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 positive integers   n   whose binary and ternary digits sum are prime,   where   n   <   200.

11l[edit]

Translation of: Nim
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, b)
   V result = 0
   L n != 0
      result += n % b
      n I/= b
   R result

V count = 0
L(n) 2..199
   I is_prime(digit_sum(n, 2)) &
     is_prime(digit_sum(n, 3))
      count++
      print(‘#3’.format(n), end' I count % 16 == 0 {"\n"} E ‘ ’)
print()
print(‘Found ’count‘ numbers.’)
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.

Action![edit]

INCLUDE "H6:SIEVE.ACT"

BYTE Func IsPrime(INT i BYTE base BYTE ARRAY primes)
  BYTE sum,d

  sum=0
  WHILE i#0
  DO
    d=i MOD base
    sum==+d
    i==/base
  OD
RETURN (primes(sum))

PROC Main()
  DEFINE MAX="199"
  BYTE ARRAY primes(MAX+1)
  INT i,count=[0]

  Put(125) PutE() ;clear the screen
  Sieve(primes,MAX+1)
  FOR i=1 TO MAX
  DO
    IF IsPrime(i,2,primes)=1 AND IsPrime(i,3,primes)=1 THEN
      PrintI(i) Put(32)
      count==+1
    FI
  OD
  PrintF("%E%EThere are %I numbers",count)
RETURN
Output:

Screenshot from Atari 8-bit computer

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 14 5 151 155 157 162 167 171 173 179 181 185 191 193 199

There are 61 numbers

ALGOL 68[edit]

BEGIN # find numbers whose digit sums in binary and ternary are prime #
    # 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;
    PR read "primes.incl.a68" PR
    []BOOL prime    = PRIMESIEVE 200;
    INT    n count := 0;
    FOR n TO UPB prime 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

Arturo[edit]

loop split.every: 10 
    select 1..199 'n [ and? prime? sum digits.base: 2 n
                            prime? sum digits.base: 3 n ] 'a -> 
        print map a => [pad to :string & 4]
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

AWK[edit]

# syntax: GAWK -f NUMBERS_WHICH_BINARY_AND_TERNARY_DIGIT_SUM_ARE_PRIME.AWK
# converted from C
BEGIN {
    start = 0
    stop = 199
    for (i=start; i<=stop; i++) {
      if (is_prime(sum_digits(i,2)) && is_prime(sum_digits(i,3))) {
        printf("%4d%1s",i,++count%10?"":"\n")
      }
    }
    printf("\nBinary and ternary digit sums are both prime %d-%d: %d\n",start,stop,count)
    exit(0)
}
function sum_digits(n,base,  sum) {
    do {
      sum += n % base
    } while (n = int(n/base))
    return(sum)
}
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)
}
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
Binary and ternary digit sums are both prime 0-199: 61

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

CLU[edit]

prime = proc (n: int) returns (bool)
    if n<2 then return(false) end
    for i: int in int$from_to(2, n-1) do
        if n//i=0 then return(false) end
    end
    return(true)
end prime

digit_sum = proc (n, base: int) returns (int)
    sum: int := 0
    while n>0 do
        sum := sum + n//base
        n := n/base
    end
    return(sum)
end digit_sum

start_up = proc ()
    po: stream := stream$primary_output()
    n: int := 0
    for i: int in int$from_to(2, 199) do
        s2: int := digit_sum(i,2)
        s3: int := digit_sum(i,3)
        if prime(s2) cand prime(s3) then
            stream$putright(po, int$unparse(i), 4)
            n := n + 1
            if n // 20 = 0 then stream$putl(po, "") end
        end
    end
end start_up
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

Fermat[edit]

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

for p=1 to 200 do
    if Isprime(Digsum(p,3)) and Isprime(Digsum(p,2)) then
       !(p,'  ');
       nadd := nadd+1;
    fi od;
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

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

Fōrmulæ[edit]

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In this page you can see the program(s) related to this task and their results.

FreeBASIC[edit]

#include"isprime.bas"

function digsum( byval n as uinteger, b as const uinteger ) as uinteger
    'finds the digit sum of n in base b
    dim as uinteger sum = 0
    while n
        sum+=n mod b
        n\=b
    wend
    return sum
end function

for n as uinteger = 1 to 200
    if isprime(digsum(n,2)) and isprime(digsum(n,3)) then print n;"  ";
next n : print
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

Go[edit]

Translation of: Wren
Library: Go-rcu
package main

import (
    "fmt"
    "rcu"
)

func main() {
    var numbers []int
    for i := 2; i < 200; i++ {
        bds := rcu.DigitSum(i, 2)
        if rcu.IsPrime(bds) {
            tds := rcu.DigitSum(i, 3)
            if rcu.IsPrime(tds) {
                numbers = append(numbers, i)
            }
        }
    }
    fmt.Println("Numbers < 200 whose binary and ternary digit sums are prime:")
    for i, n := range numbers {
        fmt.Printf("%4d", n)
        if (i+1)%14 == 0 {
            fmt.Println()
        }
    }
    fmt.Printf("\n\n%d such numbers found\n", len(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

