Additive primes

From Rosetta Code
Task
Additive primes
You are encouraged to solve this task according to the task description, using any language you may know.
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



11l[edit]

Translation of: Python
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

F digit_sum(=n)
   V sum = 0
   L n > 0
      sum += n % 10
      n I/= 10
   R sum

V additive_primes = 0
L(i) 2..499
   I is_prime(i) & is_prime(digit_sum(i))
      additive_primes++
      print(i, end' ‘ ’)
print("\nFound "additive_primes‘ additive primes less than 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 less than 500

AArch64 Assembly[edit]

Works with: as version Raspberry Pi 3B version Buster 64 bits
or android 64 bits with application Termux
/* ARM assembly AARCH64 Raspberry PI 3B or android 64 bits */
/*  program additivePrime64.s   */
 
/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
 
.equ MAXI,      500
 
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessResult:       .asciz "Prime  : @ \n"
szMessCounter:      .asciz "Number found : @ \n" 
szCarriageReturn:   .asciz "\n"
 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
sZoneConv:                  .skip 24
TablePrime:                 .skip 8 * MAXI 
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                               // entry of program 

    bl createArrayPrime
    mov x5,x0                       // prime number

    ldr x4,qAdrTablePrime           // address prime table
    mov x10,#0                      // init counter
    mov x6,#0                       // indice
1:
    ldr x2,[x4,x6,lsl #3]           // load prime
    mov x9,x2                       // save prime
    mov x7,#0                       // init digit sum
    mov x1,#10                      // divisor
2:                                  // begin loop
    mov x0,x2                       // dividende
    udiv x2,x0,x1
    msub x3,x2,x1,x0                // compute remainder
    add x7,x7,x3                    // add digit to digit sum
    cmp x2,#0                       // quotient null ?
    bne 2b                          // no -> comppute other digit

    mov x8,#1                       // indice
4:                                  // prime search loop 
    cmp x8,x5                       // maxi ?
    bge 5f                          // yes
    ldr x0,[x4,x8,lsl #3]           // load prime
    cmp x0,x7                       // prime >= digit sum ?
    add x0,x8,1
    csel x8,x0,x8,lt                // no -> increment indice
    blt 4b                          // and loop
    bne 5f                          // > 
    mov x0,x9                       // equal
    bl displayPrime
    add x10,x10,#1                  // increment counter
5:
    add x6,x6,#1                    // increment first indice
    cmp x6,x5                       // maxi ?
    blt 1b                          // and loop
    
    mov x0,x10                      // number counter
    ldr x1,qAdrsZoneConv
    bl conversion10                 // call décimal conversion
    ldr x0,qAdrszMessCounter
    ldr x1,qAdrsZoneConv            // insert conversion in message
    bl strInsertAtCharInc
    bl affichageMess                // display message
 
100:                                // standard end of the program 
    mov x0, #0                      // return code
    mov x8, #EXIT                   // request to exit program
    svc #0                          // perform the system call
qAdrszCarriageReturn:     .quad szCarriageReturn
qAdrszMessResult:         .quad szMessResult
qAdrszMessCounter:        .quad szMessCounter
qAdrTablePrime:           .quad TablePrime
/******************************************************************/
/*      créate prime array                                       */ 
/******************************************************************/
createArrayPrime:
    stp x1,lr,[sp,-16]!       // save  registres
    ldr x4,qAdrTablePrime    // address prime table
    mov x0,#1                      
    str x0,[x4]              // store 1 in array
    mov x0,#2
    str x0,[x4,#8]           // store 2 in array
    mov x0,#3
    str x0,[x4,#16]          // store 3 in array
    mov x5,#3                // prine counter 
    mov x7,#5                // first number to test
1:
    mov x6,#1                // indice
2:
    mov x0,x7                // dividende
    ldr x1,[x4,x6,lsl #3]    // load divisor
    udiv x2,x0,x1
    msub x3,x2,x1,x0         // compute remainder
    cmp x3,#0                // null remainder ?
    beq 4f                   // yes -> end loop
    cmp x2,x1                // quotient < divisor
    bge 3f
    str x7,[x4,x5,lsl #3]    // dividende is prime store in array
    add x5,x5,#1             // increment counter
    b 4f                     // and end loop
3:
    add x6,x6,#1             // else increment indice
    cmp x6,x5                // maxi ?
    blt 2b                   // no -> loop
4:
    add x7,x7,#2             // other odd number
    cmp x7,#MAXI             // maxi ?
    blt 1b                   // no -> loop
    mov x0,x5                // return counter
100:
    ldp x1,lr,[sp],16         // restaur des  2 registres
    ret
/******************************************************************/
/*      Display prime table elements                                */ 
/******************************************************************/
/* x0 contains the prime */
displayPrime:
    stp x1,lr,[sp,-16]!       // save  registres
    ldr x1,qAdrsZoneConv
    bl conversion10           // call décimal conversion
    ldr x0,qAdrszMessResult
    ldr x1,qAdrsZoneConv      // insert conversion in message
    bl strInsertAtCharInc
    bl affichageMess          // display message
100:
    ldp x1,lr,[sp],16         // restaur des  2 registres
    ret

qAdrsZoneConv:                   .quad sZoneConv  

/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
Prime  : 2
Prime  : 3
Prime  : 5
Prime  : 7
Prime  : 11
Prime  : 23
Prime  : 29
Prime  : 41
Prime  : 43
Prime  : 47
Prime  : 61
Prime  : 67
Prime  : 83
Prime  : 89
Prime  : 101
Prime  : 113
Prime  : 131
Prime  : 137
Prime  : 139
Prime  : 151
Prime  : 157
Prime  : 173
Prime  : 179
Prime  : 191
Prime  : 193
Prime  : 197
Prime  : 199
Prime  : 223
Prime  : 227
Prime  : 229
Prime  : 241
Prime  : 263
Prime  : 269
Prime  : 281
Prime  : 283
Prime  : 311
Prime  : 313
Prime  : 317
Prime  : 331
Prime  : 337
Prime  : 353
Prime  : 359
Prime  : 373
Prime  : 379
Prime  : 397
Prime  : 401
Prime  : 409
Prime  : 421
Prime  : 443
Prime  : 449
Prime  : 461
Prime  : 463
Prime  : 467
Prime  : 487
Number found : 54

Ada[edit]

with Ada.Text_Io;

procedure Additive_Primes is

   Last    : constant := 499;
   Columns : constant := 12;

   type Prime_List is array (2 .. Last) of Boolean;

   function Get_Primes return Prime_List is
      Prime : Prime_List := (others => True);
   begin
      for P in Prime'Range loop
         if Prime (P) then
            for N in 2 .. Positive'Last loop
               exit when N * P not in Prime'Range;
               Prime (N * P) := False;
            end loop;
         end if;
      end loop;
      return Prime;
   end Get_Primes;

   function Sum_Of (N : Natural) return Natural is
      Image : constant String := Natural'Image (N);
      Sum   : Natural := 0;
   begin
      for Char of Image loop
         Sum := Sum + (if Char in '0' .. '9'
                       then Natural'Value ("" & Char)
                       else 0);
      end loop;
      return Sum;
   end Sum_Of;

   package Natural_Io is new Ada.Text_Io.Integer_Io (Natural);
   use Ada.Text_Io, Natural_Io;

   Prime : constant Prime_List := Get_Primes;
   Count : Natural := 0;
begin
   Put_Line ("Additive primes <500:");
   for N in Prime'Range loop
      if Prime (N) and then Prime (Sum_Of (N)) then
         Count := Count + 1;
         Put (N, Width => 5);
         if Count mod Columns = 0 then
            New_Line;
         end if;
      end if;
   end loop;
   New_Line;

   Put ("There are ");
   Put (Count, Width => 2);
   Put (" additive primes.");
   New_Line;
end Additive_Primes;
Output:
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
There are 54 additive primes.

