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.
- Task
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.
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))
FOR n IN {1..99}:
IF prime (digit.sum (n**2)) AND prime (digit.sum (n**3)):
WRITE n/- Output:
16 17 25 28 34 37 47 52 64
Ada
-- Rosetta Code Task written in Ada
-- Sum of square and cube digits of an integer are primes
-- https://rosettacode.org/wiki/Sum_of_square_and_cube_digits_of_an_integer_are_primes
-- Loosely translated from the Nim solution
-- March 2025, R. B. E.
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
procedure Sum_of_Square_and_Cube_Digits_of_an_Integer_are_Primes is
function Is_Prime (Candidate : in Positive) return Boolean is
type Prime_Sieve_Array is array (Positive range <>) of Positive;
Prime_Sieve : Prime_Sieve_Array := (2, 3, 5, 7, 11, 13, 17, 19);
begin
for J in Prime_Sieve'Range loop
if Candidate = Prime_Sieve (J) then
return True;
end if;
end loop;
return False;
end Is_Prime;
function Sum_of_Digits (N : in Positive) return Positive is
Local_N : Natural := N;
Result : Natural := 0;
begin
while Local_N > 0 loop
Result := Result + Local_N mod 10;
Local_N := Local_N / 10;
end loop;
return Result;
end Sum_of_Digits;
N_Squared, N_Cubed : Positive;
Sum_of_the_Squared_Digits : Positive;
Sum_of_the_Cubed_Digits : Positive;
begin
for I in 5..99 loop
N_Squared := I * I;
N_Cubed := N_Squared * I;
Sum_of_the_Squared_Digits := Sum_of_Digits (N_Squared);
Sum_of_the_Cubed_Digits := Sum_of_Digits (N_Cubed);
if ((Is_Prime (Sum_of_Digits (N_Squared))) and (Is_Prime (Sum_of_Digits (N_Cubed)))) then
Put (I, 0);
Put (" ");
end if;
end loop;
New_Line;
end Sum_of_Square_and_Cube_Digits_of_an_Integer_are_Primes;
- Output:
16 17 25 28 34 37 47 52 64
ALGOL 68
BEGIN # find numbers where the digit sums of the square and cube are prime #
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
ANSI BASIC
100 REM Sum of square and cube digits of an integer are primes
110 DECLARE EXTERNAL FUNCTION SumDigits
120 DECLARE EXTERNAL FUNCTION IsPrime
130 FOR N = 0 TO 99
140 IF IsPrime(SumDigits(N * N)) <> 0 AND IsPrime(SumDigits(N * N * N)) <> 0 THEN PRINT N;
150 NEXT N
160 PRINT
170 END
180 REM **
190 EXTERNAL FUNCTION IsPrime (Num)
200 IF Num < 2 THEN
210 LET IsPrime = 0
220 EXIT FUNCTION
230 END IF
240 IF Num = 2 THEN
250 LET IsPrime = -1
260 EXIT FUNCTION
270 END IF
280 IF MOD(Num, 2) = 0 THEN
290 LET IsPrime = 0
300 EXIT FUNCTION
310 END IF
320 LET I = 3
330 DO WHILE I * I <= Num
340 IF MOD(Num, I) = 0 THEN
350 LET IsPrime = 0
360 EXIT FUNCTION
370 END IF
380 LET I = I + 2
390 LOOP
400 LET IsPrime = -1
410 END FUNCTION
420 REM **
430 EXTERNAL FUNCTION SumDigits(Num)
440 LET Sum = 0
450 DO WHILE Num <> 0
460 LET Sum = Sum + MOD(Num, 10)
470 LET Num = INT(Num / 10)
480 LOOP
490 LET SumDigits = Sum
500 END FUNCTION
- Output:
16 17 25 28 34 37 47 52 64
ASIC
Compile with the option Extended Math (E in command line).
REM Sum of square and cube digits of an integer are primes
FOR N = 1 TO 99
NumExt& = N * N
GOSUB SumDigits:
Num = Sum
GOSUB CheckIfPrime:
IF IsPrime = 1 THEN
NumExt& = NumExt& * N
GOSUB SumDigits:
Num = Sum
GOSUB CheckIfPrime:
IF IsPrime = 1 THEN
PRINT N
ENDIF
ENDIF
NEXT N
END
SumDigits:
REM Sums digits of NumExt&.
