶ 1,284:
 
=={{header|REXX}}==
<langsyntaxhighlight lang="rexx">/*REXX pgm finds & displays 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, ' ,
"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) )
Line 175 ⟶ 1,296:
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)*/
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 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. */
Line 195 ⟶ 1,315:
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found ' commas(found) title
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Line 204 ⟶ 1,324:
#= 5; sq.#= @.#**2 /*the square of the highest low prime. */
do j=@.#+2 by 2 to hip**2-1 /*find odd primes from here on. */
parse var j '' -1 _; if if _==5 then iterate /*J divisible÷ by 5? (right digdigit).*/
if j//3==0 then iterate; if j// 37==0 then iterate /*" " " 3? J ÷ by 7? */
if j// 7==0 then iterate /*" " " 7? */
do k=5 while sq.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
Line 212 ⟶ 1,331:
#= #+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</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
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
Line 232 ⟶ 1,351:
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────
 
Found 128 concatenation of two neighbor primes (P1, P2) in base ten that results in a prime, where P1 & P2 are < 100
</pre>
 
=={{header|Ring}}==
<langsyntaxhighlight lang="ring">
load "stdlib.ring"
see "working..." + nl
Line 279 ⟶ 1,398:
see nl + "Found " + row + " prime numbers" + nl
see "done..." + nl
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 299 ⟶ 1,418:
Found 128 prime numbers
done...
</pre>
 
=={{header|RPL}}==
{{works with|HP|49}}
≪ { } 2
'''DO'''
3
'''DO'''
OVER →STR OVER + STR→
'''IF''' DUP ISPRIME? '''THEN'''
4 ROLL SWAP
'''IF''' DUP2 POS NOT '''THEN''' + '''ELSE''' DROP '''END'''
UNROT
'''ELSE''' DROP '''END'''
NEXTPRIME
'''UNTIL''' DUP 100 > '''END'''
DROP NEXTPRIME
'''UNTIL''' DUP 100 > '''END'''
SORT
≫ '<span style="color:blue">P1P2</span>' STO
 
{{out}}
<pre>
1: { 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 }
</pre>
 
=={{header|Ruby}}==
<syntaxhighlight lang="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?
end
concats = concats.sort.uniq
 
concats.each_slice(10){|slice|puts slice.map{|el| el.to_s.ljust(6)}.join }</syntaxhighlight>
{{out}}
<pre>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
</pre>
 
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">var upto = 100
var arr = upto.primes
var 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."</syntaxhighlight>
{{out}}
<pre>
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.
</pre>
 
Line 305 ⟶ 1,511:
{{libheader|Wren-fmt}}
{{libheader|Wren-seq}}
<langsyntaxhighlight ecmascriptlang="wren">import "./math" for Int
import "./fmt" for Fmt
import "./seq" for Lst
 
var limit = 99
Line 321 ⟶ 1,527:
results.sort()
System.print("Two primes under 100 concatenated together to form another prime:")
Fmt.tprint("$,6d", results, 10)
for (chunk in Lst.chunks(results, 10)) Fmt.print("$,6d", chunk)
System.print("\nFound %(results.count) such concatenated primes.")</langsyntaxhighlight>
 
{{out}}
Line 342 ⟶ 1,548:
 
Found 128 such concatenated primes.
</pre>
 
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number
int 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.
");
]</syntaxhighlight>
 
{{out}}
<pre>
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.
</pre>
PureFox
9,476

edits

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