ALGOL 68[edit]

BEGIN # find additive primes - primes whose digit sum is also prime #
    # sieve the primes to max prime #
    PR read "primes.incl.a68" PR
    []BOOL prime = PRIMESIEVE 499;
    # find the additive primes #
    INT additive count := 0;
    FOR n TO UPB 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( UPB 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(~PP∘.×P)/P1↓⍳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}

ARM Assembly[edit]

Works with: as version Raspberry Pi
or android 32 bits with application Termux
/* ARM assembly Raspberry PI  */
/*  program additivePrime.s   */
 
 /* REMARK 1 : this program use routines in a include file 
   see task Include a file language arm assembly 
   for the routine affichageMess conversion10 
   see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"
 
.equ MAXI,      500
 
 
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessResult:        .asciz "Prime  : @ \n"
szMessCounter:      .asciz "Number found : @ \n" 
szCarriageReturn:   .asciz "\n"
 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
sZoneConv:                  .skip 24
TablePrime:                 .skip   4 * MAXI 
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                               @ entry of program 

    bl createArrayPrime
    mov r5,r0                       @ prime number

    ldr r4,iAdrTablePrime           @ address prime table
    mov r10,#0                      @ init counter
    mov r6,#0                       @ indice
1:
    ldr r2,[r4,r6,lsl #2]           @ load prime
    mov r9,r2                       @ save prime
    mov r7,#0                       @ init digit sum
    mov r1,#10                      @ divisor
2:                                  @ begin loop
    mov r0,r2                       @ dividende
    bl division
    add r7,r7,r3                    @ add digit to digit sum
    cmp r2,#0                       @ quotient null ?
    bne 2b                          @ no -> comppute other digit

    mov r8,#1                       @ indice
4:                                  @ prime search loop 
    cmp r8,r5                       @ maxi ?
    bge 5f                          @ yes
    ldr r0,[r4,r8,lsl #2]           @ load prime
    cmp r0,r7                       @ prime >= digit sum ?
    addlt r8,r8,#1                  @ no -> increment indice
    blt 4b                          @ and loop
    bne 5f                          @ > 
    mov r0,r9                       @ equal
    bl displayPrime
    add r10,r10,#1                  @ increment counter
5:
    add r6,r6,#1                    @ increment first indice
    cmp r6,r5                       @ maxi ?
    blt 1b                          @ and loop
    
    mov r0,r10                      @ number counter
    ldr r1,iAdrsZoneConv
    bl conversion10                 @ call décimal conversion
    ldr r0,iAdrszMessCounter
    ldr r1,iAdrsZoneConv            @ insert conversion in message
    bl strInsertAtCharInc
    bl affichageMess                @ display message
 
100:                                @ standard end of the program 
    mov r0, #0                      @ return code
    mov r7, #EXIT                   @ request to exit program
    svc #0                          @ perform the system call
iAdrszCarriageReturn:     .int szCarriageReturn
iAdrszMessResult:         .int szMessResult
iAdrszMessCounter:        .int szMessCounter
iAdrTablePrime:           .int TablePrime
/******************************************************************/
/*      créate prime array                                       */ 
/******************************************************************/
createArrayPrime:
    push {r1-r7,lr}          @ save registers
    ldr r4,iAdrTablePrime    @ address prime table
    mov r0,#1                      
    str r0,[r4]              @ store 1 in array
    mov r0,#2
    str r0,[r4,#4]           @ store 2 in array
    mov r0,#3
    str r0,[r4,#8]           @ store 3 in array
    mov r5,#3                @ prine counter 
    mov r7,#5                @ first number to test
1:
    mov r6,#1                @ indice
2:
    mov r0,r7                @ dividende
    ldr r1,[r4,r6,lsl #2]    @ load divisor
    bl division
    cmp r3,#0                @ null remainder ?
    beq 3f                   @ yes -> end loop
    cmp r2,r1                @ quotient < divisor
    strlt r7,[r4,r5,lsl #2]  @ dividende is prime store in array
    addlt r5,r5,#1           @ increment counter
    blt 3f                   @ and end loop
    add r6,r6,#1             @ else increment indice
    cmp r6,r5                @ maxi ?
    blt 2b                   @ no -> loop
3:
    add r7,#2                @ other odd number
    cmp r7,#MAXI             @ maxi ?
    blt 1b                   @ no -> loop
    mov r0,r5                @ return counter
100:
    pop {r1-r7,pc}
/******************************************************************/
/*      Display prime table elements                                */ 
/******************************************************************/
/* r0 contains the prime */
displayPrime:
    push {r1,lr}                    @ save registers
    ldr r1,iAdrsZoneConv
    bl conversion10                 @ call décimal conversion
    ldr r0,iAdrszMessResult
    ldr r1,iAdrsZoneConv            @ insert conversion in message
    bl strInsertAtCharInc
    bl affichageMess                @ display message
100:
    pop {r1,pc}

iAdrsZoneConv:                   .int sZoneConv  
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"
Prime  : 2
Prime  : 3
Prime  : 5
Prime  : 7
Prime  : 11
Prime  : 23
Prime  : 29
Prime  : 41
Prime  : 43
Prime  : 47
Prime  : 61
Prime  : 67
Prime  : 83
Prime  : 89
Prime  : 101
Prime  : 113
Prime  : 131
Prime  : 137
Prime  : 139
Prime  : 151
Prime  : 157
Prime  : 173
Prime  : 179
Prime  : 191
Prime  : 193
Prime  : 197
Prime  : 199
Prime  : 223
Prime  : 227
Prime  : 229
Prime  : 241
Prime  : 263
Prime  : 269
Prime  : 281
Prime  : 283
Prime  : 311
Prime  : 313
Prime  : 317
Prime  : 331
Prime  : 337
Prime  : 353
Prime  : 359
Prime  : 373
Prime  : 379
Prime  : 397
Prime  : 401
Prime  : 409
Prime  : 421
Prime  : 443
Prime  : 449
Prime  : 461
Prime  : 463
Prime  : 467
Prime  : 487
Number found : 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

Applesoft BASIC[edit]

 0 E = 500
 1 F = E - 1:L =  LEN ( STR$ (F)) + 1: FOR I = 2 TO L:S$ = S$ +  CHR$ (32): NEXT I: DIM P(E):P(0) =  - 1:P(1) =  - 1: FOR I = 2 TO  SQR (F): IF  NOT P(I) THEN  FOR J = I * 2 TO E STEP I:P(J) =  - 1: NEXT J
 2  NEXT I: FOR I = B TO F: IF  NOT P(I) THEN  GOSUB 4
 3  NEXT I: PRINT : PRINT N" ADDITIVE PRIMES FOUND BELOW "E;: END 
 4 S = 0: IF I THEN  FOR J = I TO 0 STEP 0:J1 =  INT (J / 10):S = S + (J - J1 * 10):J = J1: NEXT J
 5  IF  NOT P(S) THEN N = N + 1: PRINT  RIGHT$ (S$ +  STR$ (I),L);
 6  RETURN
   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

BASIC256[edit]

print "Prime", "Digit Sum"
for i = 2 to 499
    if isprime(i) then
        s = digSum(i)
        if isPrime(s) then print i, s
    end if
next i
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

function digsum(n)
    s = 0
    while n
        s += n mod 10
        n /= 10
    end while
    return s
end function

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 <stdbool.h>
#include <stdio.h>
#include <string.h>

void memoizeIsPrime( bool * result, const int N )
{
    result[2] = true;
    result[3] = true;
    int prime[N];
    prime[0] = 3;
    int end = 1;
    for (int n = 5; n < N; n += 2)
    {
        bool n_is_prime = true;
        for (int i = 0; i < end; ++i)
        {
            const int PRIME = prime[i];
            if (n % PRIME == 0)
            {
                n_is_prime = false;
                break;
            }
            if (PRIME * PRIME > n)
            {
                break;
            }
        }
        if (n_is_prime)
        {
            prime[end++] = n;
            result[n] = true;
        }
    }
}/* memoizeIsPrime */

int sumOfDecimalDigits( int n )
{
    int sum = 0;
    while (n > 0)
    {
        sum += n % 10;
        n /= 10;
    }
    return sum;
}/* sumOfDecimalDigits */

int main( void )
{
    const int N = 500;

    printf( "Rosetta Code: additive primes less than %d:\n", N );

    bool is_prime[N];
    memset( is_prime, 0, sizeof(is_prime) );
    memoizeIsPrime( is_prime, N );

    printf( "   2" );
    int count = 1;
    for (int i = 3; i < N; i += 2)
    {
        if (is_prime[i] && is_prime[sumOfDecimalDigits( i )])
        {
            printf( "%4d", i );
            ++count;
            if ((count % 10) == 0)
            {
                printf( "\n" );
            }
        }
    }
    printf( "\nThose were %d additive primes.\n", count );
    return 0;
}/* main */
Output:
Rosetta Code: 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
Those were 54 additive primes.

