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Numbers which binary and ternary digit sum are prime

From Rosetta Code
Numbers which binary and ternary digit sum are prime 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
Show numbers which binary and ternary digit sum are prime, where n < 200




ALGOL 68[edit]

BEGIN # find numbers whose digit sums in binary and ternary are prime #
# reurns a sieve of primes up to n #
PROC sieve = ( INT n )[]BOOL:
BEGIN
[ 1 : n ]BOOL p;
p[ 1 ] := FALSE; p[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO n DO p[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO n DO p[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( n ) DO
IF p[ i ] THEN FOR s FROM i * i BY i + i TO n DO p[ s ] := FALSE OD FI
OD;
p
END # prime list # ;
# returns the digit sum of n in base b #
PRIO DIGITSUM = 9;
OP DIGITSUM = ( INT n, b )INT:
BEGIN
INT d sum := 0;
INT v := ABS n;
WHILE v > 0 DO
d sum +:= v MOD b;
v OVERAB b
OD;
d sum
END # DIGITSUM # ;
INT max number = 200;
[]BOOL prime = sieve( max number );
INT n count := 0;
FOR n TO max number DO
INT d sum 2 = n DIGITSUM 2;
IF prime[ d sum 2 ] THEN
INT d sum 3 = n DIGITSUM 3;
IF prime[ d sum 3 ] THEN
# the base 2 and base 3 digit sums of n are both prime #
print( ( " ", whole( n, -3 ), IF prime[ n ] THEN "*" ELSE " " FI ) );
n count +:= 1;
IF n count MOD 14 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline ) );
print( ( "Found ", whole( n count, 0 ), " numbers whose binary and ternary digit sums are prime", newline ) );
print( ( " those that are themselves prime are suffixed with a ""*""", newline ) )
END
Output:
   5*   6    7*  10   11*  12   13*  17*  18   19*  21   25   28   31*
  33   35   36   37*  41*  47*  49   55   59*  61*  65   67*  69   73*
  79*  82   84   87   91   93   97* 103* 107* 109* 115  117  121  127*
 129  131* 133  137* 143  145  151* 155  157* 162  167* 171  173* 179*
 181* 185  191* 193* 199*
Found 61 numbers whose binary and ternary digit sums are prime
    those that are themselves prime are suffixed with a "*"

ALGOL-M[edit]

begin
integer function mod(a,b);
integer a,b;
mod := a-(a/b)*b;
 
integer function digitsum(n,base);
integer n,base;
digitsum := if n=0 then 0 else mod(n,base)+digitsum(n/base,base);
 
integer function isprime(n);
integer n;
begin
integer i;
isprime := 0;
if n < 2 then go to stop;
for i := 2 step 1 until n-1 do
begin
if mod(n,i) = 0 then go to stop;
end;
isprime := 1;
stop:
i := i;
end;
 
integer i,d2,d3,n;
n := 0;
for i := 0 step 1 until 199 do
begin
d2 := digitsum(i,2);
d3 := digitsum(i,3);
if isprime(d2) <> 0 and isprime(d3) <> 0 then
begin
if n/10 <> (n-1)/10 then write(i) else writeon(i);
n := n + 1;
end;
end;
end
Output:
     5     6     7    10    11    12    13    17    18    19
    21    25    28    31    33    35    36    37    41    47
    49    55    59    61    65    67    69    73    79    82
    84    87    91    93    97   103   107   109   115   117
   121   127   129   131   133   137   143   145   151   155
   157   162   167   171   173   179   181   185   191   193
   199

ALGOL W[edit]