61 such numbers found

GW-BASIC[edit]

10 FOR N = 2 TO 200
20 B = 2
30 GOSUB 220 : GOSUB 110
40 IF Q = 0 THEN GOTO 80
50 B = 3
60 GOSUB 220: GOSUB 110
70 IF Q = 1 THEN PRINT N;"  ";
80 NEXT N
90 PRINT
100 END
110 REM tests if a number is prime
120 Q=0
130 IF P=3 THEN Q=1:RETURN
140 IF P=1 THEN Q=0:RETURN
150 IF P=2 THEN Q=1:RETURN
160 I=1
170 I=I+1
180 IF INT(P/I)*I = P THEN RETURN
190 IF I*I<=P THEN GOTO 170
200 Q = 1
210 RETURN
220 REM finds the digit sum of N in base B, returns P
230 P = 0
240 XN = N
250 IF XN = 0 THEN RETURN
260 P = P + XN MOD B
270 XN = XN\B
280 GOTO 250
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

Mathematica / Wolfram Language[edit]

Partition[
  Select[
   Range@
    200, (PrimeQ[Total@IntegerDigits[#, 2]] && 
      PrimeQ[Total@IntegerDigits[#, 3]]) &], UpTo[8]] // TableForm
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

Nim[edit]

import strutils

func isPrime(n: Positive): bool =
  if n == 1: return false
  if n mod 2 == 0: return n == 2
  if n mod 3 == 0: return n == 3
  var d = 5
  while d * d <= n:
    if n mod d == 0: return false
    inc d, 2
    if n mod d == 0: return false
    inc d, 4
  return true

func digitSum(n, b: Natural): int =
  var n = n
  while n != 0:
    result += n mod b
    n = n div b

var count = 0
for n in 2..<200:
  if digitSum(n, 2).isPrime and digitSum(n, 3).isPrime:
    inc count
    stdout.write ($n).align(3), if count mod 16 == 0: '\n' else: ' '
echo()
echo "Found ", count, " numbers."
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.

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

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}

PL/I[edit]

See #Polyglot:PL/I and PL/M

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

See also #Polyglot:PL/I and PL/M

Plain English[edit]

To run:
Start up.
Loop.
If a counter is past 200, break.
If the counter has prime digit sums in binary and ternary, write the counter then " " on the console without advancing.
Repeat.
Wait for the escape key.
Shut down.

A sum is a number.

A base is a number.

To find a digit sum of a number given a base:
Privatize the number.
Loop.
Divide the number by the base giving a quotient and a remainder.
Add the remainder to the digit sum.
Put the quotient into the number.
If the number is 0, exit.
Repeat.

To decide if a number has prime digit sums in binary and ternary:
Find a digit sum of the number given 2.
If the digit sum is not prime, say no.
Find another digit sum of the number given 3.
If the other digit sum is not prime, say no.
Say yes.
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 

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

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

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

/* FIND NUMBERS WHOSE DIGIT SUM SQUARED AND CUBED IS PRIME */
prime_digit_sums_100H: procedure options                                        (main);

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

   /* TASK */

   DIGITSUM: PROCEDURE( N, BASE )RETURNS /* RETURNS THE DIGIT SUM OF N    */    (
                           FIXED BINARY          /* IN THE SPECIFIED BASE */    )
                           ;
      DECLARE ( N, BASE )  FIXED BINARY;
      DECLARE ( SUM, V )   FIXED BINARY;
      SUM = MODF( N, BASE );
      V   = N / BASE;
      DO WHILE( V > 0 );
         SUM = SUM + MODF( V, BASE );
         V   = V / BASE;
      END;
      RETURN( SUM );
   END DIGITSUM ;

   ISPRIME: PROCEDURE( N )RETURNS /* RETURNS TRUE  IF N IS PRIME, */            (
                          BIT             /* FALSE OTHERWISE      */            )
                          ;
      DECLARE N           FIXED BINARY;
      DECLARE I           FIXED BINARY;
      DECLARE RESULT      BIT;
      IF      N < 2            THEN RESULT = FALSE;
      ELSE IF N = 2            THEN RESULT = TRUE;
      ELSE IF MODF( N, 2 ) = 0 THEN RESULT = FALSE;
      ELSE DO;
         RESULT = TRUE;
         I      = 3;
         DO WHILE( RESULT &                                                     /*
                          AND /* */ ( I * I ) <= N );
            RESULT = MODF( N, I ) > 0;
            I      = I + 2;
         END;
      END;
      RETURN( RESULT );
   END ISPRIME ;