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.


CLU[edit]

% Sieve of Erastothenes
% Returns an array [1..max] marking the primes
sieve = proc (max: int) returns (array[bool])
    prime: array[bool] := array[bool]$fill(1, max, true)
    prime[1] := false 
    
    for p: int in int$from_to(2, max/2) do
        if prime[p] then
            for comp: int in int$from_to_by(p*2, max, p) do
                prime[comp] := false
            end
        end
    end
    return(prime)
end sieve

% Sum the digits of a number
digit_sum = proc (n: int) returns (int)
    sum: int := 0
    while n ~= 0 do
        sum := sum + n // 10
        n := n / 10
    end
    return(sum)
end digit_sum 
    
start_up = proc ()
    max = 500
    po: stream := stream$primary_output()
    
    count: int := 0
    prime: array[bool] := sieve(max)
    for i: int in array[bool]$indexes(prime) do
        if prime[i] cand prime[digit_sum(i)] then
            count := count + 1
            stream$putright(po, int$unparse(i), 5)
            if count//10 = 0 then stream$putl(po, "") end
        end
    end
    
    stream$putl(po, "\nFound " || int$unparse(count) || 
                    " additive primes < " || int$unparse(max)) 
end start_up
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

COBOL[edit]

       IDENTIFICATION DIVISION.
       PROGRAM-ID. ADDITIVE-PRIMES.
       
       DATA DIVISION.
       WORKING-STORAGE SECTION.
       01 VARIABLES.
          03 MAXIMUM            PIC 999.
          03 AMOUNT             PIC 999.
          03 CANDIDATE          PIC 999.
          03 DIGIT              PIC 9 OCCURS 3 TIMES, 
                                REDEFINES CANDIDATE.
          03 DIGITSUM           PIC 99.
          
       01 PRIME-DATA.
          03 COMPOSITE-FLAG     PIC X OCCURS 500 TIMES.
             88 PRIME           VALUE ' '.
          03 SIEVE-PRIME        PIC 999.
          03 SIEVE-COMP-START   PIC 999.
          03 SIEVE-COMP         PIC 999.
          03 SIEVE-MAX          PIC 999.
       
       01 OUT-FMT.
          03 NUM-FMT            PIC ZZZ9.
          03 OUT-LINE           PIC X(40).
          03 OUT-PTR            PIC 99.
          
       PROCEDURE DIVISION.
       BEGIN.
           MOVE 500 TO MAXIMUM.
           MOVE 1 TO OUT-PTR.
           PERFORM SIEVE.
           MOVE ZERO TO AMOUNT.
           PERFORM TEST-NUMBER 
               VARYING CANDIDATE FROM 2 BY 1
               UNTIL CANDIDATE IS GREATER THAN MAXIMUM.
           DISPLAY OUT-LINE.
           DISPLAY SPACES.
           MOVE AMOUNT TO NUM-FMT.
           DISPLAY 'Amount of additive primes found: ' NUM-FMT.
           STOP RUN.

       TEST-NUMBER.
           ADD DIGIT(1), DIGIT(2), DIGIT(3) GIVING DIGITSUM.
           IF PRIME(CANDIDATE) AND PRIME(DIGITSUM),
               ADD 1 TO AMOUNT,
               PERFORM WRITE-NUMBER.
       
       WRITE-NUMBER.
           MOVE CANDIDATE TO NUM-FMT.
           STRING NUM-FMT DELIMITED BY SIZE INTO OUT-LINE 
               WITH POINTER OUT-PTR.
           IF OUT-PTR IS GREATER THAN 40,
               DISPLAY OUT-LINE,
               MOVE SPACES TO OUT-LINE,
               MOVE 1 TO OUT-PTR.               
       
       SIEVE.
           MOVE SPACES TO PRIME-DATA.
           DIVIDE MAXIMUM BY 2 GIVING SIEVE-MAX.
           PERFORM SIEVE-OUTER-LOOP
               VARYING SIEVE-PRIME FROM 2 BY 1
               UNTIL SIEVE-PRIME IS GREATER THAN SIEVE-MAX.
          
       SIEVE-OUTER-LOOP.
           IF PRIME(SIEVE-PRIME),
               MULTIPLY SIEVE-PRIME BY 2 GIVING SIEVE-COMP-START,
               PERFORM SIEVE-INNER-LOOP
                   VARYING SIEVE-COMP 
                       FROM SIEVE-COMP-START BY SIEVE-PRIME
                   UNTIL SIEVE-COMP IS GREATER THAN MAXIMUM.
       
       SIEVE-INNER-LOOP.
           MOVE 'X' TO COMPOSITE-FLAG(SIEVE-COMP).
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

Amount of additive primes found:   54

Common Lisp[edit]

(defun sum-of-digits (n)
 "Return the sum of the digits of a number"
  (do* ((sum 0 (+ sum rem))
        rem )
       ((zerop n) sum)
    (multiple-value-setq (n rem) (floor n 10)) ))
      
(defun additive-primep (n)
  (and (primep n) (primep (sum-of-digits n))) )


; To test if a number is prime we can use a number of different methods. Here I use Wilson's Theorem (see Primality by Wilson's theorem):

(defun primep (n)
  (unless (zerop n)
    (zerop (mod (1+ (factorial (1- n))) n)) ))

(defun factorial (n)
  (if (< n 2) 1 (* n (factorial (1- n)))) )
Output:
(dotimes (i 500) (when (additive-primep i) (princ i) (princ " ")))

1 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

Crystal[edit]

# Fast/simple way to generate primes for small values.
# Uses P3 Prime Generator (PG) and its Prime Generator Sequence (PGS).

def prime?(n) # P3 Prime Generator primality test
  return false unless (n | 1 == 3 if n < 5) || (n % 6) | 4 == 5
  sqrt_n = Math.isqrt(n)  # For Crystal < 1.2.0 use Math.sqrt(n).to_i
  pc = typeof(n).new(5)
  while pc <= sqrt_n
    return false if n % pc == 0 || n % (pc + 2) == 0
    pc += 6
  end
  true
end

def additive_primes(n)
  primes = [2, 3]
  pc, inc = 5, 2
  while pc < n
    primes << pc if prime?(pc) && prime?(pc.digits.sum)
    pc += inc; inc ^= 0b110  # generate P3 sequence: 5 7 11 13 17 19 ...
  end
  primes # list of additive primes <= n
end

nn = 500
addprimes = additive_primes(nn)
maxdigits = addprimes.last.digits.size
addprimes.each_with_index { |n, idx| printf "%*d ", maxdigits, n; print "\n" if idx % 10 == 9 } # more efficient
#addprimes.each_with_index { |n, idx| print "%#{maxdigits}d " % n; print "\n" if idx % 10 == 9} # alternatively
puts "\n#{addprimes.size} additive primes below #{nn}."