begin % find numbers whose binary and ternary digit sums are prime %
 % returns the digit sum of n in base b %
integer procedure digitSum( integer value n, base ) ;
begin
integer v, dSum;
v  := abs n;
dSum := 0;
while v > 0 do begin
dSum := dSum + v rem base;
v  := v div base
end while_v_gt_0 ;
dSum
end digitSum ;
integer MAX_PRIME, MAX_NUMBER;
MAX_PRIME := 199;
begin
logical array prime( 1 :: MAX_PRIME );
integer nCount;
 % sieve the primes to MAX_PRIME %
prime( 1 ) := false; prime( 2 ) := true;
for i := 3 step 2 until MAX_PRIME do prime( i ) := true;
for i := 4 step 2 until MAX_PRIME do prime( i ) := false;
for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin
integer ii; ii := i + i;
if prime( i ) then for np := i * i step ii until MAX_PRIME do prime( np ) := false
end for_i ;
 % find the numbers %
nCount := 0;
for i := 1 until MAX_PRIME do begin
if prime( digitSum( i, 2 ) ) and prime( digitSum( i, 3 ) ) then begin
 % have another matching number %
writeon( i_w := 3, s_w := 0, " ", i );
nCount := nCount + 1;
if nCount rem 14 = 0 then write()
end if_have_a_suitable_number
end for_i ;
write( i_w := 1, s_w := 0, "Found ", nCount, " numbers with prime binary and ternary digit sums up to ", MAX_PRIME )
end
end.
Output:
   5   6   7  10  11  12  13  17  18  19  21  25  28  31
  33  35  36  37  41  47  49  55  59  61  65  67  69  73
  79  82  84  87  91  93  97 103 107 109 115 117 121 127
 129 131 133 137 143 145 151 155 157 162 167 171 173 179
 181 185 191 193 199
Found 61 numbers with prime binary and ternary digit sums up to 199

APL[edit]

Works with: Dyalog APL
(⊢(/⍨)(∧/((2=0+.=⍳|⊢)¨2 3(+/⊥⍣¯1)¨⊢))¨) ⍳200
Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117
      121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199

BASIC[edit]

None of the digit sums are higher than 9, so the easiest thing to do is to hardcode which ones are prime.

10 DEFINT I,J,K,P
20 DIM P(9): DATA 0,1,1,0,1,0,1,0,0
30 FOR I=1 TO 9: READ P(I): NEXT
40 FOR I=0 TO 199
50 J=0: K=I
60 IF K>0 THEN J=J+K MOD 2: K=K\2: GOTO 60 ELSE IF P(J)=0 THEN 90
70 J=0: K=I
80 IF K>0 THEN J=J+K MOD 3: K=K\3: GOTO 80 ELSE IF P(J) THEN PRINT I,
90 NEXT I
Output:
 5             6             7             10            11
 12            13            17            18            19
 21            25            28            31            33
 35            36            37            41            47
 49            55            59            61            65
 67            69            73            79            82
 84            87            91            93            97
 103           107           109           115           117
 121           127           129           131           133
 137           143           145           151           155
 157           162           167           171           173
 179           181           185           191           193
 199

BCPL[edit]

get "libhdr"
 
let digitsum(n, base) =
n=0 -> 0, n rem base + digitsum(n/base, base)
 
let isprime(n) = valof
$( if n<2 then resultis false
for i=2 to n-1 do
if n rem i = 0 then resultis false
resultis true
$)
 
let accept(n) =
isprime(digitsum(n,2)) & isprime(digitsum(n,3))
 
let start() be
$( let c = 0
for i=0 to 199 do
if accept(i) do
$( writef("%I4",i)
c := c + 1
if c rem 10 = 0 then wrch('*N')
$)
wrch('*N')
$)
Output:
   5   6   7  10  11  12  13  17  18  19
  21  25  28  31  33  35  36  37  41  47
  49  55  59  61  65  67  69  73  79  82
  84  87  91  93  97 103 107 109 115 117
 121 127 129 131 133 137 143 145 151 155
 157 162 167 171 173 179 181 185 191 193
 199

C[edit]

#include <stdio.h>
#include <stdint.h>
 
/* good enough for small numbers */
uint8_t prime(uint8_t n) {
uint8_t f;
if (n < 2) return 0;
for (f = 2; f < n; f++) {
if (n % f == 0) return 0;
}
return 1;
}
 
/* digit sum in given base */
uint8_t digit_sum(uint8_t n, uint8_t base) {
uint8_t s = 0;
do {s += n % base;} while (n /= base);
return s;
}
 
int main() {
uint8_t n, s = 0;
for (n = 0; n < 200; n++) {
if (prime(digit_sum(n,2)) && prime(digit_sum(n,3))) {
printf("%4d",n);
if (++s>=10) {
printf("\n");
s=0;
}
}
}
printf("\n");
return 0;
}
Output:
   5   6   7  10  11  12  13  17  18  19
  21  25  28  31  33  35  36  37  41  47
  49  55  59  61  65  67  69  73  79  82
  84  87  91  93  97 103 107 109 115 117
 121 127 129 131 133 137 143 145 151 155
 157 162 167 171 173 179 181 185 191 193
 199

