# Sum of square and cube digits of an integer are primes

Sum of square and cube digits of an integer are primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Find and show here all positive integers n less than 100 where:

• the sum of the digits of the square of n is prime; and
• the sum of the digits of the cube of n is also prime.

Example

16 satisfies the task descrption because 16 x 16 = 256 has a digit sum of 13 which is prime and 16 x 16 x 16 = 4096 has a digit sum of 19 which is also prime.

## ALGOL 68

```BEGIN # find numbers where the digit sums of the square and cube are prtime #
INT max number = 99; # maximum number to consider #
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE ( INT d sum := 9; # calculate the largest possible digit sum #
INT n     := max number * max number * max number;
WHILE ( n OVERAB 10 ) > 0 DO
d sum +:= 9
OD;
d sum
);
# returns the sum of the digits of n #
OP  DIGITSUM = ( INT n )INT:
BEGIN
INT v      := ABS n;
INT result := v MOD 10;
WHILE ( v OVERAB 10 ) > 0 DO
result +:= v MOD 10
OD;
result
END # DIGITSUM # ;
FOR i TO max number DO
INT i2 = i * i;
IF prime[ DIGITSUM i2 ] THEN
IF prime[ DIGITSUM ( i * i2 ) ] THEN
print( ( " ", whole( i, 0 ) ) )
FI
FI
OD
END```
Output:
``` 16 17 25 28 34 37 47 52 64
```

## ALGOL W

```begin
integer procedure digitSum( integer value n ) ;
begin
integer sum, v, vOver10;
sum := 0;
v   := n;
while v > 0 do begin
vover10 := v div 10;
sum     := sum + ( v - ( vover10 * 10 ) );
v       := vover10
end while_v_gt_0 ;
sum
end digitSum ;
logical procedure isPrime( integer value n ) ;
if      n < 2        then false
else if not odd( n ) then n = 2
else begin
logical prime;
integer p;
prime := true;
p     := 3;
while p * p <= n and prime do begin
prime := n rem p not = 0;
p := p + 2;
end while_p2_le_n_and_prime ;
prime
end isPrime ;
for i := 1 until 99 do begin
integer i2;
i2 := i * i;
if isPrime( digitSum( i2 ) ) then begin;
if isPrime( digitSum( i2 * i ) ) then writeon( i_w := 1, s_w := 1, i )
end
end
end.```
Output:
```16 17 25 28 34 37 47 52 64
```

## APL

```(⊢(/⍨)∧/∘((2=0+.=⍳|⊢)∘(+/⍎¨∘⍕)¨*∘2 3)¨)⍳100
```
Output:
`16 17 25 28 34 37 47 52 64`

## Arturo

```print select 1..100 'x ->
and? [prime? sum digits x^2]
[prime? sum digits x^3]
```
Output:
`16 17 25 28 34 37 47 52 64`

## AWK

```# syntax: GAWK -f SUM_OF_SQUARE_AND_CUBE_DIGITS_OF_AN_INTEGER_ARE_PRIMES.AWK
# converted from FreeBASIC
BEGIN {
start = 1
stop = 99
for (i=start; i<=stop; i++) {
if (is_prime(digit_sum(i^3,10)) && is_prime(digit_sum(i^2,10))) {
printf("%5d%1s",i,++count%10?"":"\n")
}
}
printf("\nSum of square and cube digits are prime %d-%d: %d\n",start,stop,count)
exit(0)
}
function digit_sum(n,b,  s) { # digital sum of n in base b
while (n) {
s += n % b
n = int(n/b)
}
return(s)
}
function is_prime(n,  d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
}
```
Output:
```   16    17    25    28    34    37    47    52    64
Sum of square and cube digits are prime 1-99: 9
```

## BASIC

### FreeBASIC

```function digsum(byval n as uinteger, b as const uinteger) as uinteger
'digital sum of n in base b
dim as integer s
while n
s+=n mod b
n\=b
wend
return s
end function

function isprime(n as const uinteger) as boolean
if n<2 then return false
if n<4 then return true
if n mod 2 = 0 then return false
dim as uinteger i = 3
while i*i<=n
if n mod i = 0 then return false
i+=2
wend
return true
end function

for n as uinteger = 1 to 99
if isprime(digsum(n^3,10)) andalso isprime(digsum(n^2,10)) then print n;"   ";
next n```
Output:
`16   17   25   28   34   37   47   52   64`

### QuickBASIC

Translation of: XPL0
```' Sum of square and cube digits of an integer are primes
DECLARE FUNCTION SumDigits% (Num&)
DECLARE FUNCTION IsPrime% (Num%)
CONST TRUE% = -1, FALSE% = 0
FOR N = 0 TO 99
IF IsPrime%(SumDigits%(N * N)) AND IsPrime%(SumDigits%(N * N * N)) THEN PRINT N;
NEXT N
PRINT
END

