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.

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

Optionally, show the number of additive primes.

Also see

## 11l

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

L(i) 2..499
I is_prime(i) & is_prime(digit_sum(i))
print(i, 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 less than 500
```

## AArch64 Assembly

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 */

/*******************************************/
/* 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

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
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 ?
csel x8,x0,x8,lt                // no -> increment indice
blt 4b                          // and loop
bne 5f                          // >
mov x0,x9                       // equal
bl displayPrime
5:
add x6,x6,#1                    // increment first indice
cmp x6,x5                       // maxi ?
blt 1b                          // and loop

mov x0,x10                      // number counter
bl conversion10                 // call décimal conversion
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
/******************************************************************/
/*      créate prime array                                       */
/******************************************************************/
createArrayPrime:
stp x1,lr,[sp,-16]!       // save  registres
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
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
bl conversion10           // call décimal conversion
ldr x1,qAdrsZoneConv      // insert conversion in message
bl strInsertAtCharInc
bl affichageMess          // display message
100:
ldp x1,lr,[sp],16         // restaur des  2 registres
ret

/********************************************************/
/*        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
```

## ABC

```HOW TO REPORT prime n:
REPORT n>=2 AND NO d IN {2..floor root n} HAS n mod d = 0

HOW TO RETURN digit.sum n:
SELECT:
n<10: RETURN n
ELSE: RETURN (n mod 10) + digit.sum floor (n/10)

REPORT prime n AND prime digit.sum n

PUT 0 IN n
FOR i IN {1..499}:
WRITE i>>4
PUT n+1 IN n
IF n mod 10 = 0: WRITE /

WRITE /
WRITE "There are `n` 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
There are 54 additive primes less than 500.```

## Action!

```;;; find some additive primes - primes whose digit sum is also prime
;;; Library: Action! Sieve of Eratosthenes
INCLUDE "H6:SIEVE.ACT"

PROC Main()
DEFINE MAX_PRIME = "500"

BYTE ARRAY primes(MAX_PRIME)
CARD n, digitSum, v, count

Sieve(primes,MAX_PRIME)

count = 0
FOR n = 1 TO MAX_PRIME - 1 DO
IF primes( n ) THEN
digitSum = 0
v = n
WHILE v > 0 DO
digitSum ==+ v MOD 10
v ==/ 10
OD
IF primes( digitSum ) THEN
IF n < 100 THEN
Put(' )
IF n < 10 THEN Put(' ) FI
FI
Put(' )PrintI( n )
count ==+ 1
IF count MOD 20 = 0 THEN PutE() FI
FI
FI
OD
PutE()Print( "Found " )PrintI( count )Print( " additive primes below " )PrintI( MAX_PRIME + 1 )PutE()
RETURN```
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 501
```

```with Ada.Text_Io;

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);

Prime : constant Prime_List := Get_Primes;
Count : Natural := 0;
begin
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);
New_Line;
```
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

## ALGOL 68

```BEGIN # find additive primes - primes whose digit sum is also prime #
# sieve the primes to max prime #
[]BOOL prime = PRIMESIEVE 499;
# find the additive primes #
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 ) ) );
print( ( " 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

```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

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

## AppleScript

```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

script o
property primes : sieveOfEratosthenes(limit)
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

```
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

Works with: as version Raspberry Pi
or android 32 bits with application Termux
```/* ARM assembly Raspberry PI  */

/* 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

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
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
5:
add r6,r6,#1                    @ increment first indice
cmp r6,r5                       @ maxi ?
blt 1b                          @ and loop

mov r0,r10                      @ number counter
bl conversion10                 @ call décimal conversion
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
/******************************************************************/
/*      créate prime array                                       */
/******************************************************************/
createArrayPrime:
push {r1-r7,lr}          @ save registers
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
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
bl conversion10                 @ call décimal conversion
ldr r1,iAdrsZoneConv            @ insert conversion in message
bl strInsertAtCharInc
bl affichageMess                @ display message
100:
pop {r1,pc}

/***************************************************/
/*      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

```additives: select 2..500 'x -> and? prime? x prime? sum digits x

print map a => [pad to :string & 4]

```
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

```# 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")
}
}
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
```

## BASIC

```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

``` 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

```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

```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
\$(  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

```#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
```

## C++

```#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
```

## CLU

```% 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

```       IDENTIFICATION DIVISION.