Sum = 0
TmpNum& = NumExt&
REM TmpNum& used in order not to change a value of the "parameter"
WHILE TmpNum& <> 0
NumMod10& = TmpNum& MOD 10
Sum = Sum + NumMod10&
TmpNum& = TmpNum& / 10
WEND
RETURN
CheckIfPrime:
REM Checks if Num is prime.
IF Num < 2 THEN
IsPrime = 0
ELSE
IF Num = 2 THEN
IsPrime = 1
ELSE
NumMod2 = Num MOD 2
IF NumMod2 = 0 THEN
IsPrime = 0
ELSE
IsPrime = 1
I = 3
I2& = I * I
Hi& = Num * IsPrime
WHILE I2& <= Hi&
AModI = Num MOD I
IF AModI = 0 THEN
IsPrime = 0
ENDIF
I = I + 2
I2& = I * I
Hi& = Num * IsPrime
WEND
ENDIF
ENDIF
ENDIF
RETURN
- Output:
16
17
25
28
34
37
47
52
64
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
' 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
IsPrime% = NOT FoundFac%
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
RapidQ
' Sum of square and cube digits of an integer are primes
DECLARE FUNCTION SumDigits (Num&) AS SHORT
DECLARE FUNCTION IsPrime (Num%) AS SHORT
CONST TRUE% = -1
CONST 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%) AS SHORT
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
IsPrime = NOT FoundFac%
END IF
END FUNCTION
FUNCTION SumDigits (Num&) AS SHORT
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
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:
1617 25
28
XBasic
' sum of square and cube digits of an integer are primes
PROGRAM "sumofdigitsetc"
DECLARE FUNCTION Entry ()
INTERNAL FUNCTION SumDigits (num&&)
INTERNAL FUNCTION IsPrime (num&&)
FUNCTION Entry ()
FOR n@@ = 0 TO 99
IF IsPrime(SumDigits(n@@ * n@@)) AND IsPrime(SumDigits(n@@ * n@@ * n@@)) THEN PRINT n@@;
NEXT n@@
PRINT
END FUNCTION
FUNCTION SumDigits(num&&)
sum&& = 0
DO WHILE num&& <> 0
sum&& = sum&& + num&& MOD 10
num&& = num&& \ 10
LOOP
END FUNCTION sum&&
FUNCTION IsPrime (num&&)
IF num&& < 2 THEN RETURN $$FALSE
IF num&& = 2 THEN RETURN $$TRUE
IF num&& MOD 2 = 0 THEN RETURN $$FALSE
i&& = 3
DO WHILE i&& * i&& <= num&&
IF num&& MOD i&& = 0 THEN RETURN $$FALSE
i&& = i&& + 2
LOOP
RETURN $$TRUE
END FUNCTION
END PROGRAM
- Output:
16 17 25 28 34 37 47 52 64
Yabasic
// 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
C#
// Sum of square and cube digits of an integer are primes
using System;
public class SumOfEtc
{
static bool IsPrime(int num)
{
if (num < 2)
return false;
if (num == 2)
return true;
if (num % 2 == 0)
return false;
for (int i = 3; i * i <= num; i += 2)
if (num % i == 0)
return false;
return true;
}
static int SumDigits(int num)
{
int sum = 0;
while (num != 0)
{
sum += num % 10;
num /= 10;
}
return sum;
}
public static void Main(string[] args)
{
for (int n = 0; n <= 99; n++)
if (IsPrime(SumDigits(n * n)) && IsPrime(SumDigits(n * n * n)))
Console.Write(n + " ");
Console.WriteLine();
}
}
- Output:
16 17 25 28 34 37 47 52 64
C++
#include <cstdint>
#include <iostream>
bool is_prime(const int32_t& number) {
if ( number < 2 || ( number & 1 ) == 0 ) {
return number == 2;
}
for ( int32_t i = 3; i * i <= number; i += 2 ) {
if ( number % i == 0 ) {
return false;
}
}
return true;
}
int32_t digit_sum(int32_t number) {
int32_t sum = 0;
while ( number > 0 ) {
sum += number % 10;
number /= 10;
}
return sum;
}
int main() {
for ( uint32_t n = 1; n < 100; ++n ) {
if ( is_prime(digit_sum(n * n)) && is_prime(digit_sum(n * n * n)) ) {
std::cout << n << " ";
}
}
std::cout << std::endl;
}
- 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
Cowgol
include "cowgol.coh";
sub prime(n: uint32): (p: uint8) is
if n < 2 then
p := 0;
return;
end if;
p := 1;
var d: uint32 := 2;
while d*d <= n loop
if n%d == 0 then
p := 0;
return;
end if;
d := d + 1;
end loop;
end sub;
sub digit_sum(n: uint32): (ds: uint32) is
ds := 0;
while n > 0 loop
ds := ds + n % 10;
n := n / 10;
end loop;
end sub;
var n: uint32 := 1;
while n < 100 loop
if prime(digit_sum(n*n)) != 0 and prime(digit_sum(n*n*n)) != 0 then
print_i32(n);
print_nl();
end if;
n := n + 1;
end loop;- Output:
16 17 25 28 34 37 47 52 64
Delphi
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;
Memo.Lines.Add(S);
end;
- Output:
16 17 25 28 34 37 47 52 64 Elapsed Time: 1.809 ms.