FUNCTION IsPrime% (Num%)
IF Num% < 2 THEN
IsPrime% = FALSE%
ELSEIF Num% = 2 THEN
IsPrime% = TRUE%
ELSEIF Num% MOD 2 = 0 THEN
IsPrime% = FALSE%
ELSE
I% = 3: FoundFac% = FALSE%
WHILE I% * I% <= Num% AND NOT FoundFac%
IF Num% MOD I% = 0 THEN FoundFac% = TRUE%
I% = I% + 2
WEND
END IF
END FUNCTION

FUNCTION SumDigits% (Num&)
Sum% = 0
WHILE Num& <> 0
Sum% = Sum% + Num& MOD 10
Num& = Num& \ 10
WEND
SumDigits% = Sum%
END FUNCTION
```
Output:
``` 16  17  25  28  34  37  47  52  64
```

### Tiny BASIC

Works with: TinyBasic

This can only go up to 31 because 32^3 is too big to fit in a signed 16-bit int.

```10 REM Sum of square and cube digits of an integer are primes
20 REM N, the number to be tested
30 REM D, the digital sum of its square or cube
40 REM T, temporary variable
50 REM Z, did D test as prime or not
60 LET N = 1
70 LET T = N * N * N
80 GOSUB 200
90 GOSUB 260
100 IF Z = 0 THEN GOTO 160
110 LET T = N * N
120 GOSUB 200
130 GOSUB 260
140 IF Z = 0 THEN GOTO 160
150 PRINT N
160 IF N = 31 THEN END
170 LET N = N + 1
180 GOTO 70
190 REM Calculate sum of digits
200 LET D = 0
210 IF T = 0 THEN RETURN
220 LET D = D + (T - (T / 10) * 10)
230 LET T = T / 10
240 GOTO 210
250 REM Check if is prime
260 LET Z = 0
270 IF D < 2 THEN RETURN
280 LET Z = 1
290 IF D < 4 THEN RETURN
300 LET Z = 0
310 IF (D / 2) * 2 = D THEN RETURN
320 LET T = 1
330 LET T = T + 2
340 IF T * T > D THEN GOTO 370
350 IF (D / T) * T = D THEN RETURN
360 GOTO 330
370 LET Z = 1
380 RETURN
```
Output:
```16
17
25

28```

### Yabasic

Translation of: Ring
```// Rosetta Code problem: http://rosettacode.org/wiki/Sum_of_square_and_cube_digits_of_an_integer_are_primes
// by Galileo, 04/2022

sub isPrime(n)
local i

if n < 4 return n >= 2
for i = 2 to sqrt(n)
if not mod(n, i) return false
next
return true
end sub

limit = 100

for n = 1 to limit
sums = 0
sumc = 0
sps\$ = str\$(n^2)
spc\$ = str\$(n^3)
for m = 1 to len(sps\$)
sums = sums + val(mid\$(sps\$, m, 1))
next
for p = 1 to len(spc\$)
sumc = sumc + val(mid\$(spc\$, p, 1))
next
if isPrime(sums) and isPrime(sumc) then
print n, " ";
endif
next
print```
Output:
```16 17 25 28 34 37 47 52 64
---Program done, press RETURN---```

## BQN

```# 'Library' functions from BQNCrate
Digits ← 10 {⌽𝕗|⌊∘÷⟜𝕗⍟(↕1+·⌊𝕗⋆⁼1⌈⊢)}
Prime ← 2=·+´0=(1+↕)⊸|

(∧˝∘⍉∘((Prime +´∘Digits)¨⋆⌜⟜2‿3))⊸/↕100
```
Output:
`⟨ 16 17 25 28 34 37 47 52 64 ⟩`

## C

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

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

/* The numbers involved are tiny */
bool prime(int n) {
if (n<4) return n>=2;
for (int d=2; d*d <= n; d++)
if (n%d == 0) return false;
return true;
}

int main() {
for (int i=1; i<100; i++)
if (prime(digit_sum(i*i)) & prime(digit_sum(i*i*i)))
printf("%d ", i);
printf("\n");
return 0;
}
```
Output:
`16 17 25 28 34 37 47 52 64`

## CLU