Cowgol[edit]

include "cowgol.coh";
 
sub prime(n: uint8): (p: uint8) is
p := 0;
if n >= 2 then
var f: uint8 := 2;
while f < n loop
if n % f == 0 then
return;
end if;
f := f + 1;
end loop;
p := 1;
end if;
end sub;
 
sub digit_sum(n: uint8, base: uint8): (sum: uint8) is
sum := 0;
while n > 0 loop
sum := sum + n % base;
n := n / base;
end loop;
end sub;
 
var n: uint8 := 0;
while n < 200 loop;
if prime(digit_sum(n,2)) != 0 and prime(digit_sum(n,3)) != 0 then
print_i8(n);
print_nl();
end if;
n := n + 1;
end loop;
Output:
5
6
7
10
11
12
13
17
18
19
21
25
28
31
33
35
36
37
41
47
49
55
59
61
65
67
69
73
79
82
84
87
91
93
97
103
107
109
115
117
121
127
129
131
133
137
143
145
151
155
157
162
167
171
173
179
181
185
191
193
199

F#[edit]

This task uses Extensible Prime Generator (F#)

 
// binary and ternary digit sums are prime: Nigel Galloway. April 16th., 2021
let fN2,fN3=let rec fG n g=function l when l<n->l+g |l->fG n (g+l%n)(l/n) in (fG 2 0, fG 3 0)
{0..200}|>Seq.filter(fun n->isPrime(fN2 n) && isPrime(fN3 n))|>Seq.iter(printf "%d "); printfn ""
 
Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Real: 00:00:00.005

Factor[edit]

Works with: Factor version 0.99 2021-02-05
USING: combinators combinators.short-circuit formatting io lists
lists.lazy math math.parser math.primes sequences ;
 
: dsum ( n base -- sum ) >base [ digit> ] map-sum ;
: dprime? ( n base -- ? ) dsum prime? ;
: 23prime? ( n -- ? ) { [ 2 dprime? ] [ 3 dprime? ] } 1&& ;
: l23primes ( -- list ) 1 lfrom [ 23prime? ] lfilter ;
 
: 23prime. ( n -- )
{
[ ]
[ >bin ]
[ 2 dsum ]
[ 3 >base ]
[ 3 dsum ]
} cleave
"%-8d %-9s %-6d %-7s %d\n" printf ;
 
"Base 10 Base 2 (sum) Base 3 (sum)" print
l23primes [ 200 < ] lwhile [ 23prime. ] leach
Output:
Base 10  Base 2    (sum)  Base 3  (sum)
5        101       2      12      3
6        110       2      20      2
7        111       3      21      3
10       1010      2      101     2
11       1011      3      102     3
12       1100      2      110     2
13       1101      3      111     3
17       10001     2      122     5
18       10010     2      200     2
19       10011     3      201     3
21       10101     3      210     3
25       11001     3      221     5
28       11100     3      1001    2
31       11111     5      1011    3
33       100001    2      1020    3
35       100011    3      1022    5
36       100100    2      1100    2
37       100101    3      1101    3
41       101001    3      1112    5
47       101111    5      1202    5
49       110001    3      1211    5
55       110111    5      2001    3
59       111011    5      2012    5
61       111101    5      2021    5
65       1000001   2      2102    5
67       1000011   3      2111    5
69       1000101   3      2120    5
73       1001001   3      2201    5
79       1001111   5      2221    7
82       1010010   3      10001   2
84       1010100   3      10010   2
87       1010111   5      10020   3
91       1011011   5      10101   3
93       1011101   5      10110   3
97       1100001   3      10121   5
103      1100111   5      10211   5
107      1101011   5      10222   7
109      1101101   5      11001   3
115      1110011   5      11021   5
117      1110101   5      11100   3
121      1111001   5      11111   5
127      1111111   7      11201   5
129      10000001  2      11210   5
131      10000011  3      11212   7
133      10000101  3      11221   7
137      10001001  3      12002   5
143      10001111  5      12022   7
145      10010001  3      12101   5
151      10010111  5      12121   7
155      10011011  5      12202   7
157      10011101  5      12211   7
162      10100010  3      20000   2
167      10100111  5      20012   5
171      10101011  5      20100   3
173      10101101  5      20102   5
179      10110011  5      20122   7
181      10110101  5      20201   5
185      10111001  5      20212   7
191      10111111  7      21002   5
193      11000001  3      21011   5
199      11000111  5      21101   5