puts

nn = 5000
addprimes = additive_primes(nn)
maxdigits = addprimes.last.digits.size
addprimes.each_with_index { |n, idx| printf "%*d ", maxdigits, n; print "\n" if idx % 10 == 9 } # more efficient
puts "\n#{addprimes.size} additive primes below #{nn}."
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 below 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  557  571  577  593  599  601 
 607  641  643  647  661  683  719  733  739  751 
 757  773  797  809  821  823  827  829  863  881 
 883  887  911  919  937  953  971  977  991 1013 
1019 1031 1033 1039 1051 1091 1093 1097 1103 1109 
1123 1129 1163 1181 1187 1213 1217 1231 1237 1259 
1277 1279 1291 1297 1301 1303 1307 1321 1327 1361 
1367 1381 1433 1439 1451 1453 1459 1471 1493 1499 
1523 1543 1549 1567 1583 1613 1619 1637 1657 1693 
1697 1709 1721 1723 1741 1747 1783 1787 1811 1831 
1871 1873 1877 1901 1907 1949 2003 2027 2029 2063 
2069 2081 2083 2087 2089 2111 2113 2131 2137 2153 
2179 2203 2207 2221 2243 2267 2269 2281 2287 2311 
2333 2339 2351 2357 2371 2377 2393 2399 2423 2441 
2447 2467 2531 2539 2551 2557 2579 2591 2593 2609 
2621 2647 2663 2683 2687 2711 2713 2719 2731 2753 
2777 2791 2801 2803 2843 2861 2917 2939 2953 2957 
2971 2999 3011 3019 3037 3079 3109 3121 3163 3167 
3169 3181 3187 3217 3251 3253 3257 3259 3271 3299 
3301 3307 3323 3329 3343 3347 3361 3389 3413 3433 
3457 3491 3527 3529 3541 3547 3581 3583 3613 3617 
3631 3637 3659 3671 3673 3677 3691 3701 3709 3727 
3761 3767 3833 3851 3853 3907 3923 3929 3943 3947 
3989 4001 4003 4007 4021 4027 4049 4111 4133 4139 
4153 4157 4159 4177 4201 4229 4241 4243 4261 4283 
4289 4337 4339 4357 4373 4391 4397 4409 4421 4423 
4441 4447 4463 4481 4483 4513 4517 4519 4591 4603 
4621 4643 4649 4663 4733 4751 4793 4799 4801 4861 
4889 4919 4931 4933 4937 4951 4973 4999 
338 additive primes below 5000.

Delphi[edit]

See Pascal.

Draco[edit]

proc sieve([*] bool prime) void:
    word max, p, c;
    max := dim(prime,1)-1;
    prime[0] := false;
    prime[1] := false;
    for p from 2 upto max do prime[p] := true od;
    for p from 2 upto max/2 do
        for c from p*2 by p upto max do
            prime[c] := false
        od
    od
corp

proc digit_sum(word num) byte:
    byte sum;
    sum := 0;
    while
        sum := sum + num % 10;
        num := num / 10;
        num /= 0
    do od;
    sum
corp

proc main() void:
    word MAX = 500;
    word p, n;
    [MAX]bool prime;
    sieve(prime);
    n := 0;
    for p from 2 upto MAX-1 do
        if prime[p] and prime[digit_sum(p)] then
            write(p:4);
            n := n + 1;
            if n % 20 = 0 then writeln() fi
        fi
    od;
    writeln();
    writeln("There are ", n, " additive primes below ", MAX)
corp
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
There are 54 additive primes below 500

Erlang[edit]

main(_) ->
    AddPrimes = [N || N <- lists:seq(2,500), isprime(N) andalso isprime(digitsum(N))],
    io:format("The additive primes up to 500 are:~n~p~n~n", [AddPrimes]),
    io:format("There are ~b of them.~n", [length(AddPrimes)]).

isprime(N) when N < 2 -> false;
isprime(N) -> isprime(N, 2, 0, <<1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6>>).

isprime(N, D, J, Wheel) when J =:= byte_size(Wheel) -> isprime(N, D, 3, Wheel);
isprime(N, D, _, _) when D*D > N -> true;
isprime(N, D, _, _) when N rem D =:= 0 -> false;
isprime(N, D, J, Wheel) -> isprime(N, D + binary:at(Wheel, J), J + 1, Wheel).

digitsum(N) -> digitsum(N, 0).
digitsum(0, S) -> S;
digitsum(N, S) -> digitsum(N div 10, S + N rem 10).
Output:
The additive primes up to 500 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]

There are 54 of them.

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.

Fermat[edit]

Function Digsum(n) =
    digsum := 0;
    while n>0 do
        digsum := digsum + n|10;
        n:=n\10;
    od;
    digsum.;

nadd := 0;
!!'Additive primes below 500 are';

for p=1 to 500 do
    if Isprime(p) and Isprime(Digsum(p)) then
       !!(p,' -> ',Digsum(p));
       nadd := nadd+1;
    fi od;

!!('There were ',nadd);
Output:

Additive primes below 500 are

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
There were 54

Forth[edit]

Works with: Gforth
: prime? ( n -- ? ) here + c@ 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

Free Pascal[edit]

Using Sieve of Eratosthenes to find all primes upto 500, then go through the list, sum digits and check for prime

Program AdditivePrimes;
Const max_number = 500;

Var is_prime : array Of Boolean;

Procedure sieve(Var arr: Array Of boolean );
{use Sieve of Eratosthenes to find all primes to max number}
Var i,j : NativeUInt;

Begin
  For i := 2 To high(arr) Do
    arr[i] := True;  // set all bits to be True
  For i := 2 To high(arr) Do
    Begin
      If (arr[i]) Then
        For j := 2 To (high(arr) Div i) Do
          arr[i * j] := False;
    End;
End;

Function GetSumOfDigits(num: NativeUInt): longint;
{calcualte the sum of digits of a number}
Var 
  sum  : longint = 0;
  dummy: NativeUInt;
Begin
  Repeat
    dummy := num;
    num := num Div 10;
    Inc(sum, dummy - (num SHL 3 + num SHL 1));
  Until num < 1;
  GetSumOfDigits := sum;
End;

Var x : NativeUInt = 2; {first prime}
  counter : longint = 0;
Begin
  setlength(is_prime,max_number); //set length of array to max_number
  Sieve(is_prime); //apply Sieve
  
  {since 2 is the only even prime, let's do it separate}
  If is_prime[x] And is_prime[GetSumOfDigits(x)] Then
    Begin
      write(x:4);
      inc(counter);
    End;
  inc(x);
  While x < max_number Do
    Begin
      If is_prime[x] And is_prime[GetSumOfDigits(x)] Then
        Begin
          if counter mod 10 = 0 then writeln();
          write(x:4);
          inc(counter);
        End;
      inc(x,2);
    End;
  writeln();
  writeln();
  writeln(counter,' additive primes found.');
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

54 additive primes found.

Frink[edit]

vals = toArray[select[primes[2, 500], {|x| isPrime[sum[integerDigits[x]]]}]]
println[formatTable[columnize[vals, 10]]]
println["\n" + length[vals] + " values 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 values found.

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.

J[edit]

   (#~ 1 p: [:+/@|: 10&#.inv) i.&.(p:inv) 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

Java[edit]

public class additivePrimes {

    public static void main(String[] args) {
        int additive_primes = 0;
        for (int i = 2; i < 500; i++) {
            if(isPrime(i) && isPrime(digitSum(i))){
                additive_primes++;
                System.out.print(i + " ");
            }
        }
        System.out.print("\nFound " + additive_primes + " additive primes less than 500");
    }

    static boolean isPrime(int n) {
        int counter = 1;
        if (n < 2 || (n != 2 && n % 2 == 0) || (n != 3 && n % 3 == 0)) {
            return false;
        }
        while (counter * 6 - 1 <= Math.sqrt(n)) {
            if (n % (counter * 6 - 1) == 0 || n % (counter * 6 + 1) == 0) {
                return false;
            } else {
                counter++;
            }
        }
        return true;
    }

    static int digitSum(int n) {
        int sum = 0;
        while (n > 0) {
            sum += n % 10;
            n /= 10;
        }
        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 
Found 54 additive primes less than 500

jq[edit]

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;

def add(s): reduce s as $x (null; . + $x);

def sumdigits: add(tostring | explode[] | [.] | implode | tonumber);

# 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] + .;

The task

# Input: a number n
# Output: an array of additive primes less than n
def additive_primes:
  primes
  | . as $primes
  | reduce .[] as $p (null;
      ( $p | sumdigits ) as $sum
      | if (($primes | bsearch($sum)) > -1)
        then . + [$p]
        else .
        end );

"Erdős primes under 500:",
(500 | additive_primes
 | ((nwise(10) | map(lpad(4)) | join(" ")),
   "\n\(length) additive primes found."))
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.

