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Additive primes

From Rosetta Code
Additive primes 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.
Definitions

In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.


Task

Write a program to determine (and show here) all additive primes less than 500.

Optionally, show the number of additive primes.


Also see



ALGOL 68[edit]

BEGIN # find additive primes - primes whose digit sum is also prime #
INT max prime = 499;
# sieve the primes to max prime #
[ 1 : max prime ]BOOL prime;
prime[ 1 ] := FALSE; prime[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( max prime ) DO
IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI
OD;
# find the additive primes #
INT additive count := 0;
FOR n TO max prime DO
IF prime[ n ] THEN
# have a prime #
INT digit sum := 0;
INT v := n;
WHILE v > 0 DO
digit sum +:= v MOD 10;
v OVERAB 10
OD;
IF prime( digit sum ) THEN
# the digit sum is prime #
print( ( " ", whole( n, -3 ) ) );
IF ( additive count +:= 1 ) MOD 20 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline, "Found ", whole( additive count, 0 ), " additive primes below ", whole( max prime + 1, 0 ), newline ) )
END
Output:
   2   3   5   7  11  23  29  41  43  47  61  67  83  89 101 113 131 137 139 151
 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337
 353 359 373 379 397 401 409 421 443 449 461 463 467 487
Found 54 additive primes below 500

ALGOL W[edit]

begin % find some additive primes - primes whose digit sum is also prime %
 % 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 ;
integer MAX_NUMBER;
MAX_NUMBER := 500;
begin
logical array prime( 1 :: MAX_NUMBER );
integer aCount;
 % sieve the primes to MAX_NUMBER %
Eratosthenes( prime, MAX_NUMBER );
 % find the primes that are additive primes %
aCount := 0;
for i := 1 until MAX_NUMBER - 1 do begin
if prime( i ) then begin
integer dSum, v;
v  := i;
dSum := 0;
while v > 0 do begin
dSum := dSum + v rem 10;
v  := v div 10
end while_v_gt_0 ;
if prime( dSum ) then begin
writeon( i_w := 4, s_w := 0, " ", i );
aCount := aCount + 1;
if aCount rem 20 = 0 then write()
end if_prime_dSum
end if_prime_i
end for_i ;
write( i_w := 1, s_w := 0, "Found ", aCount, " additive primes below ", MAX_NUMBER )
end
end.
Output:
    2    3    5    7   11   23   29   41   43   47   61   67   83   89  101  113  131  137  139  151
  157  173  179  191  193  197  199  223  227  229  241  263  269  281  283  311  313  317  331  337
  353  359  373  379  397  401  409  421  443  449  461  463  467  487
Found 54 additive primes below 500

APL[edit]

((+⌿(4/10)⊤P)∊P)/P←(~P∊P∘.×P)/P←1↓⍳500
Output:
2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283
      311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487

AppleScript[edit]

on sieveOfEratosthenes(limit)
script o
property numberList : {missing value}
end script
 
repeat with n from 2 to limit
set end of o's numberList to n
end repeat
 
repeat with n from 2 to (limit ^ 0.5) div 1
if (item n of o's numberList is n) then
repeat with multiple from n * n to limit by n
set item multiple of o's numberList to missing value
end repeat
end if
end repeat
 
return o's numberList's numbers
end sieveOfEratosthenes
 
on sumOfDigits(n) -- n assumed to be a positive decimal integer.
set sum to n mod 10
set n to n div 10
repeat until (n = 0)
set sum to sum + n mod 10
set n to n div 10
end repeat
 
return sum
end sumOfDigits
 
on additivePrimes(limit)
script o
property primes : sieveOfEratosthenes(limit)
property additives : {}
end script
 
repeat with p in o's primes
if (sumOfDigits(p) is in o's primes) then set end of o's additives to p's contents
end repeat
 
return o's additives
end additivePrimes
 
-- Task code:
tell additivePrimes(499) to return {|additivePrimes<500|:it, numberThereof:count}
Output:
{|additivePrimes<500|:{2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 241, 263, 269, 281, 283, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 461, 463, 467, 487}, numberThereof:54}

Arturo[edit]

additives: select 2..500 'x -> and? prime? x prime? sum digits x
 
loop split.every:10 additives 'a ->
print map a => [pad to :string & 4]
 
print ["\nFound" size additives "additive primes up to 500"]
Output:
   2    3    5    7   11   23   29   41   43   47 
  61   67   83   89  101  113  131  137  139  151 
 157  173  179  191  193  197  199  223  227  229 
 241  263  269  281  283  311  313  317  331  337 
 353  359  373  379  397  401  409  421  443  449 
 461  463  467  487 