FOCAL[edit]

01.10 S P(2)=1;S P(3)=1;S P(5)=1;S P(7)=1
01.20 S V=10
01.30 F N=0,199;D 3
01.40 T !
01.50 Q
 
02.10 S A=0
02.20 S M=N
02.30 S T=FITR(M/B)
02.40 S A=A+M-T*B
02.50 S M=T
02.60 I (-M)2.3
 
03.10 S B=2;D 2;S X=A
03.20 S B=3;D 2;S Y=A
03.30 I (-P(X)*P(Y))3.4;R
03.40 T %4,N
03.50 S V=V-1
03.60 I (-V)3.7;T !;S V=10
03.70 R
Output:
=    5=    6=    7=   10=   11=   12=   13=   17=   18=   19
=   21=   25=   28=   31=   33=   35=   36=   37=   41=   47
=   49=   55=   59=   61=   65=   67=   69=   73=   79=   82
=   84=   87=   91=   93=   97=  103=  107=  109=  115=  117
=  121=  127=  129=  131=  133=  137=  143=  145=  151=  155
=  157=  162=  167=  171=  173=  179=  181=  185=  191=  193
=  199

Haskell[edit]

import Data.Bifunctor (first)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (isPrime)
 
--------- BINARY AND TERNARY DIGIT SUMS BOTH PRIME -------
 
digitSumsPrime :: Int -> [Int] -> Bool
digitSumsPrime n = all (isPrime . digitSum n)
 
digitSum :: Int -> Int -> Int
digitSum n base = go n
where
go 0 = 0
go n = uncurry (+) (first go $ quotRem n base)
 
--------------------------- TEST -------------------------
main :: IO ()
main =
putStrLn $
show (length xs)
<> " matches in [1..199]\n\n"
<> table xs
where
xs =
[1 .. 199]
>>= \x -> [show x | digitSumsPrime x [2, 3]]
 
------------------------- DISPLAY -----------------------
 
table :: [String] -> String
table xs =
let w = length (last xs)
in unlines $
unwords
<$> chunksOf
10
(justifyRight w ' ' <$> xs)
 
justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)
61 matches in [1..199]

  5   6   7  10  11  12  13  17  18  19
 21  25  28  31  33  35  36  37  41  47
 49  55  59  61  65  67  69  73  79  82
 84  87  91  93  97 103 107 109 115 117
121 127 129 131 133 137 143 145 151 155
157 162 167 171 173 179 181 185 191 193
199

J[edit]

((1*./@p:2 3+/@(#.^:_1)"0])"0#]) i.200
Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199

Julia[edit]

using Primes
 
btsumsareprime(n) = isprime(sum(digits(n, base=2))) && isprime(sum(digits(n, base=3)))
 
foreach(p -> print(rpad(p[2], 4), p[1] % 20 == 0 ? "\n" : ""), enumerate(filter(btsumsareprime, 1:199)))
 
Output:
5   6   7   10  11  12  13  17  18  19  21  25  28  31  33  35  36  37  41  47  
49  55  59  61  65  67  69  73  79  82  84  87  91  93  97  103 107 109 115 117
121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193
199

MAD[edit]

            NORMAL MODE IS INTEGER
 
INTERNAL FUNCTION(P)
ENTRY TO PRIME.
WHENEVER P.L.2, FUNCTION RETURN 0B
THROUGH TEST, FOR DV=2, 1, DV.G.SQRT.(P)
TEST WHENEVER P-P/DV*DV.E.0, FUNCTION RETURN 0B
FUNCTION RETURN 1B
END OF FUNCTION
 
INTERNAL FUNCTION(N,BASE)
ENTRY TO DGTSUM.
SUM = 0
DN = N
DIGIT NX = DN/BASE
SUM = SUM + DN-NX*BASE
DN = NX
WHENEVER DN.G.0, TRANSFER TO DIGIT
FUNCTION RETURN SUM
END OF FUNCTION
 
