Primes whose sum of digits is 25

Task

Show primes which sum of its decimal digits is 25

Find primes n such that n < 5000

Stretch goal

Show the count of all such primes that do not contain any zeroes in the range:

(997 ≤ n ≤ 1,111,111,111,111,111,111,111,111).

11l

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)
   V result = 0
   L n != 0
      result += n % 10
      n I/= 10
   R result

V c = 0
L(n) 5000
   I digit_sum(n) == 25 & is_prime(n)
      c++
      print(‘#4’.format(n), end' I c % 6 == 0 {"\n"} E ‘ ’)
print()
print(‘Found ’c‘ primes whose sum of digits is 25’)

Output:

 997 1699 1789 1879 1987 2689
2797 2887 3499 3697 3769 3877
3967 4597 4759 4957 4993 
Found 17 primes whose sum of digits is 25

Action!

Library: Action! Sieve of Eratosthenes

INCLUDE "H6:SIEVE.ACT"

BYTE FUNC SumOfDigits(INT x)
  BYTE s,d

  s=0
  WHILE x#0
  DO
    d=x MOD 10
    s==+d
    x==/10
  OD
RETURN (s)

PROC Main()
  DEFINE MAX="4999"
  BYTE ARRAY primes(MAX+1)
  INT i,count=[0]

  Put(125) PutE() ;clear the screen
  Sieve(primes,MAX+1)
  FOR i=2 TO MAX
  DO
    IF primes(i)=1 AND SumOfDigits(i)=25 THEN
      PrintI(i) Put(32)
      count==+1
    FI
  OD
  PrintF("%E%EThere are %I primes",count)
RETURN

Output:

Screenshot from Atari 8-bit computer

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

There are 17 primes

Ada

-- Rosetta Code Task written in Ada
-- Primes whose sum of digits is 25
-- https://rosettacode.org/wiki/Primes_whose_sum_of_digits_is_25
-- November 2024, R. B. E.

with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;

procedure Primes_Whose_Sum_of_Digits_is_25 is

  Max_Prime_Candidate : constant Positive := 5_000; -- per task description

  function Is_Prime (N : in Natural) return Boolean is
    Temp : Natural := 5;
  begin
    if N < 2 then
      return False;
    end if;
    if N mod 2 = 0 then
      return N = 2;
    end if;
    if N mod 3 = 0 then
      return N = 3;
    end if;
    while Temp * Temp <= N loop
      if N mod Temp = 0 then
        return False;
      end if;
      Temp := Temp + 2;
      if N mod Temp = 0 then
        return False;
      end if;
    end loop;
    return True;
  end Is_Prime;

  function Is_Sum_of_Digits_Equal_to_25 (N : Positive) return Boolean is
    Local_N : Natural := N;
    Sum : Natural := 0;
    Current_Remainder : Natural;
  begin
    while Local_N > 0 loop
      Current_Remainder := Local_N mod 10;
      Sum := Sum + Current_Remainder;
      Local_N := Local_N / 10;
    end loop;
  return Sum = 25;
  end Is_Sum_of_Digits_Equal_to_25;

  Prime_Count : Natural := 0;

begin
  for I in 1..Max_Prime_Candidate loop
    if Is_Sum_of_Digits_Equal_to_25 (I) then
      if (Is_Prime (I)) then
        Prime_Count := Prime_Count + 1;
        Put (I, 0);
        Put (" ");
      end if;
    end if;
  end loop;
  New_Line;
  Put ("There are ");
  Put (Prime_Count, 0);
  Put (" primes less than ");
  Put (Max_Prime_Candidate, 0);
  Put_Line (" whose sum of digits is 25");
end Primes_Whose_Sum_of_Digits_is_25;

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993
There are 17 primes less than 5000 whose sum of digits is 25

Note that ALGOL 68G under Windows is fully interpreted so runtime is not of the same order as the Phix and Go samples. Under Linux with optimisation and compilation, it should be faster than under Windows.