```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

% The numbers tested for primality are very small,
% so this simple test suffices.
prime = proc (n: int) returns (bool)
if n<2 then return(false) end
d: int := 2
while d*d <= n do
if n//d=0 then return(false) end
d := d+1
end
return(true)
end prime

accept = proc (n: int) returns (bool)
return(prime(digit_sum(n**2)) cand prime(digit_sum(n**3)))
end accept

start_up = proc ()
po: stream := stream\$primary_output()
for i: int in int\$from_to(1, 99) do
if accept(i) then
stream\$puts(po, int\$unparse(i) || " ")
end
end
end start_up```
Output:
`16 17 25 28 34 37 47 52 64`

## COBOL

```       IDENTIFICATION DIVISION.
PROGRAM-ID. SQUARE-CUBE-DIGITS-PRIME.

DATA DIVISION.
WORKING-STORAGE SECTION.
01 NUMBER-SEARCH-VARS.
03 CAND             PIC 9(6).
03 SQUARE           PIC 9(6).
03 CUBE             PIC 9(6).

01 SUM-DIGITS-VARS.
03 SUM-NUM          PIC 9(6).
03 DIGITS           PIC 9 OCCURS 6 TIMES INDEXED BY D
REDEFINES SUM-NUM.
03 SUM              PIC 99.

01 PRIME-TEST-VARS.
03 DIVISOR          PIC 99.
03 DIV-TEST         PIC 99V9999.
03 FILLER           REDEFINES DIV-TEST.
05 FILLER        PIC 99.
05 FILLER        PIC 9999.
88 DIVISIBLE  VALUE ZERO.
03 PRIME-FLAG       PIC X.
88 PRIME         VALUE '*'.

01 OUT-FMT             PIC Z9.

PROCEDURE DIVISION.
BEGIN.
PERFORM CHECK-NUMBER VARYING CAND FROM 1 BY 1
UNTIL CAND IS EQUAL TO 100.
STOP RUN.

CHECK-NUMBER.
MULTIPLY CAND BY CAND GIVING SQUARE.
MULTIPLY CAND BY SQUARE GIVING CUBE.
MOVE SQUARE TO SUM-NUM.
PERFORM SUM-DIGITS.
PERFORM PRIME-TEST.
IF PRIME,
MOVE CUBE TO SUM-NUM,
PERFORM SUM-DIGITS,
PERFORM PRIME-TEST,
IF PRIME,
MOVE CAND TO OUT-FMT,
DISPLAY OUT-FMT.

SUM-DIGITS.
MOVE ZERO TO SUM.
PERFORM SUM-DIGIT VARYING D FROM 1 BY 1
UNTIL D IS GREATER THAN 6.

SUM-DIGIT.
ADD DIGITS(D) TO SUM.

PRIME-TEST.
MOVE '*' TO PRIME-FLAG.
PERFORM CHECK-DIVISOR VARYING DIVISOR FROM 2 BY 1
UNTIL NOT PRIME, OR DIVISOR IS EQUAL TO SUM.

CHECK-DIVISOR.
DIVIDE SUM BY DIVISOR GIVING DIV-TEST.
IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.
```
Output:
```16
17
25
28
34
37
47
52
64```

## Delphi

Works with: Delphi version 6.0

```procedure GetDigits(N: integer; var IA: TIntegerDynArray);
{Get an array of the integers in a number}
{Numbers returned from least to most significant}
var T,I,DC: integer;
begin
DC:=Trunc(Log10(N))+1;
SetLength(IA,DC);
for I:=0 to DC-1 do
begin
T:=N mod 10;
N:=N div 10;
IA[I]:=T;
end;
end;

procedure SquareCubeDigitsPrime(Memo: TMemo);
var Dg1,Dg2: TIntegerDynArray;
var SQ,CU: integer;
var Sum1,Sum2: integer;
var I,J: integer;
var S: string;
begin
S:='';
for I:=1 to 100-1 do
begin
SQ:=I*I;
CU:=I*I*I;
GetDigits(SQ,Dg1);
GetDigits(CU,Dg2);
Sum1:=0;
for J:=0 to High(Dg1) do Sum1:=Sum1+Dg1[J];
Sum2:=0;
for J:=0 to High(Dg2) do Sum2:=Sum2+Dg2[J];
if IsPrime(Sum1) and IsPrime(Sum2) then
S:=S+' '+IntToStr(I);
end;
end;
```
Output:
``` 16 17 25 28 34 37 47 52 64