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),
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

```(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)) ))

(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

```# 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

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.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

nn = 5000
addprimes.each_with_index { |n, idx| printf "%*d ", maxdigits, n; print "\n" if idx % 10 == 9 } # more efficient
```
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

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

```

## Dart

```import 'dart:math';

void main() {
const limit = 500;
print('Additive primes less than \$limit :');
int count = 0;
for (int n = 1; n < limit; ++n) {
if (isPrime(digit_sum(n)) && isPrime(n)) {
print('   \$n');
++count;
}
}
}

bool isPrime(int n) {
if (n <= 1) return false;
if (n == 2) return true;
for (int i = 2; i <= sqrt(n); ++i) {
if (n % i == 0) return false;
}
return true;
}

int digit_sum(int n) {
int sum = 0;
for (int m = n; m > 0; m ~/= 10) sum += m % 10;
return sum;
}
```

## Delphi

Works with: Delphi version 6.0

Many Rosette Code problems have similar operations. This problem was solved using subroutines that were written and used for other problems. Instead of packing all the operations in a single block of code, this example shows the advantage of breaking operations into separate modules that aids in code resuse.

```{These routines would normally be in libraries but are shown here for clarity}

function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N+0.0));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;

function SumDigits(N: integer): integer;
{Sum the integers in a number}
var T: integer;
begin
Result:=0;
repeat
begin
T:=N mod 10;
N:=N div 10;
Result:=Result+T;
end
until N<1;
end;

procedure ShowDigitSumPrime(Memo: TMemo);
var N,Sum,Cnt: integer;
var NS,S: string;
begin
Cnt:=0;
S:='';
for N:=1 to 500-1 do
if IsPrime(N) then
begin
Sum:=SumDigits(N);
if IsPrime(Sum) then
begin
Inc(Cnt);
S:=S+Format('%6d',[N]);
if (Cnt mod 8)=0 then S:=S+CRLF;
end;
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
Count = 54
Elapsed Time: 2.812 ms.

```

See Pascal.

## Draco

```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```

## EasyLang

```func prime n .
if n mod 2 = 0 and n > 2
return 0
.
i = 3
sq = sqrt n
while i <= sq
if n mod i = 0
return 0
.
i += 2
.
return 1
.
func digsum n .
while n > 0
sum += n mod 10
n = n div 10
.
return sum
.
for i = 2 to 500
if prime i = 1
s = digsum i
if prime s = 1
write i & " "
.
.
.
print ""```

## Erlang

```main(_) ->
AddPrimes = [N || N <- lists:seq(2,500), isprime(N) andalso isprime(digitsum(N))],
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#

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

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

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

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

Output:
```

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

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 ;

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
```

## FreeBASIC

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

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();
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

```

## Frink

```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.
```

## FutureBasic

```local fn IsPrime( n as NSUInteger ) as BOOL
NSUInteger i
BOOL       result = YES

if ( n < 2 ) then exit fn = NO
for i = 2 to n + 1
if ( i * i <= n ) and ( n mod i == 0 )
exit fn = NO
end if
next
end fn = result

local fn DigSum( n as NSUInteger ) as NSUInteger
NSUInteger s = 0
while ( n > 0 )
s += ( n mod 10 )
n /= 10
wend
end fn = s

void local fn AdditivePrimes( n as NSUInteger )
NSUInteger i, s = 0, counter = 0

for i = 2 to n
if ( fn IsPrime(i) ) and ( fn IsPrime( fn DigSum(i) ) )
s++
printf @"%4ld \b", i : counter++
if counter == 10 then counter = 0 : print
end if
next
printf @"\n\nFound %lu additive primes less than %lu.", s, n
end fn

HandleEvents```
Output:
```Additive Primes:
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.
```

## Fōrmulæ

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

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution

Test case 1. Write a program to determine all additive primes less than 500.

Test case 2. Show the number of additive primes.

## Go

```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() {
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
}
}
}
```
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