Haskell[edit]

Naive solution which doesn't rely on advanced number theoretic libraries.

import Data.List (unfoldr)

-- infinite list of primes
primes = 2 : sieve [3,5..]
  where sieve (x:xs) = x : sieve (filter (\y -> y `mod` x /= 0) xs)

-- primarity test, effective for numbers less then billion
isPrime n = all (\p -> n `mod` p /= 0) $ takeWhile (< sqrtN) primes
  where sqrtN = round . sqrt . fromIntegral $ n

-- decimal digits of a number
digits = unfoldr f
  where f 0 = Nothing
        f n = let (q, r) = divMod n 10 in Just (r,q)

-- test for an additive prime 
isAdditivePrime n = isPrime n && (isPrime . sum . digits) n

The task

λ> isPrime 12373
True

λ> isAdditivePrime 12373
False

λ> isPrime 12347
True

λ> isAdditivePrime 12347
True

λ> takeWhile (< 500) $ filter isAdditivePrime primes
[2,3,5,7,11,13,23,29,31,41,43,47,61,67,83,89,101,103,113,131,137,139,151,157,173,179,191,193,197,199,211,223,227,229,241,263,269,281,283,311,313,317,331,337,353,359,373,379,397,401,409,421,443,449,461,463,467,487]

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.

Kotlin[edit]

Translation of: Python
fun isPrime(n: Int): Boolean {
    if (n <= 3) return n > 1
    if (n % 2 == 0 || n % 3 == 0) return false
    var i = 5
    while (i * i <= n) {
        if (n % i == 0 || n % (i + 2) == 0) return false
        i += 6
    }
    return true
}

fun digitSum(n: Int): Int {
    var sum = 0
    var num = n
    while (num > 0) {
        sum += num % 10
        num /= 10
    }
    return sum
}

fun main() {
    var additivePrimes = 0
    for (i in 2 until 500) {
        if (isPrime(i) and isPrime(digitSum(i))) {
            additivePrimes++
            print("$i ")
        }
    }
    println("\nFound $additivePrimes additive primes less than 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 less than 500

Ksh[edit]

#!/bin/ksh

# Prime numbers for which the sum of their decimal digits are also primes

#	# Variables:
#
integer MAX_n=500

#	# Functions:
#
#	# Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
	typeset _n ; integer _n=$1
	typeset _i ; integer _i

	(( _n < 2 )) && return 0
	for (( _i=2 ; _i*_i<=_n ; _i++ )); do
		(( ! ( _n % _i ) )) && return 0
	done
	return 1
}

#	# Function _sumdigits(n) return sum of n's digits
#
function _sumdigits {
	typeset _n ; _n=$1
	typeset _i _sum ; integer _i _sum=0

	for ((_i=0; _i<${#_n}; _i++)); do
		(( _sum+=${_n:${_i}:1} ))
	done
	echo ${_sum}
}

 ######
# main #
 ######

integer i digsum
for ((i=2; i<MAX_n; i++)); do
	_isprime ${i} && (( ! $? )) && continue

	digsum=$(_sumdigits ${i})
	_isprime ${digsum} ; (( $? )) && printf "%4d " ${i}
done
print
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 


langur[edit]

Works with: langur version 0.10
val .isPrime = f .i == 2 or .i > 2 and not any f(.x) .i div .x, pseries 2 to .i ^/ 2

val .sumDigits = f fold f{+}, s2n toString .i

writeln "Additive primes less than 500:"

var .count = 0

for .i in [2] ~ series(3..500, 2) {
    if .isPrime(.i) and .isPrime(.sumDigits(.i)) {
        write $"\.i:3;  "
        .count += 1
        if .count div 10: writeln()
    }
}

writeln $"\n\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.

Lua[edit]

This task uses primegen from: Extensible_prime_generator#Lua

function sumdigits(n)
  local sum = 0
  while n > 0 do
    sum = sum + n % 10
    n = math.floor(n/10)
  end
  return sum
end

primegen:generate(nil, 500)
aprimes = primegen:filter(function(n) return primegen.tbd(sumdigits(n)) end)
print(table.concat(aprimes, " "))
print("Count:", #aprimes)
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
Count:  54

Mathematica/Wolfram Language[edit]

ClearAll[AdditivePrimeQ]
AdditivePrimeQ[n_Integer] := PrimeQ[n] \[And] PrimeQ[Total[IntegerDigits[n]]]
Select[Range[500], AdditivePrimeQ]
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}

Modula-2[edit]

MODULE AdditivePrimes;
FROM InOut IMPORT WriteString, WriteCard, WriteLn;

CONST
    Max = 500;

VAR
    N: CARDINAL;
    Count: CARDINAL;
    Prime: ARRAY [2..Max] OF BOOLEAN;

PROCEDURE DigitSum(n: CARDINAL): CARDINAL;
BEGIN
    IF n < 10 THEN 
        RETURN n;
    ELSE 
        RETURN (n MOD 10) + DigitSum(n DIV 10);
    END;
END DigitSum;

PROCEDURE Sieve;
VAR i, j, max2: CARDINAL;
BEGIN
    FOR i := 2 TO Max DO
        Prime[i] := TRUE;
    END;
    
    FOR i := 2 TO Max DIV 2 DO
        IF Prime[i] THEN;
            j := i*2;
            WHILE j <= Max DO 
                Prime[j] := FALSE;
                j := j + i;
            END;
        END;
    END;
END Sieve;
   
BEGIN
    Count := 0;
    Sieve();
    FOR N := 2 TO Max DO
        IF Prime[N] AND Prime[DigitSum(N)] THEN
            WriteCard(N, 4);
            Count := Count + 1;
            IF Count MOD 10 = 0 THEN WriteLn(); END;
        END;
    END;
    WriteLn();
    WriteString('There are '); WriteCard(Count,0);
    WriteString(' additive primes less than '); WriteCard(Max,0);
    WriteString('.');
    WriteLn();
END AdditivePrimes.
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
There are 54 additive primes less than 500.

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

Pari/GP[edit]

This is a good task for demonstrating several different ways to approach a simple problem.

hasPrimeDigitsum(n)=isprime(sumdigits(n)); \\ see A028834 in the OEIS

v1 = select(isprime, select(hasPrimeDigitsum, [1..499]));
v2 = select(hasPrimeDigitsum, select(isprime, [1..499]));
v3 = select(hasPrimeDigitsum, primes([1, 499]));

s=0; forprime(p=2,499, if(hasPrimeDigitsum(p), s++)); s;
[#v1, #v2, #v3, s]
Output:
%1 = [54, 54, 54, 54]

Pascal[edit]

Works with: Free Pascal
Works with: Delphi
checking isPrime(sum of digits) before testimg isprime(num) improves speed.
Tried to speed up calculation of sum of digits.
program AdditivePrimes;
{$IFDEF FPC}
{$MODE DELPHI}{$CODEALIGN proc=16}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
{$DEFINE DO_OUTPUT}

uses
  sysutils;

const
  RANGE = 500; // 1000*1000;//
  MAX_OFFSET = 0; // 1000*1000*1000;//

type
  tNum = array [0 .. 15] of byte;

  tNumSum = record
    dgtNum, dgtSum: tNum;
    dgtLen, num: Uint32;
  end;

  tpNumSum = ^tNumSum;

function isPrime(n: Uint32): boolean;
const
  wheeldiff: array [0 .. 7] of Uint32 = (+6, +4, +2, +4, +2, +4, +6, +2);
var
  p: NativeUInt;
  flipflop: Int32;
begin
  if n < 64 then
    EXIT(n in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
      53, 59, 61])
  else
  begin
    IF (n AND 1 = 0) OR (n mod 3 = 0) OR (n mod 5 = 0) then
      EXIT(false);
    result := true;
    p := 1;
    flipflop := 6;

    while result do
    Begin
      p := p + wheeldiff[flipflop];
      if p * p > n then
        BREAK;
      result := n mod p <> 0;
      flipflop := flipflop - 1;
      if flipflop < 0 then
        flipflop := 7;
    end
  end
end;

procedure IncNum(var NumSum: tNumSum; delta: Uint32);
const
  BASE = 10;
var
  carry, dg: Uint32;
  le: Int32;
Begin
  if delta = 0 then
    EXIT;
  le := 0;
  with NumSum do
  begin
    num := num + delta;
    repeat
      carry := delta div BASE;
      delta := delta - BASE * carry;
      dg := dgtNum[le] + delta;
      IF dg >= BASE then
      Begin
        dg := dg - BASE;
        inc(carry);
      end;
      dgtNum[le] := dg;
      inc(le);
      delta := carry;
    until carry = 0;
    if dgtLen < le then
      dgtLen := le;
    // correct sum of digits // le is >= 1
    delta := dgtSum[le];
    repeat
      dec(le);
      delta := delta + dgtNum[le];
      dgtSum[le] := delta;
    until le = 0;
  end;
end;

var
  NumSum: tNumSum;
  s: AnsiString;
  i, k, cnt, Nr: NativeUInt;
  ColWidth, MAXCOLUMNS, NextRowCnt: NativeUInt;