Elapsed Time: 1.809 ms.
```

## F#

This task uses Extensible Prime Generator (F#)

```// Sum of square and cube digits of an integer are primes. Nigel Galloway: December 22nd., 2021
let rec fN g=function 0->g |n->fN(g+n%10)(n/10)
[1..99]|>List.filter(fun g->isPrime(fN 0 (g*g)) && isPrime(fN 0 (g*g*g)))|>List.iter(printf "%d "); printfn ""
```
Output:
```16 17 25 28 34 37 47 52 64
```

## Factor

Works with: Factor version 0.99 2021-06-02
```USING: kernel math math.functions math.primes math.text.utils prettyprint sequences ;

100 <iota> [ [ sq ] [ 3 ^ ] bi [ 1 digit-groups sum prime? ] both? ] filter .
```
Output:
```V{ 16 17 25 28 34 37 47 52 64 }
```

## FOCAL

```01.10 F I=1,100;D 2
01.20 Q

02.10 F P=2,3;S N=I^P;D 3;D 4;I (C)2.3
02.20 T %2,I,!
02.30 R

03.10 S S=0
03.20 S M=FITR(N/10)
03.30 S S=S+(N-M*10)
03.40 S N=M
03.50 I (-N)3.2

04.10 S C=0
04.20 I (1-S)4.3;S C=-1;R
04.30 I (2-S)4.4;S C=0;R
04.40 F D=2,FSQT(S)+1;D 5;I (C)4.5
04.50 R

05.10 S Z=S/D
05.20 I (FITR(Z)-Z)5.3;S C=-1
05.30 R```
Output:
```= 16
= 17
= 25
= 28
= 34
= 37
= 47
= 52
= 64```

## Go

Library: Go-rcu
```package main

import (
"fmt"
"rcu"
)

func main() {
for i := 1; i < 100; i++ {
if !rcu.IsPrime(rcu.DigitSum(i*i, 10)) {
continue
}
if rcu.IsPrime(rcu.DigitSum(i*i*i, 10)) {
fmt.Printf("%d ", i)
}
}
fmt.Println()
}
```
Output:
```16 17 25 28 34 37 47 52 64
```

```import Data.Bifunctor (first)
import Data.Numbers.Primes (isPrime)

---- SQUARE AND CUBE BOTH HAVE PRIME DECIMAL DIGIT SUMS --

p :: Int -> Bool
p =
((&&) . primeDigitSum . (^ 2))
<*> (primeDigitSum . (^ 3))

--------------------------- TEST -------------------------
main :: IO ()
main = print \$ filter p [2 .. 99]

------------------------- GENERIC ------------------------
primeDigitSum :: Int -> Bool
primeDigitSum = isPrime . digitSum 10

digitSum :: Int -> Int -> Int
digitSum base = go
where
go 0 = 0
go n = uncurry (+) . first go \$ quotRem n base
```
Output:
`[16,17,25,28,34,37,47,52,64]`

## J

```((1*./@p:[:+/@|:10#.^:_1^&2 3)"0#]) i.100
```
Output:
`16 17 25 28 34 37 47 52 64`

## jq

Works with: jq

Also works with gojq and fq

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 23
| until( (. * .) > \$n or (\$n % . == 0); .+2)
| . * . > \$n
end;

# emit an array of the decimal digits of the integer input, least significant digit first.
def digits:
recurse( if . >= 10 then ((. - (.%10)) / 10) else empty end) | . % 10;

def digitSum:
def add(s): reduce s as \$_ (0; .+\$_);

```range(1;100)
| (.*.) as \$sq
|  select( (\$sq | digitSum | is_prime) and (\$sq * . | digitSum | is_prime ) )```
Output:
```16
17
25
28
34
37
47
52
64
```