There are 1525141 sum25 primes that contain no zeroes

ALGOL W

begin % find some primes whose digits sum to 25 %
    % sets p( 1 :: n ) to a sieve of primes up to n %
    procedure Eratosthenes ( logical array p( * ) ; integer value n ) ;
    begin
        p( 1 ) := false; p( 2 ) := true;
        for i := 3 step 2 until n do p( i ) := true;
        for i := 4 step 2 until n do p( i ) := false;
        for i := 3 step 2 until truncate( sqrt( n ) ) do begin
            integer ii; ii := i + i;
            if p( i ) then for pr := i * i step ii until n do p( pr ) := false
        end for_i ;
    end Eratosthenes ;
    integer MAX_NUMBER;
    MAX_NUMBER := 4999;
    begin
        logical array prime( 1 :: MAX_NUMBER );
        integer       pCount;
        % sieve the primes to MAX_NUMBER %
        Eratosthenes( prime, MAX_NUMBER );
        % find the primes whose digits sum to 25 %
        pCount := 0;
        for i := 1 until MAX_NUMBER do begin
            if prime( i ) then begin
                integer dSum, v;
                v    := i;
                dSum := 0;
                while v > 0 do begin
                    dSum := dSum + ( v rem 10 );
                    v    := v div 10
                end while_v_gt_0 ;
                if dSum = 25 then begin
                    writeon( i_w := 4, s_w := 0, " ", i );
                    pCount := pCount + 1;
                    if pCount rem 20 = 0 then write()
                end if_prime_pReversed
            end if_prime_i
        end for_i ;
        write( i_w := 1, s_w := 0, "Found ", pCount, " sum25 primes below ", MAX_NUMBER + 1 )
    end
end.

Output:

  997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993
Found 17 sum25 primes below 5000

AppleScript

Functional

Not fast. This approach takes over 20 seconds here.

use AppleScript version "2.4"
use framework "Foundation"
use scripting additions


--------- PRIMES WITH DECIMAL DIGITS SUMMING TO 25 -------

-- primes :: [Int]
on primes()
    -- A non-finite list of primes.
    
    set ca to current application
    script
        property dict : ca's NSMutableDictionary's alloc's init()
        property n : 2
        on |λ|()
            set xs to dict's objectForKey:(n as string)
            repeat until missing value = xs
                repeat with x in (xs as list)
                    set m to x as number
                    set k to (n + m) as string
                    
                    set ys to (dict's objectForKey:(k))
                    if missing value ≠ ys then
                        set zs to ys
                    else
                        set zs to ca's NSMutableArray's alloc's init()
                    end if
                    
                    (zs's addObject:(m))
                    
                    (dict's setValue:(zs) forKey:(k))
                    (dict's removeObjectForKey:(n as string))
                end repeat
                
                set n to 1 + n
                set xs to (dict's objectForKey:(n as string))
            end repeat
            
            set p to n
            dict's setValue:({n}) forKey:((n * n) as string)
            set n to 1 + n
            set xs to missing value
            return p
        end |λ|
    end script
end primes

-- digitSum :: Int -> Int
on digitSum(n)
    -- Sum of the decimal digits of n.
    
    set m to 0
    set cs to characters of (n as string)
    repeat with c in cs
        set m to m + ((id of c) - 48)
    end repeat
end digitSum

--------------------------- TEST -------------------------
on run
    script q
        on |λ|(x)
            5000 > x
        end |λ|
    end script
    
    script p
        on |λ|(n)
            25 = digitSum(n)
        end |λ|
    end script
    
    
    set startTime to current date
    set xs to takeWhile(q, filterGen(p, primes()))
    set elapsedSeconds to ((current date) - startTime) as string
    
    showList(xs)
end run

------------------------- GENERIC ------------------------

-- filterGen :: (a -> Bool) -> Gen [a] -> Gen [a]
on filterGen(p, gen)
    -- Non-finite stream of values which are 
    -- drawn from gen, and satisfy p
    script
        property mp : mReturn(p)'s |λ|
        on |λ|()
            set v to gen's |λ|()
            repeat until mp(v)
                set v to gen's |λ|()
            end repeat
            return v
        end |λ|
    end script
end filterGen


-- intercalateS :: String -> [String] -> String
on intercalate(delim, xs)
    set {dlm, my text item delimiters} to ¬
        {my text item delimiters, delim}
    set s to xs as text
    set my text item delimiters to dlm
    s
end intercalate


-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    -- The list obtained by applying f
    -- to each element of xs.
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map


-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
    -- 2nd class handler function lifted into 1st class script wrapper. 
    if script is class of f then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn


-- showList :: [a] -> String
on showList(xs)
    "[" & intercalate(",", map(my str, xs)) & "]"
end showList