   DECLARE ( I, PCOUNT ) FIXED BINARY;

   PCOUNT = 0;
   DO I = 1 TO 199;
      IF ISPRIME( DIGITSUM( I, 2 ) ) THEN DO;
         IF ISPRIME( DIGITSUM( I, 3 ) ) THEN DO;
            CALL PRCHAR( ' ' );
            IF I <  10 THEN CALL PRCHAR( ' ' );
            IF I < 100 THEN CALL PRCHAR( ' ' );
            CALL PRNUMBER( I );
            PCOUNT = PCOUNT + 1;
            IF PCOUNT > 9 THEN DO;
               PCOUNT = 0;
               CALL PRNL;
            END;
         END;
      END;
   END;

EOF: end prime_digit_sums_100H;
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

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 n cols .                               /*obtain optional argument from the CL.*/
if    n=='' |    n==","  then    n=  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.     */
title= ' positive integers whose binary and ternary digit sums are prime, N  < ' commas(n)
if cols>0 then say ' index │'center(title, 1 + cols*(w+1)     )      /*maybe show title.*/
if cols>0 then say '───────┼'center(""   , 1 + cols*(w+1), '─')      /*maybe show  sep. */
found= 0;                   idx= 1               /*initialize # of finds and the index. */
$=                                               /*a list of  numbers  found  (so far). */
   do j=1  for n-1                               /*find #s whose B2 & B3 sums are prime.*/
   b2= sumDig( tBase(j, 2) );   if \!.b2  then iterate   /*convert to base2, sum digits.*/      /* ◄■■■■■■■■ a filter. */
   b3= sumDig( tBase(j, 3) );   if \!.b3  then iterate   /*   "     " base3   "    "    */      /* ◄■■■■■■■■ a filter. */
   found= found + 1                              /*bump the number of  found integers.  */
   if cols<1            then iterate             /*Only showing the summary?  Then skip.*/
   $= $  right( commas(j), w)                    /*add a commatized integer ───► $ list.*/
   if found//cols\==0   then iterate             /*have we populated a line of output?  */
   say center(idx, 7)'│'  substr($, 2);   $=     /*display what we have so far  (cols). */
   idx= idx + cols                               /*bump the  index  count for the output*/
   end   /*j*/

if $\==''  then say center(idx, 7)"│"  substr($, 2)  /*possible display residual output.*/
if cols>0  then say '───────┴'center(""   , 1 + cols*(w+1), '─')     /*show foot sep ?  */
say
say 'Found '       commas(found)      title                          /*show summary.    */
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:   @= 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
        !.=0;        do p=1  for words(@);   _= 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 │                   positive integers whose binary and ternary digit sums are prime, N  <  200
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   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  positive integers whose binary and ternary digit sums are prime, N  <  200

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...

Sidef[edit]

1..^200 -> grep {|n| [2,3].all { n.sumdigits(_).is_prime } }
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]

Tiny BASIC[edit]

This isn't a very interesting problem. The most illustrative part of this solution is that it only uses four variables; several have multiple purposes. Efficiency is important when the language has only 26 variable names in total.

    REM B      digital base input to sumdig, also output of primality routine
    REM N      input to sumdig routine
    REM P      input to primality routine, output of sumdig routine
    REM T      temp variable in sumdig routine, loop var in prime routine
    
    LET N = 1
 20 LET N = N + 1
    LET B = 2
    GOSUB 200
    GOSUB 100
    IF B = 0 THEN GOTO 30
    LET B = 3
    GOSUB 200
    GOSUB 100
    IF B = 1 THEN PRINT N
    
 30 IF N < 200 THEN GOTO 20
    END

100 REM PRIMALITY BY TRIAL DIVISION
    LET B = 0
    IF P = 1 THEN RETURN
    LET B = 1
    IF P = 2 THEN RETURN
    LET T = 2
110 IF (P/T)*T = P THEN LET B = 0
    IF B = 0 THEN RETURN
    LET T = T + 1
    IF T*T <= P THEN GOTO 110
    RETURN

200 REM digital sum of N in base B
    LET T = N
    LET P = 0
210 IF T = 0 THEN RETURN
    LET P = P + T - (T/B)*B
    LET T = T/B
    GOTO 210

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.

XPL0[edit]

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

func SumDigits(N, Base); \Return sum of digits in N for Base
int     N, Base, Sum;
[Sum:= 0;
repeat  N:= N/Base;
        Sum:= Sum + rem(0);
until   N=0;
return Sum;
];

int Count, N;
[Count:= 0;
for N:= 0 to 200-1 do
    if IsPrime(SumDigits(N,2)) & IsPrime(SumDigits(N,3)) 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, " such numbers found below 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     
61 such numbers found below 200.