## Julia

```using Primes

is_sqcubsumprime(n) = isprime(sum(digits(n*n))) && isprime(sum(digits(n*n*n)))
println(filter(is_sqcubsumprime, 1:100)) # [16, 17, 25, 28, 34, 37, 47, 52, 64]
```

```            NORMAL MODE IS INTEGER

BOOLEAN PRIME
DIMENSION PRIME(100)
PRIME(0)=0B
PRIME(1)=0B
THROUGH SET, FOR P=2, 1, P.G.100
SET         PRIME(P)=1B
THROUGH SIEVE, FOR P=2, 1, P*P.G.100
THROUGH SIEVE, FOR C=P*P, P, C.G.100
SIEVE       PRIME(C)=0B

THROUGH CHECK, FOR I=1, 1, I.GE.100
WHENEVER .NOT.PRIME(DIGSUM.(I*I)), TRANSFER TO CHECK
WHENEVER .NOT.PRIME(DIGSUM.(I*I*I)), TRANSFER TO CHECK
PRINT FORMAT FMT, I
CHECK       CONTINUE

INTERNAL FUNCTION(N)
ENTRY TO DIGSUM.
SUM=0
NN=N
LOOP        WHENEVER NN.G.0
NXT=NN/10
SUM=SUM+NN-NXT*10
NN=NXT
TRANSFER TO LOOP
END OF CONDITIONAL
FUNCTION RETURN SUM
END OF FUNCTION

VECTOR VALUES FMT = \$I2*\$
END OF PROGRAM```
Output:
```16
17
25
28
34
37
47
52
64```

## Nim

```const Primes = {2, 3, 5, 7, 11, 13, 17, 19}

func digitSum(n: Positive): int =
## Return the sum of digits of "n".
var n = n.Natural
while n != 0:
result += n mod 10
n = n div 10

for n in 5..99:
let n² = n * n
if digitSum(n²) in Primes and digitSum(n * n²) in Primes:
stdout.write n, ' '
echo()
```
Output:
`16 17 25 28 34 37 47 52 64 `

## OCaml

```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

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

let is_square_and_cube_digit_sum_prime n =
is_prime (digit_sum (n * n)) && is_prime (digit_sum (n * n * n))

let () =
Seq.ints 1 |> Seq.take_while ((>) 100)
|> Seq.filter is_square_and_cube_digit_sum_prime
|> Seq.iter (Printf.printf " %u") |> print_newline
```
Output:
` 16 17 25 28 34 37 47 52 64`

## Perl

Library: ntheory
```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Sum_of_square_and_cube_digits_of_an_integer_are_primes
use warnings;
use ntheory qw( is_prime vecsum );

my @results = grep
is_prime( vecsum( split //, \$_ ** 2 ) ) &&
is_prime( vecsum( split //, \$_ ** 3 ) ), 1 .. 100;
print "@results\n";
```
Output:
```16 17 25 28 34 37 47 52 64
```

## Phix

```with javascript_semantics
function ipsd(integer n) return is_prime(sum(sq_sub(sprintf("%d",n),'0'))) end function
function scdp(integer n) return ipsd(n*n) and ipsd(n*n*n) end function
pp(filter(tagset(99),scdp))
```
Output:
```{16,17,25,28,34,37,47,52,64}
```

## PL/0

```const maxnumber = 99;
var   n, sum, prime, i, i2, i3;
procedure sumdigitsofn;
var v, vover10;
begin
sum := 0;
v   := n;
while v > 0 do begin
vover10 := v / 10;
sum := sum + ( v - ( vover10 * 10 ) );
v := vover10
end
end;
procedure isnprime;
var p;
begin
prime := 1;
if n < 2 then prime := 0;
if n > 2 then begin
prime := 0;
if odd( n ) then prime := 1;
p := 3;
while p * p <= n * prime do begin
if n - ( ( n / p ) * p ) = 0 then prime := 0;
p := p + 2;
end
end
end;
begin
i := 0;
while i <= maxnumber do begin
i  := i + 1;
i2 := i * i;
n  := i2;
call sumdigitsofn;
n  := sum;
call isnprime;
if prime = 1 then begin
n := i2 * i;
call sumdigitsofn;
n := sum;
call isnprime;
if prime = 1 then ! i
end
end
end.
```
Output:
```         16
17
25
28
34
37
47
52
64
```

## Python

### Procedural

```#!/usr/bin/python

def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True

def digSum(n, b):
s = 0
while n:
s += (n % b)
n = n // b
return s

if __name__ == '__main__':
for n in range(11, 99):
if isPrime(digSum(n**3, 10)) and isPrime(digSum(n**2, 10)):
print(n, end = "  ")
```
Output:
`16  17  25  28  34  37  47  52  64`