THROUGH NBR, FOR I=0, 1, I.GE.200
WHENEVER PRIME.(DGTSUM.(I,2)) .AND. PRIME.(DGTSUM.(I,3))
PRINT FORMAT FMT, I
END OF CONDITIONAL
NBR CONTINUE
 
VECTOR VALUES FMT = $I3*$
END OF PROGRAM
Output:
  5
  6
  7
 10
 11
 12
 13
 17
 18
 19
 21
 25
 28
 31
 33
 35
 36
 37
 41
 47
 49
 55
 59
 61
 65
 67
 69
 73
 79
 82
 84
 87
 91
 93
 97
103
107
109
115
117
121
127
129
131
133
137
143
145
151
155
157
162
167
171
173
179
181
185
191
193
199

Perl[edit]

Library: ntheory
use strict;
use warnings;
use feature 'say';
use List::Util 'sum';
use ntheory <is_prime todigitstring>;
 
sub test_digits { 0 != is_prime sum split '', todigitstring(shift, shift) }
 
my @p;
test_digits($_,2) and test_digits($_,3) and push @p, $_ for 1..199;
say my $result = @p . " matching numbers:\n" . (sprintf "@{['%4d' x @p]}", @p) =~ s/(.{40})/$1\n/gr;
Output:
61 matching numbers:
   5   6   7  10  11  12  13  17  18  19
  21  25  28  31  33  35  36  37  41  47
  49  55  59  61  65  67  69  73  79  82
  84  87  91  93  97 103 107 109 115 117
 121 127 129 131 133 137 143 145 151 155
 157 162 167 171 173 179 181 185 191 193
 199

PL/M[edit]

100H:
/* CP/M CALLS */
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;
 
/* PRINT NUMBER */
PRINT$NUMBER: PROCEDURE (N);
DECLARE S (8) BYTE INITIAL ('.....',13,10,'$');
DECLARE (N, P) ADDRESS, C BASED P BYTE;
P = .S(5);
DIGIT:
P = P - 1;
C = N MOD 10 + '0';
N = N / 10;
IF N > 0 THEN GO TO DIGIT;
CALL PRINT(P);
END PRINT$NUMBER;
 
/* SIMPLE PRIMALITY TEST */
PRIME: PROCEDURE (N) BYTE;
DECLARE (N, I) BYTE;
IF N < 2 THEN RETURN 0;
DO I=2 TO N-1;
IF N MOD I = 0 THEN RETURN 0;
END;
RETURN 1;
END PRIME;
 
/* SUM OF DIGITS */
DIGIT$SUM: PROCEDURE (N, BASE) BYTE;
DECLARE (N, BASE, SUM) BYTE;
SUM = 0;
DO WHILE N > 0;
SUM = SUM + N MOD BASE;
N = N / BASE;
END;
RETURN SUM;
END DIGIT$SUM;
 
/* TEST NUMBERS 0 .. 199 */
DECLARE I BYTE;
DO I=0 TO 199;
IF PRIME(DIGIT$SUM(I,2)) AND PRIME(DIGIT$SUM(I,3)) THEN
CALL PRINT$NUMBER(I);
END;
 
CALL EXIT;
EOF
Output:
5
6
7
10
11
12
13
17
18
19
21
25
28
31
33
35
36
37
41
47
49
55
59
61
65
67
69
73
79
82
84
87
91
93
97
103
107
109
115
117
121
127
129
131
133
137
143
145
151
155
157
162
167
171
173
179
181
185
191
193
199

Phix[edit]

function to_base(atom n, integer base)
    string result = ""
    while true do
        result &= remainder(n,base)
        n = floor(n/base)
        if n=0 then exit end if
    end while
    return result
end function

function prime23(integer n)
    return is_prime(sum(to_base(n,2)))
       and is_prime(sum(to_base(n,3)))
end function

sequence res = filter(tagset(199),prime23)
printf(1,"%d numbers found: %V\n",{length(res),shorten(res,"",5)})
Output:
61 numbers found: {5,6,7,10,11,"...",181,185,191,193,199}

Python[edit]

'''Binary and Ternary digit sums both prime'''
 
 
# digitSumsPrime :: Int -> [Int] -> Bool
def digitSumsPrime(n):
'''True if the digits of n in each
given base have prime sums.
'''

def go(bases):
return all(
isPrime(digitSum(b)(n))
for b in bases
)
return go
 
 
# digitSum :: Int -> 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
 
 
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Matching integers in the range [1..199]'''
xs = [
str(n) for n in range(1, 200)
if digitSumsPrime(n)([2, 3])
]
print(f'{len(xs)} matches in [1..199]\n')
print(table(10)(xs))
 