-- str :: a -> String
on str(x)
    x as string
end str


-- takeWhile :: (a -> Bool) -> Gen [a] -> [a]
on takeWhile(p, xs)
    set ys to {}
    set v to |λ|() of xs
    tell mReturn(p)
        repeat while (its |λ|(v))
            set end of ys to v
            set v to xs's |λ|()
        end repeat
    end tell
    return ys
end takeWhile

Output:

[997,1699,1789,1879,1987,2689,2797,2887,3499,3697,3769,3877,3967,4597,4759,4957,4993]

Idiomatic

Primes with silly properties are getting a bit tedious. But hey. This takes just under 0.02 seconds.

on sieveOfEratosthenes(limit)
    script o
        property numberList : {missing value}
    end script
    
    repeat with n from 2 to limit
        set end of o's numberList to n
    end repeat
    
    repeat with n from 2 to (limit ^ 0.5) div 1
        if (item n of o's numberList is n) then
            repeat with multiple from n * n to limit by n
                set item multiple of o's numberList to missing value
            end repeat
        end if
    end repeat
    
    return o's numberList's numbers
end sieveOfEratosthenes

on sumOfDigits(n) -- n assumed to be a positive decimal integer.
    set sum to n mod 10
    set n to n div 10
    repeat until (n = 0)
        set sum to sum + n mod 10
        set n to n div 10
    end repeat
    
    return sum
end sumOfDigits

on numbersWhoseDigitsSumTo(numList, targetSum)
    script o
        property numberList : numList
        property output : {}
    end script
    
    repeat with n in o's numberList
        if (sumOfDigits(n) = targetSum) then set end of o's output to n's contents
    end repeat
    
    return o's output
end numbersWhoseDigitsSumTo

-- Task code:
return numbersWhoseDigitsSumTo(sieveOfEratosthenes(4999), 25)

Output:

{997, 1699, 1789, 1879, 1987, 2689, 2797, 2887, 3499, 3697, 3769, 3877, 3967, 4597, 4759, 4957, 4993}

Arturo

primes: select 1..5000 => prime?

loop split.every: 3 select primes 'p [25 = sum digits p] 'a -> 
    print map a => [pad to :string & 5]

Output:

  997  1699  1789 
 1879  1987  2689 
 2797  2887  3499 
 3697  3769  3877 
 3967  4597  4759 
 4957  4993

AWK

# syntax: GAWK -f PRIMES_WHICH_SUM_OF_DIGITS_IS_25.AWK
BEGIN {
    start = 1
    stop = 5000
    for (i=start; i<=stop; i++) {
      if (is_prime(i)) {
        sum = 0
        for (j=1; j<=length(i); j++) {
          sum += substr(i,j,1)
        }
        if (sum == 25) {
          printf("%d ",i)
          count++
        }
      }
    }
    printf("\nPrime numbers %d-%d whose digits sum to 25: %d\n",start,stop,count)
    exit(0)
}
function is_prime(x,  i) {
    if (x <= 1) {
      return(0)
    }
    for (i=2; i<=int(sqrt(x)); i++) {
      if (x % i == 0) {
        return(0)
      }
    }
    return(1)
}

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993
Prime numbers 1-5000 whose digits sum to 25: 17

BASIC

BASIC256

Translation of: FreeBASIC

function isprime(num)
	for i = 2 to int(sqr(num))
		if (num mod i = 0) then return False
	next i
	return True
end function

function digit_sum(num)
	sum25 = 0
	for j = 1 to length(num)
		sum25 += int(mid(string(num),j,1))
	next j
	return sum25
end function

inicio = 1: final = 5000
total = 0
for i = inicio to final
	if isprime(i) and (digit_sum(i) = 25) then
		total += 1
		print i; " ";
	end if
next i
print chr(13) + chr(13)
print "Se encontraron "; total; " primos sum25 por debajo de "; final
end

Output:

Igual que la entrada de FreeBASIC.

C

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

bool is_prime(int n) {
    int i = 5;

    if (n < 2) {
        return false;
    }
    if (n % 2 == 0) {
        return n == 2;
    }
    if (n % 3 == 0) {
        return n == 3;
    }

    while (i * i <= n) {
        if (n % i == 0) {
            return false;
        }
        i += 2;

        if (n % i == 0) {
            return false;
        }
        i += 4;
    }

    return true;
}

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

int main() {
    int n;

    for (n = 2; n < 5000; n++) {
        if (is_prime(n) && digit_sum(n) == 25) {
            printf("%d ", n);
        }
    }

    return 0;
}

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

C++

Library: GMP

Stretch goal solved the same way as Phix and Go.