```

## J

```   (#~ 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

```public class additivePrimes {

public static void main(String[] args) {
for (int i = 2; i < 500; i++) {
if(isPrime(i) && isPrime(digitSum(i))){
System.out.print(i + " ");
}
}
}

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

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] + .;```

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

"Erdős primes under 500:",
| ((nwise(10) | map(lpad(4)) | join(" ")),
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

```

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
```

```λ> isPrime 12373
True

False

λ> isPrime 12347
True

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

```using Primes

let
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
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

```

## Kotlin

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() {
for (i in 2 until 500) {
if (isPrime(i) and isPrime(digitSum(i))) {
print("\$i ")
}
}
}
```
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

```#!/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 `

## Lambdatalk

```{def isprime
{def isprime.loop
{lambda {:n :m :i}
{if {> :i :m}
then true
else {if {= {% :n :i} 0}
then false
else {isprime.loop :n :m {+ :i 2}}
}}}}
{lambda {:n}
{if {or {= :n 2} {= :n 3} {= :n 5} {= :n 7}}
then true
else {if {or {< : n 2} {= {% :n 2} 0}}
then false
else {isprime.loop :n {sqrt :n} 3}
}}}}
-> isprime

{def digit.sum
{def digit.sum.loop
{lambda {:n :sum}
{if {> :n 0}
then {digit.sum.loop {floor {/ :n 10}}
{+ :sum {% :n 10}}}
else :sum}}}
{lambda {:n}
{digit.sum.loop :n 0}}}
-> digit.sum

{S.replace \s by space in
{S.map {lambda {:i}
{if {and {isprime :i}
{isprime {digit.sum :i}}}
then :i
else}}
{S.serie 2 500}}}
->
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

i.e 54 additive primes until 500.
```

## langur

```val isPrime = fn(i) {
i == 2 or i > 2 and
not any(fn x: i div x, pseries(2 .. i ^/ 2))
}

val sumDigits = fn i: fold(fn{+}, s2n(string(i)))

writeln "Additive primes less than 500:"

var cnt = 0

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

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

```

## Lua

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

```ClearAll[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}`

## Maxima

```/* Function that returns a list of digits given a nonnegative integer */
decompose(num) := block([digits, remainder],
digits: [],
while num > 0 do
(remainder: mod(num, 10),
digits: cons(remainder, digits),
num: floor(num/10)),
digits
)\$

/* Routine that extracts from primes between 2 and 500, inclusive, the additive primes */
block(
primes(2,500),
sublist(%%,lambda([x],primep(apply("+",decompose(x))))));

/* Number of additive primes in the rank */
length(%);
```
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
```

## MiniScript

```isPrime = function(n)
if n <= 3 then return n > 1
if n % 2 == 0 or n % 3 == 0 then return false

i = 5
while i ^ 2 <= n
if n % i == 0 or n % (i + 2) == 0 then return false
i += 6
end while
return true
end function

digitSum = function(n)
sum = 0
while n > 0
sum += n % 10
n = floor(n / 10)
end while
return sum
end function

for i in range(2, 500)
if isPrime(i) and isPrime(digitSum(i)) then additive.push(i)
end for
print "There are " + additive.len + " additive primes under 500."
```
Output:
```miniscript.exe additive-prime.ms
There are 54 additive 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]
```

## Miranda

```main :: [sys_message]
main = [Stdout (table 5 10 nums), Stdout countmsg]
where nums = filter additive_prime [1..500]
countmsg = "Found " ++ show (#nums) ++ " additive primes < 500\n"

table :: num->num->[num]->[char]
table w c ls = lay [concat (map (rjustify w . show) l) | l <- split c ls]

split :: num->[*]->[[*]]
split n ls = [ls], if #ls < n
= take n ls:split n (drop n ls), otherwise

additive_prime n = prime (dsum n) & prime n

dsum :: num->num
dsum n = n, if n<10
= n mod 10 + dsum (n div 10), otherwise

prime :: num->bool
prime n = n>=2 & #[d | d<-[2..entier (sqrt n)]; n mod d=0] = 0```
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```

## Modula-2

```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();
```
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.```