BEGIN
  ColWidth := Trunc(ln(MAX_OFFSET + RANGE) / ln(10)) + 2;
  MAXCOLUMNS := 80;
  NextRowCnt := MAXCOLUMNS DIV ColWidth;

  fillchar(NumSum, SizeOf(NumSum), #0);
  NumSum.dgtLen := 1;
  IncNum(NumSum, MAX_OFFSET);
  setlength(s, ColWidth);
  fillchar(s[1], ColWidth, ' ');
  // init string
  with NumSum do
  Begin
    For i := dgtLen - 1 downto 0 do
      s[ColWidth - i] := AnsiChar(dgtNum[i] + 48);
    // reset digits lenght to get the max changed digits since last update of string
    dgtLen := 0;
  end;
  cnt := 0;
  Nr := NextRowCnt;
  For i := 0 to RANGE do
    with NumSum do
    begin
      if isPrime(dgtSum[0]) then
        if isPrime(num) then
        Begin
          cnt := cnt + 1;
          dec(Nr);

          // correct changed digits in string s
          For k := dgtLen - 1 downto 0 do
            s[ColWidth - k] := AnsiChar(dgtNum[k] + 48);
          dgtLen := 0;
{$IFDEF DO_OUTPUT}
          write(s);
          if Nr = 0 then
          begin
            writeln;
            Nr := NextRowCnt;
          end;
{$ENDIF}
        end;
      IncNum(NumSum, 1);
    end;
  if Nr <> NextRowCnt then
    write(#10);
  writeln(cnt, ' additive primes found.');
END.
Output:
TIO.RUN
   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.

//OFFSET : 1000*1000*1000, RANGE = 1000*1000 no output
18103 additive primes found.
Real time: 1.951 s User time: 1.902 s Sys. time: 0.038 s CPU share: 99.46 %

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]

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

Phixmonti[edit]

/# Rosetta Code problem: http://rosettacode.org/wiki/Additive_primes
by Galileo, 05/2022 #/

include ..\Utilitys.pmt

def isprime
    dup 1 <= if drop false
    else dup 2 == not if
        ( dup sqrt 2 swap ) for
            over swap mod not if drop false exitfor endif
        endfor
        endif
    endif
    false == not
enddef

def digitsum
    0 swap dup 0 > while dup 10 mod rot + swap 10 / int dup 0 > endwhile
    drop
enddef

0 500 for
    dup isprime over digitsum isprime and if print " " print 1 + else drop endif
endfor

"Additive primes found: " print print
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 found: 54
=== Press any key to exit ===

Picat[edit]

main =>
    PCount = 0,
    foreach (I in 2..499)
        if prime(I) && prime(sum_digits(I)) then
            PCount := PCount + 1,
            printf("%4d ", I)
        end
    end,
    printf("\n\n%d additive primes found.\n", PCount).

sum_digits(N) = S =>
    S = sum([ord(C)-ord('0') : C in to_string(N)]).
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.

PicoLisp[edit]

(de prime? (N)
   (let D 0
      (or
         (= N 2)
         (and
            (> N 1)
            (bit? 1 N)
            (for (D 3  T  (+ D 2))
               (T (> D (sqrt N)) T)
               (T (=0 (% N D)) NIL) ) ) ) ) )
(de additive (N)
   (and
      (prime? N)
      (prime? (sum format (chop N))) ) )
(let C 0
   (for (N 0 (> 500 N) (inc N))
      (when (additive N)
         (printsp N)
         (inc 'C) ) )
   (prinl)
   (prinl "Total count: " C) )
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 
Total count: 54

PILOT[edit]

C :z=2
  :c=0
  :max=500
*number
C :n=z
U :*digsum 
C :n=s
U :*prime
J (p=0):*next
C :n=z
U :*prime
J (p=0):*next
T :#z
C :c=c+1
*next
C :z=z+1
J (z<max):*number
T :There are #c additive primes below #max
E :

*prime
C :p=1
E (n<4):
C :p=0
E (n=2*(n/2)):
C :i=3
  :m=n/2
*ptest
E (n=i*(n/i)):
C :i=i+2
J (i<=m):*ptest
C :p=1
E :

*digsum
C :s=0
  :i=n
*digit
C :j=i/10
  :s=s+(i-j*10)
  :i=j
J (i>0):*digit
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
There are 54 additive primes below 500

PL/I[edit]

See #Polyglot:PL/I and PL/M

PL/M[edit]

See #Polyglot:PL/I and PL/M

Polyglot:PL/I and PL/M[edit]

Works with: 8080 PL/M Compiler
... under CP/M (or an emulator)

Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page. Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.

/* FIND ADDITIVE PRIMES - PRIMES WHOSE DIGIT SUM IS ALSO PRIME */
additive_primes_100H: procedure options                                         (main);

/* PROGRAM-SPECIFIC %REPLACE STATEMENTS MUST APPEAR BEFORE THE %INCLUDE AS */
/* E.G. THE CP/M PL/I COMPILER DOESN'T LIKE THEM TO FOLLOW PROCEDURES      */
   /* PL/I                                                                      */
      %replace dclsieve by         500;
   /* PL/M */                                                                   /*
      DECLARE  DCLSIEVE LITERALLY '501';
   /* */

/* PL/I DEFINITIONS                                                             */
%include 'pg.inc';
/* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */    /*
   DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE';
   DECLARE FIXED  LITERALLY ' ',       BIT       LITERALLY 'BYTE';
   DECLARE STATIC LITERALLY ' ',       RETURNS   LITERALLY ' ';
   DECLARE FALSE  LITERALLY '0',       TRUE LITERALLY '1';
   DECLARE HBOUND LITERALLY 'LAST',    SADDR  LITERALLY '.';
   BDOSF: PROCEDURE( FN, ARG )BYTE;
                               DECLARE FN BYTE, ARG ADDRESS; GOTO 5;   END; 
   BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5;   END;
   PRCHAR:   PROCEDURE( C );   DECLARE C BYTE;      CALL BDOS( 2, C ); END;
   PRSTRING: PROCEDURE( S );   DECLARE S ADDRESS;   CALL BDOS( 9, S ); END;
   PRNL:     PROCEDURE;        CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END;
   PRNUMBER: PROCEDURE( N );
      DECLARE N ADDRESS;
      DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
      N$STR( W := LAST( N$STR ) ) = '$';
      N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
      DO WHILE( ( V := V / 10 ) > 0 );
         N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
      END; 
      CALL BDOS( 9, .N$STR( W ) );
   END PRNUMBER;
   MODF:     PROCEDURE( A, B )ADDRESS;
      DECLARE ( A, B ) ADDRESS;
      RETURN A MOD B;
   END MODF;
/* END LANGUAGE DEFINITIONS */