### Functional

```'''Square and cube both have prime decimal digit sums'''

# p :: Int -> Bool
def p(n):
'''True if the square and the cube of N both have
decimal digit sums which are prime.
'''
return primeDigitSum(n ** 2) and primeDigitSum(n ** 3)

# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Matches in the range [1..99]'''
print([
x for x in range(2, 100)
if p(x)
])

# ----------------------- GENERIC ------------------------

# primeDigitSum :: Int -> Bool
def primeDigitSum(n):
'''True if the sum of the decimal digits of n is prime.
'''
return isPrime(digitSum(10)(n))

# digitSum :: Int -> Int
def digitSum(base):
'''The sum of the digits of n in a given base.
'''
def go(n):
q, r = divmod(n, base)
return go(q) + r if n else 0
return go

# isPrime :: Int -> Bool
def isPrime(n):
'''True if n is prime.'''
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False

def q(x):
return 0 == n % x or 0 == n % (2 + x)

return not any(map(q, range(5, 1 + int(n ** 0.5), 6)))

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
`[16, 17, 25, 28, 34, 37, 47, 52, 64]`

## Quackery

`isprime` is defined at Primality by trial division#Quackery.

```  [ 0 swap
[ dup while
10 /mod
rot + swap
again ]
drop ]        is digitsum ( n --> n )

98 times
[ i^ 1+ 2 **
digitsum isprime if
[  i^ 1+ 3 **
digitsum isprime if
[ i^ 1+ echo sp ] ] ]```
Output:
`16 17 25 28 34 37 47 52 64`

## Raku

```say ^100 .grep: { .².comb.sum.is-prime && .³.comb.sum.is-prime }
```
Output:
`(16 17 25 28 34 37 47 52 64)`

## Ring

```load "stdlib.ring"
see "working..." +nl

limit = 100

for n = 1 to limit
sums = 0
sumc = 0
sps = string(pow(n,2))
spc = string(pow(n,3))
for m = 1 to len(sps)
sums = sums + sps[m]
next
for p = 1 to len(spc)
sumc = sumc + spc[p]
next
if isprime(sums) and isprime(sumc)
see "" + n + " "
ok
next

see nl + "done..." + nl```
Output:
```working...
16 17 25 28 34 37 47 52 64
done...
```

## Ruby

```require 'prime'

p (1..100).select{|n|(n*n).digits.sum.prime? && (n**3).digits.sum.prime?}
```
Output:
```[16, 17, 25, 28, 34, 37, 47, 52, 64]
```

## Rust

```fn is_prime( number : u32 ) -> bool {
if number < 2 {
false
}
else {
let limit : u32 = (number as f32).sqrt( ).floor( ) as u32 ;
let mut nums : Vec<u32> = Vec::new( ) ;
for i in 2..=limit {
nums.push( i ) ;
}
nums.iter( ).filter( | n | number % *n == 0 ).count( ) == 0
}
}

fn to_digits( mut number : u32 ) -> Vec<u32> {
let mut digits : Vec<u32> = Vec::new( ) ;
while number != 0 {
let remainder : u32 = number % 10 ;
digits.push( remainder ) ;
number /= 10 ;
}
digits
}

fn digit_sum( number : u32 ) -> u32 {
let digits : Vec<u32> = to_digits( number ) ;
digits.iter( ).sum( )
}

fn main() {
let mut solution : Vec<u32> = Vec::new( ) ;
for i in 2..=100 {
let square = i * i ;
let cube = square * i ;
if is_prime( digit_sum( square ) ) && is_prime( digit_sum(cube ) ) {
solution.push( i ) ;
}
}
println!("{:?}" , solution);
}
```
Output:
```[16, 17, 25, 28, 34, 37, 47, 52, 64]
```

## Sidef

```1..99 -> grep { .square.digits_sum.is_prime && .cube.digits_sum.is_prime }.say
```
Output:
```[16, 17, 25, 28, 34, 37, 47, 52, 64]
```

## Wren

Library: Wren-math
```import "./math" for Int

for (i in 1..99) {
if (Int.isPrime(Int.digitSum(i*i)) && Int.isPrime(Int.digitSum(i*i*i))) System.write("%(i) ")
}
System.print()```
Output:
```16 17 25 28 34 37 47 52 64
```

## XPL0

```func IsPrime(N);        \Return 'true' if N is prime
int  N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];

func SumDigits(N);      \Return the sum of digits in N
int  N, Sum;
[Sum:= 0;
while N do
[N:= N/10;
Sum:= Sum + rem(0);
];
return Sum;
];

int N;
[for N:= 0 to 100-1 do
if IsPrime(SumDigits(N*N)) & IsPrime(SumDigits(N*N*N)) then
[IntOut(0, N);  ChOut(0, ^ )];
]```
Output:
```16 17 25 28 34 37 47 52 64
```