## Modula-3

Translation of: Modula-2
```MODULE AdditivePrimes EXPORTS Main;

IMPORT SIO,Fmt;

CONST
Max = 500;

VAR
Count:CARDINAL := 0;
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 J: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;
INC(J,I)
END
END
END;
END Sieve;

BEGIN
Sieve();
FOR N := 2 TO Max DO
IF Prime[N] AND Prime[DigitSum(N)] THEN
SIO.PutText(Fmt.F("%4s",Fmt.Int(N)));
INC(Count);
IF Count MOD 10 = 0 THEN SIO.Nl() END
END
END;
SIO.PutText(Fmt.F("\nThere are %s additive primes less than %s.\n",
Fmt.Int(Count),Fmt.Int(Max)));
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

```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```

## Oberon-07

Translation of: Modula-3
```MODULE AdditivePrimes;

IMPORT
Out;

CONST
Max = 500;

VAR
Count, n :INTEGER;
Prime    :ARRAY Max + 1 OF BOOLEAN;

PROCEDURE DigitSum( n :INTEGER ):INTEGER;
VAR   result    :INTEGER;
BEGIN
result := 0;
IF n < 10 THEN result := n
ELSE result := ( n MOD 10 ) + DigitSum( n DIV 10 )
END
RETURN result
END DigitSum;

PROCEDURE Sieve;
VAR     i, j    :INTEGER;
BEGIN
Prime[ 0 ] := FALSE; Prime[ 1 ] := FALSE;
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
Sieve;
FOR n := 2 TO Max DO
IF Prime[ n ] & Prime[ DigitSum( n ) ] THEN
Out.Int( n, 4 );
Count := Count + 1;
IF Count MOD 20 = 0 THEN Out.Ln END
END
END;
Out.Ln;Out.String( "There are " );Out.Int( Count, 1 );
Out.String( " additive primes less than " );Out.Int( Max, 1 );
Out.String( "." );Out.Ln
```
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.
```

## OCaml

```let rec digit_sum n =
if n < 10 then n else n mod 10 + digit_sum (n / 10)

let is_prime n =
let rec test x =
let q = n / x in x > q || x * q <> n && n mod (x + 2) <> 0 && test (x + 6)
in if n < 5 then n lor 1 = 3 else n land 1 <> 0 && n mod 3 <> 0 && test 5

is_prime n && is_prime (digit_sum n)

let () =
Seq.ints 0 |> Seq.take_while ((>) 500) |> Seq.filter is_additive_prime
|> Seq.iter (Printf.printf " %u") |> print_newline
```
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`

## Pari/GP

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

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);
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

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

## Perl

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

```with javascript_semantics
function additive(string p) return is_prime(sum(sq_sub(p,'0'))) end function
```
Output:
```54 additive primes found: 2 3 5 7 11 23 ... 443 449 461 463 467 487
```

## Phixmonti

```/# 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

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

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

```

## PicoLisp

```(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) ) ) ) ) )
(and
(prime? N)
(prime? (sum format (chop N))) ) )
(let C 0
(for (N 0 (> 500 N) (inc 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

```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```

## Polyglot:PL/I and PL/M

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 */

/* 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 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;
DECLARE ( A, B ) ADDRESS;
RETURN A MOD B;
END MODF;
/* END LANGUAGE DEFINITIONS */

/* 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 PRNUMBER( MAXPRIME );
CALL PRNL;

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

```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

```#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
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

## Python

```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:
for i in range(2, 500):
if is_prime(i) and is_prime(digit_sum(i)):
print(i, end=" ")

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

`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 ]

## R

```digitsum <- function(x) sum(floor(x / 10^(0:(nchar(x) - 1))) %% 10)

is.prime <- function(n) n == 2L || all(n %% 2L:max(2,floor(sqrt(n))) != 0)

range_int <- 2:500
v <- sapply(range_int, \(x) is.prime(x) && is.prime(digitsum(x)))

print(range_int[v])
```
Output:
```Found 54 additive primes less than 500
[1]   2   3   5   7  11  23  29  41  43  47  61  67  83  89 101 113 131 137 139 151 157 173 179
[24] 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401
[47] 409 421 443 449 461 463 467 487```

## Racket