 
# ----------------------- GENERIC ------------------------
 
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divible, the final list will be shorter than n.
'''

def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
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 p(x):
return 0 == n % x or 0 == n % (2 + x)
 
return not any(map(p, range(5, 1 + int(n ** 0.5), 6)))
 
 
# table :: Int -> [String] -> String
def table(n):
'''A list of strings formatted as
rows of n (right justified) columns.
'''

def go(xs):
w = len(xs[-1])
return '\n'.join(
' '.join(row) for row in chunksOf(n)([
s.rjust(w, ' ') for s in xs
])
)
return go
 
 
# MAIN ---
if __name__ == '__main__':
main()
 
61 matches in [1..199]

  5   6   7  10  11  12  13  17  18  19
 21  25  28  31  33  35  36  37  41  47
 49  55  59  61  65  67  69  73  79  82
 84  87  91  93  97 103 107 109 115 117
121 127 129 131 133 137 143 145 151 155
157 162 167 171 173 179 181 185 191 193
199

Raku[edit]

say (^200).grep(-> $n {all (2,3).map({$n.base($_).comb.sum.is-prime}) }).batch(10)».fmt('%3d').join: "\n";
Output:
  5   6   7  10  11  12  13  17  18  19
 21  25  28  31  33  35  36  37  41  47
 49  55  59  61  65  67  69  73  79  82
 84  87  91  93  97 103 107 109 115 117
121 127 129 131 133 137 143 145 151 155
157 162 167 171 173 179 181 185 191 193
199

REXX[edit]

/*REXX program finds and displays integers whose base 2 and base 3 digit sums are prime.*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 200 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
@b2b3= ' numbers < ' commas(hi) " whose binary and ternary digit sums are prime"
if cols>0 then say ' index │'center(@b2b3, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
finds= 0; idx= 1 /*initialize # of finds and the index. */
$= /*a list of numbers found (so far). */
do j=1 to hi-1 /*find #s whose B2 & B3 sums are prime.*/
b2= sumDig( tBase(j, 2) ); if \!.b2 then iterate /*convert to base2, sum digits*/
b3= sumDig( tBase(j, 3) ); if \!.b3 then iterate /* " " base3 " " */
finds= finds + 1 /*bump the number of found integers. */
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(j) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add an integer ──► $ list, allow big#*/
if finds//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
 
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
say
say 'Found ' commas(finds) @b2b3
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 ?
sumDig: procedure; parse arg x 1 s 2;do j=2 for length(x)-1;s=s+substr(x,j,1);end;return s
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP:  !.=0; @= '2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97'
#= words(@); do p=1 for #; _= word(@, p);  !._= 1; end; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
tBase: procedure; parse arg x,toBase; y=; $= 0123456789
do while x>=toBase; y= substr($, x//toBase+1, 1)y; x= x%toBase
end /*while*/
return substr($, x+1, 1)y
output   when using the default inputs:
 index │                         numbers  <  200  whose binary and ternary digit sums are prime
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          5          6          7         10         11         12         13         17         18         19
  11   │         21         25         28         31         33         35         36         37         41         47
  21   │         49         55         59         61         65         67         69         73         79         82
  31   │         84         87         91         93         97        103        107        109        115        117
  41   │        121        127        129        131        133        137        143        145        151        155
  51   │        157        162        167        171        173        179        181        185        191        193
  61   │        199

Found  61  numbers  <  200  whose binary and ternary digit sums are prime

Ring[edit]

 
load "stdlib.ring"
 
see "working..." + nl
see "Numbers < 200 whose binary and ternary digit sums are prime:" + nl
 
decList = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
baseList = ["0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"]
 
num = 0
limit = 200
 
for n = 1 to limit
strBin = decimaltobase(n,2)
strTer = decimaltobase(n,3)
sumBin = 0
for m = 1 to len(strBin)
sumBin = sumBin + number(strBin[m])
next
sumTer = 0
for m = 1 to len(strTer)
sumTer = sumTer + number(strTer[m])
next
if isprime(sumBin) and isprime(sumTer)
num = num + 1
see "" + num + ". {" + n + "," + strBin + ":" + sumBin + "," + strTer + ":" + sumTer + "}" + nl
ok
next
 
see "Found " + num + " such numbers" + nl
see "done..." + nl
 
func decimaltobase(nr,base)
binList = []
binary = 0
remainder = 1
while(nr != 0)
remainder = nr % base
ind = find(decList,remainder)
rem = baseList[ind]
add(binList,rem)
nr = floor(nr/base)
end
binlist = reverse(binList)
binList = list2str(binList)
binList = substr(binList,nl,"")
return binList
 