#include <algorithm>
#include <chrono>
#include <iomanip>
#include <iostream>
#include <string>

#include <gmpxx.h>

bool is_probably_prime(const mpz_class& n) {
    return mpz_probab_prime_p(n.get_mpz_t(), 3) != 0;
}

bool is_prime(int n) {
    if (n < 2)
        return false;
    if (n % 2 == 0)
        return n == 2;
    if (n % 3 == 0)
        return n == 3;
    for (int p = 5; p * p <= n; p += 4) {
        if (n % p == 0)
            return false;
        p += 2;
        if (n % p == 0)
            return false;
    }
    return true;
}

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

int count_all(const std::string& str, int rem) {
    int count = 0;
    if (rem == 0) {
        switch (str.back()) {
        case '1':
        case '3':
        case '7':
        case '9':
            if (is_probably_prime(mpz_class(str)))
                ++count;
            break;
        default:
            break;
        }
    } else {
        for (int i = 1; i <= std::min(9, rem); ++i)
            count += count_all(str + char('0' + i), rem - i);
    }
    return count;
}

int main() {
    std::cout.imbue(std::locale(""));
    const int limit = 5000;
    std::cout << "Primes < " << limit << " whose digits sum to 25:\n";
    int count = 0;
    for (int p = 1; p < limit; ++p) {
        if (digit_sum(p) == 25 && is_prime(p)) {
            ++count;
            std::cout << std::setw(6) << p << (count % 10 == 0 ? '\n' : ' ');
        }
    }
    std::cout << '\n';

    auto start = std::chrono::steady_clock::now();
    count = count_all("", 25);
    auto end = std::chrono::steady_clock::now();
    std::cout << "\nThere are " << count
              << " primes whose digits sum to 25 and include no zeros.\n";
    std::cout << "Time taken: "
              << std::chrono::duration<double>(end - start).count() << "s\n";
    return 0;
}

Output:

//https://tio.run/#cpp-gcc -lgmp -O3
Primes < 5,000 whose digits sum to 25:
   997  1,699  1,789  1,879  1,987  2,689  2,797  2,887  3,499  3,697
 3,769  3,877  3,967  4,597  4,759  4,957  4,993 

There are 1,525,141 primes whose digits sum to 25 and include no zeros.
Time taken: 10.6088s
.....
Real time: 11.214 s
User time: 11.075 s
Sys. time: 0.082 s
CPU share: 99.50 %
Exit code: 0

D

Translation of: C

import std.bigint;
import std.stdio;

bool isPrime(BigInt n) {
    if (n < 2) {
        return false;
    }

    if (n % 2 == 0) {
        return n == 2;
    }
    if (n % 3 == 0) {
        return n == 3;
    }

    auto i = BigInt(5);
    while (i * i <= n) {
        if (n % i == 0){
            return false;
        }
        i += 2;

        if (n % i == 0){
            return false;
        }
        i += 4;
    }

    return true;
}

int digitSum(BigInt n) {
    int result;
    while (n > 0) {
        result += n % 10;
        n /= 10;
    }
    return result;
}

void main() {
    for (auto n = BigInt(2); n < 5_000; n++) {
        if (n.isPrime && n.digitSum == 25) {
            write(n, ' ');
        }
    }
    writeln;
}

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Delphi

Library: System.SysUtils

Library: PrimTrial

Translation of: Ring

program Primes_which_sum_of_digits_is_25;

{$APPTYPE CONSOLE}

uses
  System.SysUtils,
  PrimTrial;

var
  row: Integer = 0;
  limit1: Integer = 25;
  limit2: Integer = 5000;

function Sum25(n: Integer): boolean;
var
  sum: Integer;
  str: string;
  c: char;
begin
  sum := 0;
  str := n.ToString;
  for c in str do
    inc(sum, strToInt(c));
  Result := sum = limit1;
end;

begin
  for var n := 1 to limit2-1 do
  begin
    if isPrime(n) and sum25(n) then
    begin
      inc(row);
      write(n: 4, ' ');
      if (row mod 5) = 0 then
        writeln;
    end;
  end;
  readln;
end.