EasyLang
fastfunc digsum h .
while h > 0
sum += h mod 10
h = h div 10
.
return sum
.
fastfunc isprim num .
if num < 2
return 0
.
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
for i = 1 to 99
if isprim digsum (i * i) = 1 and isprim digsum (i * i * i) = 1
write i & " "
.
.
- Output:
16 17 25 28 34 37 47 52 64
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
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
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
Haskell
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
Java
import java.util.function.Function;
import java.util.function.Predicate;
import java.util.stream.IntStream;
public final class SumOfSquareAndCubeDigitsOfAnIntegerArePrimes {
public static void main(String[] args) {
Predicate<Integer> isPrime = n ->
n > 1 && IntStream.rangeClosed(2, (int) Math.sqrt(n)).allMatch( i -> n % i != 0 );
Function<Integer, Integer> digitSum = number -> {
int sum = 0;
while ( number > 0 ) {
sum += number % 10;
number /= 10;
}
return sum;
};
System.out.println(IntStream.range(1, 100)
.filter( n -> isPrime.test(digitSum.apply(n * n)) && isPrime.test(digitSum.apply(n * n * n)) )
.boxed().toList());
}
}
- Output:
[16, 17, 25, 28, 34, 37, 47, 52, 64]
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 $_ (0; .+$_);
add(digits);The Task
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]
MAD
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
Mathematica |Wolfram Language
isSqCubSumPrime[n_Integer] := Module[{sq = n^2, cub = n^3},
PrimeQ[Total[IntegerDigits[sq]]] && PrimeQ[Total[IntegerDigits[cub]]]
];
Select[Range[100], isSqCubSumPrime] // Print
- Output:
{16, 17, 25, 28, 34, 37, 47, 52, 64}
Miranda
main :: [sys_message]
main = [Stdout (show [n | n<-[1..99]; and (map (prime.digitsum.(n^)) [2,3])])]
prime :: num->bool
prime n = n>=2 & and [n mod d ~= 0 | d <- [2..entier (sqrt n)]]
digitsum :: num->num
digitsum = sum . map (mod 10) . takewhile (> 0) . iterate (div 10)- Output:
[16,17,25,28,34,37,47,52,64]
Modula-2
MODULE SumOfEtc;
(* Sum of square and cube digits of an integer are primes *)
FROM STextIO IMPORT
WriteLn, WriteString;
FROM SWholeIO IMPORT
WriteInt;
VAR
N: CARDINAL;
PROCEDURE IsPrime(Num: CARDINAL): BOOLEAN;
VAR
I: CARDINAL;
BEGIN
IF Num < 2 THEN
RETURN FALSE
END;
IF Num = 2 THEN
RETURN TRUE
END;
IF Num MOD 2 = 0 THEN
RETURN FALSE
END;
I := 3;
WHILE (I * I <= Num) DO
IF Num MOD I = 0 THEN
RETURN FALSE
END;
I := I + 2;
END;
RETURN TRUE;
END IsPrime;
PROCEDURE SumDigits(Num: CARDINAL): CARDINAL;
VAR
Sum: CARDINAL;
BEGIN
Sum := 0;
WHILE Num <> 0 DO
Sum := Sum + Num MOD 10;
Num := Num DIV 10;
END;
RETURN Sum
END SumDigits;
BEGIN
FOR N := 0 TO 99 DO
IF IsPrime(SumDigits(N * N)) AND IsPrime(SumDigits(N * N * N)) THEN
WriteInt(N, 1);
WriteString(' ')
END;
END;
WriteLn;
END SumOfEtc.