Found 54 additive primes up to 500

AWK[edit]

 
# syntax: GAWK -f ADDITIVE_PRIMES.AWK
BEGIN {
start = 1
stop = 500
for (i=start; i<=stop; i++) {
if (is_prime(i) && is_prime(sum_digits(i))) {
printf("%4d%1s",i,++count%10?"":"\n")
}
}
printf("\nAdditive primes %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)
}
function sum_digits(n, i,sum) {
for (i=1; i<=length(n); i++) {
sum += substr(n,i,1)
}
return(sum)
}
 
Output:
   2    3    5    7   11   23   29   41   43   47
  61   67   83   89  101  113  131  137  139  151
 157  173  179  191  193  197  199  223  227  229
 241  263  269  281  283  311  313  317  331  337
 353  359  373  379  397  401  409  421  443  449
 461  463  467  487
Additive primes 1-500: 54

BASIC[edit]

10 DEFINT A-Z: E=500
20 DIM P(E): P(0)=-1: P(1)=-1
30 FOR I=2 TO SQR(E)
40 IF NOT P(I) THEN FOR J=I*2 TO E STEP I: P(J)=-1: NEXT
50 NEXT
60 FOR I=B TO E: IF P(I) GOTO 100
70 J=I: S=0
80 IF J>0 THEN S=S+J MOD 10: J=J\10: GOTO 80
90 IF NOT P(S) THEN N=N+1: PRINT I,
100 NEXT
110 PRINT: PRINT N;" additive primes found below ";E
Output:
 2             3             5             7             11
 23            29            41            43            47
 61            67            83            89            101
 113           131           137           139           151
 157           173           179           191           193
 197           199           223           227           229
 241           263           269           281           283
 311           313           317           331           337
 353           359           373           379           397
 401           409           421           443           449
 461           463           467           487
 54  additive primes found below  500

BCPL[edit]

get "libhdr"
manifest $( limit = 500 $)
 
let dsum(n) =
n=0 -> 0,
dsum(n/10) + n rem 10
 
let sieve(prime, n) be
$( 0!prime := false
1!prime := false
for i=2 to n do i!prime := true
for i=2 to n/2
if i!prime
$( let j=i+i
while j<=n
$( j!prime := false
j := j+i
$)
$)
$)
 
let additive(prime, n) = n!prime & dsum(n)!prime
 
let start() be
$( let prime = vec limit
let num = 0
sieve(prime, limit)
for i=2 to limit
if additive(prime,i)
$( writed(i,5)
num := num + 1
if num rem 10 = 0 then wrch('*N')
$)
writef("*N*NFound %N additive primes < %N.*N", num, limit)
$)
Output:
    2    3    5    7   11   23   29   41   43   47
   61   67   83   89  101  113  131  137  139  151
  157  173  179  191  193  197  199  223  227  229
  241  263  269  281  283  311  313  317  331  337
  353  359  373  379  397  401  409  421  443  449
  461  463  467  487

Found 54 additive primes < 500.

C++[edit]

#include <iomanip>
#include <iostream>
 
bool is_prime(unsigned int n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (unsigned int p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}
 
unsigned int digit_sum(unsigned int n) {
unsigned int sum = 0;
for (; n > 0; n /= 10)
sum += n % 10;
return sum;
}
 
int main() {
const unsigned int limit = 500;
std::cout << "Additive primes less than " << limit << ":\n";
unsigned int count = 0;
for (unsigned int n = 1; n < limit; ++n) {
if (is_prime(digit_sum(n)) && is_prime(n)) {
std::cout << std::setw(3) << n;
if (++count % 10 == 0)
std::cout << '\n';
else
std::cout << ' ';
}
}
std::cout << '\n' << count << " additive primes found.\n";
}
Output:
Additive primes less than 500:
  2   3   5   7  11  23  29  41  43  47
 61  67  83  89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487 
54 additive primes found.