   /* TASK */

   /* PRIME ELEMENTS ARE 0, 1, ... 500 IN PL/M AND 1, 2, ... 500 IN PL/I */
   /* ELEMENT 0 IN PL/M IS IS UNUSED */
   DECLARE PRIME( DCLSIEVE ) BIT;
   DECLARE ( MAXPRIME, MAXROOT, ACOUNT, I, J, DSUM, V ) FIXED BINARY;
   /* SIEVE THE PRIMES UP TO MAX PRIME */
   PRIME( 1 ) = FALSE; PRIME( 2 ) = TRUE;
   MAXPRIME = HBOUND( PRIME                                                     , 1
                    );
   MAXROOT  = 1; /* FIND THE ROOT OF MAXPRIME TO AVOID 16-BIT OVERFLOW */
   DO WHILE( MAXROOT * MAXROOT < MAXPRIME ); MAXROOT = MAXROOT + 1; END;
   DO I = 3 TO MAXPRIME BY 2; PRIME( I ) = TRUE;  END;
   DO I = 4 TO MAXPRIME BY 2; PRIME( I ) = FALSE; END;
   DO I = 3 TO MAXROOT BY 2;
      IF PRIME( I ) THEN DO;
         DO J = I * I TO MAXPRIME BY I; PRIME( J ) = FALSE; END;
      END;
   END;
   /* FIND THE PRIMES THAT ARE ADDITIVE PRIMES */
   ACOUNT = 0;
   DO I = 1 TO MAXPRIME;
      IF PRIME( I ) THEN DO;
         V    = I;
         DSUM = 0;
         DO WHILE( V > 0 );
            DSUM = DSUM + MODF( V, 10 );
            V    = V / 10;
         END;
         IF PRIME( DSUM ) THEN DO;
            CALL PRCHAR( ' ' );
            IF I <  10 THEN CALL PRCHAR( ' ' );
            IF I < 100 THEN CALL PRCHAR( ' ' );
            CALL PRNUMBER( I );
            ACOUNT = ACOUNT + 1;
            IF MODF( ACOUNT, 12 ) = 0 THEN CALL PRNL;
         END;
      END;
   END;
   CALL PRNL;
   CALL PRSTRING( SADDR( 'FOUND $' ) );
   CALL PRNUMBER( ACOUNT );
   CALL PRSTRING( SADDR( ' ADDITIVE PRIMES BELOW $' ) );
   CALL PRNUMBER( MAXPRIME );
   CALL PRNL;

EOF: end additive_primes_100H;
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

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

PureBasic[edit]

#MAX=500
Global Dim P.b(#MAX) : FillMemory(@P(),#MAX,1,#PB_Byte)
If OpenConsole()=0 : End 1 : EndIf
For n=2 To Sqr(#MAX)+1 : If P(n) : m=n*n : While m<=#MAX : P(m)=0 : m+n : Wend : EndIf : Next

Procedure.i qsum(v.i)
  While v : qs+v%10 : v/10 : Wend
  ProcedureReturn qs
EndProcedure

For i=2 To #MAX
  If P(i) And P(qsum(i)) : c+1 : Print(RSet(Str(i),5)) : If c%10=0 : PrintN("") : EndIf : EndIf
Next
PrintN(~"\n\n"+Str(c)+" additive primes below 500.")
Input()
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 below 500.

Python[edit]

def is_prime(n: int) -> bool:
    if n <= 3:
        return n > 1
    if n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i ** 2 <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True

def digit_sum(n: int) -> int:
    sum = 0
    while n > 0:
        sum += n % 10
        n //= 10
    return sum

def main() -> None:
    additive_primes = 0
    for i in range(2, 500):
        if is_prime(i) and is_prime(digit_sum(i)):
            additive_primes += 1
            print(i, end=" ")
    print(f"\nFound {additive_primes} additive primes less than 500")

if __name__ == "__main__":
    main()
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 less than 500

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.


Racket[edit]

#lang racket

(require math/number-theory)

(define (sum-of-digits n (σ 0))
  (if (zero? n) σ (let-values (((q r) (quotient/remainder n 10)))
                    (sum-of-digits q (+ σ r)))))

(define (additive-prime? n)
  (and (prime? n) (prime? (sum-of-digits n))))

(define additive-primes<500 (filter additive-prime? (range 1 500)))
(printf "There are ~a additive primes < 500~%" (length additive-primes<500))
(printf "They are: ~a~%" additive-primes<500)
Output:
There are 54 additive primes < 500
They 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)

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

Red[edit]

cross-sum: function [n][out: 0 foreach m form n [out: out + to-integer to-string m]]
additive-primes: function [n][collect [foreach p ps: primes n [if find ps cross-sum p [keep p]]]]

length? probe new-line/skip additive-primes 500 true 10
[
    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

Uses primes defined in https://rosettacode.org/wiki/Sieve_of_Eratosthenes#Red.

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  < "     commas(n)
if cols>0  then say ' index │'center(title,  1 + cols*(w+1) )
if cols>0  then say '───────┼'center(""   ,  1 + cols*(w+1), '─')
found= 0;                  idx= 1                /*initialize # of additive primes & IDX*/
$=                                               /*a list of additive primes  (so far). */
       do j=1  for #;      p= @.j                /*obtain the  Jth  prime.              */
       _= sumDigs(p);      if \!._  then iterate /*is sum of J's digs a prime? No, skip.*/       /* ◄■■■■■■■■ a filter. */
       found= found + 1                          /*bump the count of additive primes.   */
       if cols<0                    then iterate /*Build the list  (to be shown later)? */
       c= commas(p)                              /*maybe add commas to the number.      */
       $= $  right(c, max(w, length(c) ) )       /*add additive 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   /*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(found)      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
                    !.= 0;   !.2= 1;  !.3= 1;  !.5= 1;  !.7= 1;  !.11= 1;  !.13= 1
                           #= 6;  sq.#= @.# ** 2 /*the number of primes;  prime squared.*/
        do j=@.#+2  by 2  for max(0, n%2-@.#%2-1)       /*find odd primes from here on. */
        parse var  j   ''  -1  _                 /*obtain the last digit of the  J  var.*/
        if     _==5  then iterate;  if j// 3==0  then iterate  /*J ÷ by 5?   J ÷ by  3? */
        if j// 7==0  then iterate;  if j//11==0  then iterate  /*" "  " 7?   " "  " 11? */
                                                 /* [↓]  divide by the primes.   ___    */
              do k=6  while sq.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;  sq.#= j*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...

Ruby[edit]

require "prime"

additive_primes = Prime.lazy.select{|prime| prime.digits.sum.prime? }

N = 500
res = additive_primes.take_while{|n| n < N}.to_a
puts res.join(" ")
puts "\n#{res.size} additive primes below #{N}."
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 below 500.


Rust[edit]

Flat implementation[edit]

fn main() {
    let limit = 500;
    let column_w = limit.to_string().len() + 1;
    let mut pms = Vec::with_capacity(limit / 2 - limit / 3 / 2 - limit / 5 / 3 / 2 + 1);
    let mut count = 0;
    for u in (2..3).chain((3..limit).step_by(2)) {
        if pms.iter().take_while(|&&p| p * p <= u).all(|&p| u % p != 0) {
            pms.push(u);
            let dgs = std::iter::successors(Some(u), |&n| (n > 9).then(|| n / 10)).map(|n| n % 10);
            if pms.binary_search(&dgs.sum()).is_ok() {
                print!("{}{u:column_w$}", if count % 10 == 0 { "\n" } else { "" });
                count += 1;
            }
        }
    }
    println!("\n---\nFound {count} additive primes less than {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 less than 500

With crate "primal"[edit]

primal implements the sieve of Eratosthenes with optimizations (10+ times faster for large limits)

// [dependencies]
// primal = "0.3.0"

fn sum_digits(u: usize) -> usize {
    std::iter::successors(Some(u), |&n| (n > 9).then(|| n / 10)).fold(0, |s, n| s + n % 10)
}

fn main() {
    let limit = 500;
    let column_w = limit.to_string().len() + 1;
    let sieve_primes = primal::Sieve::new(limit);
    let count = sieve_primes
        .primes_from(2)
        .filter(|&p| p < limit && sieve_primes.is_prime(sum_digits(p)))
        .zip(["\n"].iter().chain(&[""; 9]).cycle())
        .inspect(|(u, sn)| print!("{sn}{u:column_w$}"))
        .count();
    println!("\n---\nFound {count} additive primes less than {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 less than 500

Sage[edit]

limit = 500
additivePrimes = list(filter(lambda x: x > 0,
                             list(map(lambda x: int(x) if sum([int(digit) for digit in x]) in Primes() else 0, 
                                      list(map(str,list(primes(1,limit))))))))
print(f"{additivePrimes}\nFound {len(additivePrimes)} additive primes less than {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 less than 500

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.