- 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
Pascal
Free Pascal
program SumOfEtc;
{ Sum of square and cube digits of an integer are primes }
var
N: integer;
function IsPrime(Num: integer): boolean;
var
I: integer;
FoundFac: boolean;
begin
if Num < 2 then
Result := False
else if Num = 2 then
Result := True
else if Num mod 2 = 0 then
Result := False
else
begin
I := 3;
FoundFac := False;
while (I * I <= Num) and not FoundFac do
begin
if Num mod I = 0 then
FoundFac := True;
I := I + 2;
end;
Result := not FoundFac;
end;
end;
function SumDigits(Num: longint): integer;
var
Sum: integer;
begin
Sum := 0;
while Num <> 0 do
begin
Sum := Sum + Num mod 10;
Num := Num div 10;
end;
Result := Sum;
end;
begin
for N := 0 to 99 do
if IsPrime(SumDigits(N * N)) and IsPrime(SumDigits(N * N * N)) then
Write(N, ' ');
WriteLn;
end.
- Output:
16 17 25 28 34 37 47 52 64
Perl
#!/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}
PHP
<?php
// Editing Sum of square and cube digits of an integer are primes
function is_prime(int $num): bool {
if ($num < 2) {
return false;
}
if ($num == 2) {
return true;
}
if ($num % 2 == 0) {
return false;
}
for ($i = 3; $i * $i <= $num; $i += 2) {
if ($num % $i == 0) {
return false;
}
}
return true;
}
function sum_digits(int $num): int {
$sum = 0;
while ($num != 0) {
$sum += $num % 10;
$num = intdiv($num, 10);
}
return $sum;
}
for ($n = 0; $n <= 99; $n++) {
if (is_prime(sum_digits($n * $n)) && is_prime(sum_digits($n * $n * $n))) {
echo $n . ' ';
}
}
echo PHP_EOL;
?>
- 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)
Refal
$ENTRY Go {
= <Prout <Filter SumOfSquareAndCubeDigitsPrime <Iota 1 99>>>;
}
Iota {
s.End s.End = s.End;
s.Start s.End = s.Start <Iota <Add 1 s.Start> s.End>;
};
Filter {
s.F = ;
s.F t.X e.Y, <Mu s.F t.X>: {
True = t.X <Filter s.F e.Y>;
False = <Filter s.F e.Y>;
};
};
Prime {
0 = False;
1 = False;
s.N = <Prime s.N 2>;
s.N s.D, <Compare s.N <Mul s.D s.D>>: '-' = True;
s.N s.D, <Mod s.N s.D>: 0 = False;
s.N s.D = <Prime s.N <Add 1 s.D>>;
};
DigitSum {
0 = 0;
s.N, <Divmod s.N 10>: (s.R) s.D = <Add s.D <DigitSum s.R>>;
};
SumOfSquareAndCubeDigitsPrime {
s.N, <Mul s.N s.N>: s.Sq,
<Mul s.Sq s.N>: s.Cb,
<Prime <DigitSum s.Sq>>: True,
<Prime <DigitSum s.Cb>>: True = True;
s.N = False;
};- 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...
RPL
« 0
WHILE OVER REPEAT
SWAP 10 IDIV2 ROT +
END NIP
» '∑DIG' STO
« { }
2 100 FOR j
IF j SQ ∑DIG ISPRIME? THEN
IF j 3 ^ ∑DIG ISPRIME? THEN
j +
END END
NEXT
» 'TASK' STO
- Output:
1: { 16 17 25 28 34 37 47 52 64 }
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]
SETL
program sum_of_digits_of_square_and_cube_are_prime;
print({n in {1..99} | prime(digitsum(n**2)) and prime(digitsum(n**3))});
op prime(n);
return n>=2 and not exists d in {2..floor sqrt n} | n mod d=0;
end op;
op digitsum(n);
return +/[[n mod 10, n div:= 10](1) : until n=0];
end op;
end program;- 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
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
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