F#[edit]

This task uses Extensible Prime Generator (F#)

 
// Additive Primes. Nigel Galloway: March 22nd., 2021
let rec fN g=function n when n<10->n+g |n->fN(g+n%10)(n/10)
primes32()|>Seq.takeWhile((>)500)|>Seq.filter(fN 0>>isPrime)|>Seq.iter(printf "%d "); printfn ""
 
Output:
2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487

Factor[edit]

Works with: Factor version 0.99 2021-02-05
USING: formatting grouping io kernel math math.primes
prettyprint sequences ;
 
: sum-digits ( n -- sum )
0 swap [ 10 /mod rot + swap ] until-zero ;
 
499 primes-upto [ sum-digits prime? ] filter
[ 9 group simple-table. nl ]
[ length "Found  %d additive primes < 500.\n" printf ] bi
Output:
2   3   5   7   11  23  29  41  43
47  61  67  83  89  101 113 131 137
139 151 157 173 179 191 193 197 199
223 227 229 241 263 269 281 283 311
313 317 331 337 353 359 373 379 397
401 409 421 443 449 461 463 467 487

Found  54  additive primes  <  500.

Forth[edit]

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!
2
begin
2dup dup * >
while
dup prime? if
2dup dup * do
i notprime!
dup +loop
then
1+
repeat
2drop ;
 
: digit_sum ( u -- u )
dup 10 < if exit then
10 /mod recurse + ;
 
: print_additive_primes ( n -- )
." Additive primes less than " dup 1 .r ." :" cr
dup prime_sieve
0 swap
1 do
i prime? if
i digit_sum prime? if
i 3 .r
1+ dup 10 mod 0= if cr else space then
then
then
loop
cr . ." additive primes found." cr ;
 
500 print_additive_primes
bye
Output:
Additive primes less than 500:
  2   3   5   7  11  23  29  41  43  47
 61  67  83  89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487 
54 additive primes found.

FreeBASIC[edit]

As with the other special primes tasks, use one of the primality testing algorithms as an include.

#include "isprime.bas"
 
function digsum( n as uinteger ) as uinteger
dim as uinteger s
while n
s+=n mod 10
n\=10
wend
return s
end function
 
dim as uinteger s
 
print "Prime","Digit Sum"
for i as uinteger = 2 to 499
if isprime(i) then
s = digsum(i)
if isprime(s) then
print i, s
end if
end if
next i
Output:
Prime         Digit Sum
2             2
3             3
5             5
7             7
11            2
23            5
29            11
41            5
43            7
47            11
61            7
67            13
83            11
89            17
101           2
113           5
131           5
137           11
139           13
151           7
157           13
173           11
179           17
191           11
193           13
197           17
199           19
223           7
227           11
229           13
241           7
263           11
269           17
281           11
283           13
311           5
313           7
317           11
331           7
337           13
353           11
359           17
373           13
379           19
397           19
401           5
409           13
421           7
443           11
449           17
461           11
463           13
467           17
487           19

Go[edit]

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 sumDigits(n int) int {
sum := 0
for n > 0 {
sum += n % 10
n /= 10
}
return sum
}
 
func main() {
fmt.Println("Additive primes less than 500:")
i := 2
count := 0
for {
if isPrime(i) && isPrime(sumDigits(i)) {
count++
fmt.Printf("%3d ", i)
if count%10 == 0 {
fmt.Println()
}
}
if i > 2 {
i += 2
} else {
i++
}
if i > 499 {
break
}
}
fmt.Printf("\n\n%d additive primes found.\n", count)
}
Output:
Additive primes less than 500:
  2    3    5    7   11   23   29   41   43   47  
 61   67   83   89  101  113  131  137  139  151  
157  173  179  191  193  197  199  223  227  229  
241  263  269  281  283  311  313  317  331  337  
353  359  373  379  397  401  409  421  443  449  
461  463  467  487
 
54 additive primes found.

Julia[edit]

using Primes
 
let
p = primesmask(500)
println("Additive primes under 500:")
pcount = 0
for i in 2:499
if p[i] && p[sum(digits(i))]
pcount += 1
print(lpad(i, 4), pcount % 20 == 0 ? "\n" : "")
end
end
println("\n\n$pcount additive primes found.")
end
 
Output:
Erdős primes under 500:
   2   3   5   7  11  23  29  41  43  47  61  67  83  89 101 113 131 137 139 151
 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337
 353 359 373 379 397 401 409 421 443 449 461 463 467 487

54 additive primes found.