```#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)))))

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

```
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

```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

```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

```/*REXX program counts/displays the number of additive primes less than 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=5                                        /*width of a number in any column.     */
title= 'additive primes that are  < 'commas(n)
If cols>0  Then Say ' index ¦'center(title,cols*(w+1)+1)
If cols>0  Then Say '-------+'center(''   ,cols*(w+1)+1,'-')
found=0
ol=''                                      /*a list of additive primes  (so far). */
idx=1
Do j=1 By 1
p=p.j                                    /*obtain the  Jth  prime.              */
If p>n Then Leave                        /* no more needed                      */
_=sumDigs(p)
If !._ Then Do
found=found+1                          /*bump the count of additive primes.   */
c=commas(p)                            /*maybe add commas To the number.      */
If words(ol)=10 Then Do                /* a line is complete                  */
Say center(idx,7)'¦' substr(ol,2)    /*display what we have so far  (cols). */
ol=''                                /* prepare for next line               */
idx=idx+10
End
End
End   /*j*/

If ol\=='' Then
Say center(idx,7)'¦' substr(ol,2)        /*possible display residual output.    */
If cols>0  Then
Say '--------'center('',cols*(w+1)+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
pl=2 3 5 7 11 13
!.=0
Do np=1 By 1 While pl<>''
Parse Var pl p pl
p.np=p
sq.np=p*p
!.p=1
End
np=np-1
Do j=p.np+2 by 2 While j<n
Parse Var j '' -1 _                    /*obtain the last digit of the  J  var.*/
If _==5  Then Iterate
If j// 3==0 Then Iterate
If j// 7==0 Then Iterate
If j//11==0 Then Iterate
Do k=6 By 1 While sq.k<=j              /*divide J by other primes <=sqrt(j)   */
If j//p.k==0 Then Iterate j          /* not prime - try next                */
End   /*k*/
np=np+1                                /*bump prime count; assign prime & flag*/
p.np=j
sq.np=j*j
!.j=1
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

```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...
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
done...
```

## RPL

Works with: HP version 49g
```≪ →STR 0
1 3 PICK SIZE FOR j
OVER j DUP SUB STR→ + NEXT NIP
≫ '∑DIGITS' STO

≪ { } 1
DO
NEXTPRIME
IF DUP ∑DIGITS ISPRIME? THEN SWAP OVER + SWAP END
UNTIL DUP 500 ≥ END
DROP DUP SIZE
```
Output:
```2: { 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 }
1: 54
```

## Ruby

```require "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

```

## Rust

### Flat implementation

```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"

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

```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))))))))
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

```\$ 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.
```

## SETL

```program additive_primes;
loop for i in [i : i in [1..499] | additive_prime i] do
if (n +:= 1) mod 10 = 0 then
print;
end if;
end loop;
print;
print("There are " + str n + " additive primes less than 500.");

return prime n and prime digitsum n;
end op;

op prime(n);
return n>=2 and not exists d in {2..floor sqrt n} | n mod d = 0;
end op;

op digitsum(n);
loop while n>0;
s +:= n mod 10;
n div:= 10;
end loop;
return s;
end op;
end program;```
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.```

## Sidef

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

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

```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 )
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

```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
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" : " ")
}
}
```
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
```

## uBasic/4tH

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```

## Uiua

Works with: Uiua version 0.10.0-dev.1
```[]     # list of primes to be populated
↘2⇡500 # candidates (starting at 2)

# Take the first remaining candidate, which will be prime, save it,
# then remove every candidate that it divides. Repeat until none left.
⍢(▽≠0◿⊃⊢(.↘1)⟜(⊂⊢)|>0⧻)
# Tidy up.
⇌◌

# Build sum of digits of each.
≡(/+≡⋕°⋕)...
# Mask out those that result in non-primes.
⊏⊚±⬚0⊏⊗
# Return values and length.
⧻.```
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
```

## V (Vlang)

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() {
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
}
}
}```
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

```

## VTL-2

```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

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
}

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()
}
}
```
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

```

## XPL0

```func IsPrime(N);        \Return 'true' if N is a prime number
int  N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true;
];

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

```// 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---```