Sidef[edit]

func additive_primes(upto, base = 10) {
    upto.primes.grep { .sumdigits(base).is_prime }
}

additive_primes(500).each_slice(10, {|*a|
    a.map { '%3s' % _ }.join(' ').say
})
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

TSE SAL[edit]

INTEGER PROC FNMathGetSquareRootI( INTEGER xI )
 INTEGER squareRootI = 0
 IF ( xI > 0 )
  WHILE( ( squareRootI * squareRootI ) <= xI )
   squareRootI = squareRootI + 1
  ENDWHILE
  squareRootI = squareRootI - 1
 ENDIF
 RETURN( squareRootI )
END
//
INTEGER PROC FNMathCheckIntegerIsPrimeB( INTEGER nI )
 INTEGER I = 0
 INTEGER primeB = FALSE
 INTEGER stopB = FALSE
 INTEGER restI = 0
 INTEGER limitI = 0
 primeB = FALSE
 IF ( nI <= 0 )
  RETURN( FALSE )
 ENDIF
 IF ( nI == 1 )
  RETURN( FALSE )
 ENDIF
 IF ( nI == 2 )
  RETURN( TRUE )
 ENDIF
 IF ( nI == 3 )
  RETURN( TRUE )
 ENDIF
 IF ( nI MOD 2 == 0 )
  RETURN( FALSE )
 ENDIF
 IF ( ( nI MOD 6 ) <> 1 ) AND ( ( nI MOD 6 ) <> 5 )
  RETURN( FALSE )
 ENDIF
 limitI = FNMathGetSquareRootI( nI )
 I = 3
 REPEAT
  restI = ( nI MOD I )
  IF ( restI == 0 )
   primeB = FALSE
   stopB = TRUE
  ENDIF
  IF ( I > limitI )
   primeB = TRUE
   stopB = TRUE
  ENDIF
  I = I + 2
 UNTIL ( stopB )
 RETURN( primeB )
END
//
INTEGER PROC FNMathCheckIntegerDigitSumI( INTEGER J )
 STRING s[255] = Str( J )
 STRING cS[255] = ""
 INTEGER minI = 1
 INTEGER maxI = Length( s )
 INTEGER I = 0
 INTEGER K = 0
 FOR I = minI TO maxI
  cS = s[ I ]
  K = K + Val( cS )
 ENDFOR
 RETURN( K )
END
//
INTEGER PROC FNMathCheckIntegerDigitSumIsPrimeB( INTEGER I )
 INTEGER J = FNMathCheckIntegerDigitSumI( I )
 INTEGER B = FNMathCheckIntegerIsPrimeB( J )
 RETURN( B )
END
//
INTEGER PROC FNMathGetPrimeAdditiveAllToBufferB( INTEGER maxI, INTEGER bufferI )
 INTEGER B = FALSE
 INTEGER B1 = FALSE
 INTEGER B2 = FALSE
 INTEGER B3 = FALSE
 INTEGER minI = 2
 INTEGER I = 0
 FOR I = minI TO maxI
  B1 = FNMathCheckIntegerIsPrimeB( I )
  B2 = FNMathCheckIntegerDigitSumIsPrimeB( I )
  B3 = B1 AND B2
  IF ( B3 )
   PushPosition()
   PushBlock()
   GotoBufferId( bufferI )
   AddLine( Str( I ) )
   PopBlock()
   PopPosition()
  ENDIF
 ENDFOR
 B = TRUE
 RETURN( B )
END
//
PROC Main()
 STRING s1[255] = "500" // change this
 INTEGER bufferI = 0
 PushPosition()
 bufferI = CreateTempBuffer()
 PopPosition()
 IF ( NOT ( Ask( " = ", s1, _EDIT_HISTORY_ ) ) AND ( Length( s1 ) > 0 ) ) RETURN() ENDIF
 Message( FNMathGetPrimeAdditiveAllToBufferB( Val( s1 ), bufferI ) ) // gives e.g. TRUE
 GotoBufferId( bufferI )
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

Swift[edit]

import Foundation

func isPrime(_ n: Int) -> Bool {
    if n < 2 {
        return false
    }
    if n % 2 == 0 {
        return n == 2
    }
    if n % 3 == 0 {
        return n == 3
    }
    var p = 5
    while p * p <= n {
        if n % p == 0 {
            return false
        }
        p += 2
        if n % p == 0 {
            return false
        }
        p += 4
    }
    return true
}

func digitSum(_ num: Int) -> Int {
    var sum = 0
    var n = num
    while n > 0 {
        sum += n % 10
        n /= 10
    }
    return sum
}

let limit = 500
print("Additive primes less than \(limit):")
var count = 0
for n in 1..<limit {
    if isPrime(digitSum(n)) && isPrime(n) {
        count += 1
        print(String(format: "%3d", n), terminator: count % 10 == 0 ? "\n" : " ")
    }
}
print("\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.

uBasic/4tH[edit]

Translation of: BASIC256
print "Prime", "Digit Sum"
for i = 2 to 499
  if func(_isPrime(i)) then 
     s = func(_digSum(i)) 
     if func(_isPrime(s)) then
       print i, s
     endif
  endif
next
end

_isPrime
  param (1)
  local (1)

  if a@ < 2 then return (0)
  if a@ % 2 = 0 then return (a@ = 2)
  if a@ % 3 = 0 then return (a@ = 3)
  b@ = 5
  do while (b@ * b@) < (a@ + 1)
    if a@ % b@ = 0 then unloop : return (0)
    b@ = b@ + 2
  loop
return (1)
 
_digSum
  param (1)
  local (1)

  b@ = 0
  do while a@
    b@ = b@ + (a@ % 10)
    a@ = a@ / 10
  loop
return (b@)
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

0 OK, 0:176

Vlang[edit]

Translation of: go
fn is_prime(n int) bool {
    if n < 2 {
        return false
    } else if n%2 == 0 {
        return n == 2
    } else if n%3 == 0 {
        return n == 3
    } else {
        mut d := 5
        for d*d <= n {
            if n%d == 0 {
                return false
            }
            d += 2
            if n%d == 0 {
                return false
            }
            d += 4
        }
        return true
    }
}
 
fn sum_digits(nn int) int {
    mut n := nn
    mut sum := 0
    for n > 0 {
        sum += n % 10
        n /= 10
    }
    return sum
}
 
fn main() {
    println("Additive primes less than 500:")
    mut i := 2
    mut count := 0
    for {
        if is_prime(i) && is_prime(sum_digits(i)) {
            count++
            print("${i:3}  ")
            if count%10 == 0 {
                println('')
            }
        }
        if i > 2 {
            i += 2
        } else {
            i++
        }
        if i > 499 {
            break
        }
    }
    println("\n\n$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.

VTL-2[edit]

10 M=499
20 :1)=1
30 P=2
40 :P)=0
50 P=P+1
60 #=M>P*40
70 P=2
80 C=P*2
90 :C)=1
110 C=C+P
120 #=M>C*90
130 P=P+1
140 #=M/2>P*80
150 P=2
160 N=0
170 #=:P)*290
180 S=0
190 K=P
200 K=K/10
210 S=S+%
220 #=0<K*200
230 #=:S)*290
240 ?=P
250 $=9
260 N=N+1
270 #=N/10*0+%=0=0*290
280 ?=""
290 P=P+1
300 #=M>P*170
310 ?=""
320 ?="There are ";
330 ?=N
340 ?=" additive primes below ";
350 ?=M+1
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
There are 54 additive primes below 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.

Yabasic[edit]

// Rosetta Code problem: http://rosettacode.org/wiki/Additive_primes
// by Galileo, 06/2022

limit = 500

dim flags(limit)

for i = 2 to  limit
    for k = i*i to limit step i 
        flags(k) = 1
    next
    if flags(i) = 0 primes$ = primes$ + str$(i) + " "
next

dim prim$(1)

n = token(primes$, prim$())

for i = 1 to n
    sum = 0
    num$ = prim$(i)
    for j = 1 to len(num$)
        sum = sum + val(mid$(num$, j, 1))
    next
    if instr(primes$, str$(sum) + " ") print prim$(i), " "; : count = count + 1
next

print "\nFound: ", count
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
---Program done, press RETURN---