Nim[edit]

import math, strutils
 
const N = 499
 
# Sieve of Erathostenes.
var composite: array[2..N, bool] # Initialized to false, ie. prime.
 
for n in 2..sqrt(N.toFloat).int:
if not composite[n]:
for k in countup(n * n, N, n):
composite[k] = true
 
 
func digitSum(n: Positive): Natural =
## Compute sum of digits.
var n = n.int
while n != 0:
result += n mod 10
n = n div 10
 
 
echo "Additive primes less than 500:"
var count = 0
for n in 2..N:
if not composite[n] and not composite[digitSum(n)]:
inc count
stdout.write ($n).align(3)
stdout.write if count mod 10 == 0: '\n' else: ' '
echo()
 
echo "\nNumber of additive primes found: ", count
Output:
Additive primes less than 500:
  2   3   5   7  11  23  29  41  43  47
 61  67  83  89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487 

Number of additive primes found: 54

Perl[edit]

Library: ntheory
use strict;
use warnings;
use ntheory 'is_prime';
use List::Util <sum max>;
 
sub pp {
my $format = ('%' . (my $cw = 1+length max @_) . 'd') x @_;
my $width = ".{@{[$cw * int 60/$cw]}}";
(sprintf($format, @_)) =~ s/($width)/$1\n/gr;
}
 
my($limit, @ap) = 500;
is_prime($_) and is_prime(sum(split '',$_)) and push @ap, $_ for 1..$limit;
 
print @ap . " additive primes < $limit:\n" . pp(@ap);
Output:
54 additive primes < 500:
   2   3   5   7  11  23  29  41  43  47  61  67  83  89 101
 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229
 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397
 401 409 421 443 449 461 463 467 487

Phix[edit]

function additive(integer p) return is_prime(sum(sq_sub(sprint(p),'0'))) end function
sequence res = filter(get_primes_le(500),additive)
string r = join(shorten(apply(res,sprint),"",6))
printf(1,"%d additive primes found: %s\n",{length(res),r})
Output:
54 additive primes found: 2 3 5 7 11 23 ... 443 449 461 463 467 487

PL/M[edit]

100H: /* FIND ADDITIVE PRIMES - PRIMES WHOSE DIGIT SUM IS ALSO PRIME */
 
DECLARE CR LITERALLY '0DH';
DECLARE LF LITERALLY '0AH';
 
BDOS: PROCEDURE( FN, ARG ); /* CP/M BDOS SYSTEM CALL */
DECLARE FN BYTE, ARG ADDRESS;
GOTO 5;
END BDOS;
PRINT$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PRINT$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PRINT$NL: PROCEDURE; CALL PRINT$STRING( .( CR, LF, '$' ) ); END;
PRINT$NUMBER: PROCEDURE( N, WIDTH );
DECLARE N ADDRESS, WIDTH BYTE;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, ( N$POS, W ) BYTE;
V = N; W = WIDTH + 1;
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( W > 0 );
W = W - 1;
V = V / 10;
IF V = 0 THEN N$STR( W ) = ' ';
ELSE N$STR( W ) = '0' + ( V MOD 10 );
END;
CALL PRINT$STRING( .N$STR( W + 1 ) );
END PRINT$NUMBER;
 
DECLARE MAX$PRIME LITERALLY '501';
DECLARE FALSE LITERALLY '0';
DECLARE TRUE LITERALLY '1';
DECLARE PRIME( MAX$PRIME ) BYTE; /* ELEMENT 0 IS UNUSED */
DECLARE ( A$COUNT, I, J ) ADDRESS;
/* SIEVE THE PRIMES UP TO MAX$PRIME */
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 LAST( PRIME ) / 2 BY 2;
IF PRIME( I ) THEN DO;
DO J = I * I TO LAST( PRIME ) BY I; PRIME( J ) = FALSE; END;
END;
END;
/* FIND THE PRIMES THAT ARE ADDATIVE PRIMES */
A$COUNT = 0;
DO I = 1 TO LAST( PRIME );
IF PRIME( I ) THEN DO;
DECLARE D$SUM BYTE, V ADDRESS;
V = I;
D$SUM = 0;
DO WHILE V > 0;
D$SUM = D$SUM + ( V MOD 10 );
V = V / 10;
END;
IF PRIME( D$SUM ) THEN DO;
CALL PRINT$NUMBER( I, 4 );
A$COUNT = A$COUNT + 1;
IF A$COUNT MOD 12 = 0 THEN CALL PRINT$NL;
END;
END;
END;
CALL PRINT$NL;
CALL PRINT$NUMBER( A$COUNT, 4 );
CALL PRINT$STRING( .' ADDITIVE PRIMES FOUND BELOW$' );
CALL PRINT$NUMBER( LAST( PRIME ), 4 );
CALL PRINT$NL;
EOF
 