Output:
working...
Numbers < 200 whose binary and ternary digit sums are prime:
1. {5,101:2,12:3}
2. {6,110:2,20:2}
3. {7,111:3,21:3}
4. {10,1010:2,101:2}
5. {11,1011:3,102:3}
6. {12,1100:2,110:2}
7. {13,1101:3,111:3}
8. {17,10001:2,122:5}
9. {18,10010:2,200:2}
10. {19,10011:3,201:3}
11. {21,10101:3,210:3}
12. {25,11001:3,221:5}
13. {28,11100:3,1001:2}
14. {31,11111:5,1011:3}
15. {33,100001:2,1020:3}
16. {35,100011:3,1022:5}
17. {36,100100:2,1100:2}
18. {37,100101:3,1101:3}
19. {41,101001:3,1112:5}
20. {47,101111:5,1202:5}
21. {49,110001:3,1211:5}
22. {55,110111:5,2001:3}
23. {59,111011:5,2012:5}
24. {61,111101:5,2021:5}
25. {65,1000001:2,2102:5}
26. {67,1000011:3,2111:5}
27. {69,1000101:3,2120:5}
28. {73,1001001:3,2201:5}
29. {79,1001111:5,2221:7}
30. {82,1010010:3,10001:2}
31. {84,1010100:3,10010:2}
32. {87,1010111:5,10020:3}
33. {91,1011011:5,10101:3}
34. {93,1011101:5,10110:3}
35. {97,1100001:3,10121:5}
36. {103,1100111:5,10211:5}
37. {107,1101011:5,10222:7}
38. {109,1101101:5,11001:3}
39. {115,1110011:5,11021:5}
40. {117,1110101:5,11100:3}
41. {121,1111001:5,11111:5}
42. {127,1111111:7,11201:5}
43. {129,10000001:2,11210:5}
44. {131,10000011:3,11212:7}
45. {133,10000101:3,11221:7}
46. {137,10001001:3,12002:5}
47. {143,10001111:5,12022:7}
48. {145,10010001:3,12101:5}
49. {151,10010111:5,12121:7}
50. {155,10011011:5,12202:7}
51. {157,10011101:5,12211:7}
52. {162,10100010:3,20000:2}
53. {167,10100111:5,20012:5}
54. {171,10101011:5,20100:3}
55. {173,10101101:5,20102:5}
56. {179,10110011:5,20122:7}
57. {181,10110101:5,20201:5}
58. {185,10111001:5,20212:7}
59. {191,10111111:7,21002:5}
60. {193,11000001:3,21011:5}
61. {199,11000111:5,21101:5}
Found 61 such numbers
done...

Wren[edit]

Library: Wren-math
Library: Wren-fmt
Library: Wren-seq
import "/math" for Int
import "/fmt" for Fmt
import "/seq" for Lst
 
var numbers = []
for (i in 2..199) {
var bds = Int.digitSum(i, 2)
if (Int.isPrime(bds)) {
var tds = Int.digitSum(i, 3)
if (Int.isPrime(tds)) numbers.add(i)
}
}
System.print("Numbers < 200 whose binary and ternary digit sums are prime:")
for (chunk in Lst.chunks(numbers, 14)) Fmt.print("$4d", chunk)
System.print("\nFound %(numbers.count) such numbers.")
Output:
Numbers < 200 whose binary and ternary digit sums are prime:
   5    6    7   10   11   12   13   17   18   19   21   25   28   31
  33   35   36   37   41   47   49   55   59   61   65   67   69   73
  79   82   84   87   91   93   97  103  107  109  115  117  121  127
 129  131  133  137  143  145  151  155  157  162  167  171  173  179
 181  185  191  193  199

Found 61 such numbers.