Output:
   2   3   5   7  11  23  29  41  43  47  61  67
  83  89 101 113 131 137 139 151 157 173 179 191
 193 197 199 223 227 229 241 263 269 281 283 311
 313 317 331 337 353 359 373 379 397 401 409 421
 443 449 461 463 467 487
  54 ADDITIVE PRIMES FOUND BELOW 500


Processing[edit]

IntList primes = new IntList();
 
void setup() {
sieve(500);
int count = 0;
for (int i = 2; i < 500; i++) {
if (primes.hasValue(i) && primes.hasValue(sumDigits(i))) {
print(i + " ");
count++;
}
}
println();
print("Number of additive primes less than 500: " + count);
}
 
int sumDigits(int n) {
int sum = 0;
for (int i = 0; i <= floor(log(n) / log(10)); i++) {
sum += floor(n / pow(10, i)) % 10;
}
return sum;
}
 
void sieve(int max) {
for (int i = 2; i <= max; i++) {
primes.append(i);
}
for (int i = 0; i < primes.size(); i++) {
for (int j = i + 1; j < primes.size(); j++) {
if (primes.get(j) % primes.get(i) == 0) {
primes.remove(j);
j--;
}
}
}
}
Output:
2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487 
Number of additive primes less than 500: 54

Quackery[edit]

eratosthenes and isprime are defined at Sieve of Eratosthenes#Quackery.

digitsum is defined at Sum digits of an integer#Quackery.

  500 eratosthenes
 
[]
500 times
[ i^ isprime if
[ i^ 10 digitsum
isprime if
[ i^ join ] ] ]
dup echo cr cr
size echo say " additive primes found."
Output:
[ 2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487 ]

54 additive primes found.


Raku[edit]

unit sub MAIN ($limit = 500);
say "{+$_} additive primes < $limit:\n{$_».fmt("%" ~ $limit.chars ~ "d").batch(10).join("\n")}",
with ^$limit .grep: { .is-prime and .comb.sum.is-prime }
Output:
54 additive primes < 500:
  2   3   5   7  11  23  29  41  43  47
 61  67  83  89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487

REXX[edit]

/*REXX program counts/displays the number of additive primes under a specified number N.*/
parse arg n cols . /*get optional number of primes to find*/
if n=='' | n=="," then n= 500 /*Not specified? Then assume default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " */
call genP n /*generate all primes under N. */
w= 10 /*width of a number in any column. */
title= " additive primes that are < " n
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
Aprimes= 0; idx= 1 /*initialize # of additive primes & idx*/
$= /*a list of additive primes (so far). */
do j=2 until j>=n; if \!.j then iterate /*Is J not a prime? No, then skip it.*/ /* ◄■■■■■■■■ a filter. */
_= sumDigs(j); if \!._ then iterate /*is sum of J's digs a prime? No, skip.*/ /* ◄■■■■■■■■ a filter. */
Aprimes= Aprimes + 1 /*bump the count of additive primes. */
if cols<0 then iterate /*Build the list (to be shown later)? */
c= commas(j) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add additive prime──►list, allow big#*/
if Aprimes//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 /*j*/
 
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'found ' commas(Aprimes) title
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 ?
sumDigs: parse arg x 1 s 2; do k=2 for length(x)-1; s= s + substr(x,k,1); end; return s
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: parse arg n; @.=.; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; #= 7
w= length(n);  !.=0; !.2=1;  !.3=1;  !.5=1;  !.7=1;  !.11=1;  !.13=1;  !.17=1
do [email protected].7+2 by 2 while j<n /*continue on with the next odd prime. */
parse var j '' -1 _ /*obtain the last digit of the J var.*/
if _ ==5 then iterate /*is this integer a multiple of five? */
if j // 3 ==0 then iterate /* " " " " " " three? */
/* [↓] divide by the primes. ___ */
do k=4 to # while k*k<=j /*divide J by other primes ≤ √ J */
if j//@.k == 0 then iterate j /*÷ by prev. prime? ¬prime ___ */
end /*k*/ /* [↑] only divide up to √ J */
#= # + 1; @.#= j;  !.j= 1 /*bump prime count; assign prime & flag*/
end /*j*/; return
output   when using the default inputs:
 index │                                        additive primes that are  <  500
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          2          3          5          7         11         23         29         41         43         47
  11   │         61         67         83         89        101        113        131        137        139        151
  21   │        157        173        179        191        193        197        199        223        227        229
  31   │        241        263        269        281        283        311        313        317        331        337
  41   │        353        359        373        379        397        401        409        421        443        449
  51   │        461        463        467        487
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

found  54  additive primes that are  <  500

Ring[edit]

 
load "stdlib.ring"
 
see "working..." + nl
see "Additive primes are:" + nl
 
row = 0
limit = 500
 
for n = 1 to limit
num = 0
if isprime(n)
strn = string(n)
for m = 1 to len(strn)
num = num + number(strn[m])
next
if isprime(num)
row = row + 1
see "" + n + " "
if row%10 = 0
see nl
ok
ok
ok
next
 
see nl + "found " + row + " additive primes." + nl
see "done..." + nl
 
Output:
working...
Additive primes are:
2 3 5 7 11 23 29 41 43 47 
61 67 83 89 101 113 131 137 139 151 
157 173 179 191 193 197 199 223 227 229 
241 263 269 281 283 311 313 317 331 337 
353 359 373 379 397 401 409 421 443 449 
461 463 467 487 
found 54 additive primes.
done...

Seed7[edit]

$ include "seed7_05.s7i";
 
const func boolean: isPrime (in integer: number) is func
result
var boolean: prime is FALSE;
local
var integer: upTo is 0;
var integer: testNum is 3;
begin
if number = 2 then
prime := TRUE;
elsif odd(number) and number > 2 then
upTo := sqrt(number);
while number rem testNum <> 0 and testNum <= upTo do
testNum +:= 2;
end while;
prime := testNum > upTo;
end if;
end func;
 
const func integer: digitSum (in var integer: number) is func
result
var integer: sum is 0;
begin
while number > 0 do
sum +:= number rem 10;
number := number div 10;
end while;
end func;
 
const proc: main is func
local
var integer: n is 0;
var integer: count is 0;
begin
for n range 2 to 499 do
if isPrime(n) and isPrime(digitSum(n)) then
write(n lpad 3 <& " ");
incr(count);
if count rem 9 = 0 then
writeln;
end if;
end if;
end for;
writeln("\nFound " <& count <& " additive primes < 500.");
end func;
Output:
  2   3   5   7  11  23  29  41  43
 47  61  67  83  89 101 113 131 137
139 151 157 173 179 191 193 197 199
223 227 229 241 263 269 281 283 311
313 317 331 337 353 359 373 379 397
401 409 421 443 449 461 463 467 487

Found 54 additive primes < 500.

Wren[edit]

Library: Wren-math
Library: Wren-fmt
import "/math" for Int
import "/fmt" for Fmt
 
var sumDigits = Fn.new { |n|
var sum = 0
while (n > 0) {
sum = sum + (n % 10)
n = (n/10).floor
}
return sum
}
 
System.print("Additive primes less than 500:")
var primes = Int.primeSieve(499)
var count = 0
for (p in primes) {
if (Int.isPrime(sumDigits.call(p))) {
count = count + 1
Fmt.write("$3d ", p)
if (count % 10 == 0) System.print()
}
}
System.print("\n\n%(count) additive primes found.")
Output:
Additive primes less than 500:
  2    3    5    7   11   23   29   41   43   47  
 61   67   83   89  101  113  131  137  139  151  
157  173  179  191  193  197  199  223  227  229  
241  263  269  281  283  311  313  317  331  337  
353  359  373  379  397  401  409  421  443  449  
461  463  467  487  

54 additive primes found.

XPL0[edit]

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;
];
 
func SumDigits(N); \Return the sum of the digits in N
int N, Sum;
[Sum:= 0;
repeat N:= N/10;
Sum:= Sum + rem(0);
until N=0;
return Sum;
];
 
int Count, N;
[Count:= 0;
for N:= 0 to 500-1 do
if IsPrime(N) & IsPrime(SumDigits(N)) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
];
CrLf(0);
IntOut(0, Count);
Text(0, " additive primes found below 500.
");
]
Output:
2       3       5       7       11      23      29      41      43      47
61      67      83      89      101     113     131     137     139     151
157     173     179     191     193     197     199     223     227     229
241     263     269     281     283     311     313     317     331     337
353     359     373     379     397     401     409     421     443     449
461     463     467     487     
54 additive primes found below 500.