Output:

 997 1699 1789 1879 1987
2689 2797 2887 3499 3697
3769 3877 3967 4597 4759
4957 4993

EasyLang

fastfunc isprim num .
   i = 2
   while i <= sqrt num
      if num mod i = 0
         return 0
      .
      i += 1
   .
   return 1
.
fastfunc nextprim prim .
   repeat
      prim += 1
      until isprim prim = 1
   .
   return prim
.
func digok n .
   while n > 0
      dsum += n mod 10
      n = n div 10
   .
   return if dsum = 25
.
p = 2
repeat
   if digok p = 1
      write p & " "
   .
   p = nextprim p
   until p >= 5000
.

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

F#

// Primes  to 5000 who's sum of digits is 25. Nigel Galloway: April 1st., 2021
let rec fN g=function n when n<10->n+g=25 |n->fN(g+n%10)(n/10)
primes32()|>Seq.takeWhile((>)5000)|>Seq.filter fN|>Seq.iter(printf "%d "); printfn ""

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Factor

Works with: Factor version 0.99 2021-02-05

USING: kernel lists lists.lazy math math.primes.lists prettyprint ;

: digit-sum ( n -- sum )
    0 swap [ 10 /mod rot + swap ] until-zero ;

: lprimes25 ( -- list ) lprimes [ digit-sum 25 = ] lfilter ;

lprimes25 [ 5,000 < ] lwhile [ . ] leach

Output:

Forth

Works with: Gforth

: prime? ( n -- ? ) here + c@ 0= ;
: notprime! ( n -- ) here + 1 swap c! ;

: prime_sieve { n -- }
  here n erase
  0 notprime!
  1 notprime!
  n 4 > if
    n 4 do i notprime! 2 +loop
  then
  3
  begin
    dup dup * n <
  while
    dup prime? if
      n over dup * do
        i notprime!
      dup 2* +loop
    then
    2 +
  repeat
  drop ;

: digit_sum ( u -- u )
  dup 10 < if exit then
  10 /mod recurse + ;

: prime25? { p -- ? }
  p prime? if
    p digit_sum 25 =
  else
    false
  then ;  

: .prime25 { n -- }
  ." Primes < " n . ." whose digits sum to 25:" cr
  n prime_sieve
  0
  n 0 do
    i prime25? if
      i 5 .r
      1+ dup 10 mod 0= if cr then
    then
  loop
  cr ." Count: " . cr ;

5000 .prime25
bye

Output:

Primes < 5000 whose digits sum to 25:
  997 1699 1789 1879 1987 2689 2797 2887 3499 3697
 3769 3877 3967 4597 4759 4957 4993
Count: 17

FreeBASIC

Translation of: AWK

Function isprime(num As Ulongint) As Boolean
    For i As Integer = 2 To Sqr(num)
        If (num Mod i = 0) Then Return False
    Next i
    Return True 
End Function

Function digit_sum(num As Integer) As Integer
    Dim As Integer sum25 = 0
    For j As Integer = 1 To Len(num)
        sum25 += Val(Mid(Str(num),j,1))
    Next j
    Return sum25
End Function

Dim As Integer inicio = 1, final = 5000, total = 0
For i As Integer = inicio To final
    If (isprime(i)) And (digit_sum(i) = 25) Then
        total += 1
        Print Using " ####"; i;
        If (total Mod 9) = 0 Then Print
    End If
Next i
Print !"\n\nSe encontraron"; total; " primos sum25 por debajo de"; finalSleep

Output:

  997 1699 1789 1879 1987 2689 2797 2887 3499
 3697 3769 3877 3967 4597 4759 4957 4993

Se encontraron 17 primos sum25 por debajo de 5000

Frink

println[select[primes[2,4999], {|x| sum[integerDigits[x]] == 25}]]

Output:

[997, 1699, 1789, 1879, 1987, 2689, 2797, 2887, 3499, 3697, 3769, 3877, 3967, 4597, 4759, 4957, 4993]

Go

Library: GMP(Go wrapper)

This uses the Phix routine for the stretch goal though I've had to plug in a GMP wrapper to better the Phix time. Using Go's native big.Int, the time was slightly slower than Phix at 1 minute 28 seconds.

package main

import (
    "fmt"
    big "github.com/ncw/gmp"
    "time"
)

// for small numbers
func sieve(limit int) []bool {
    limit++
    // True denotes composite, false denotes prime.
    c := make([]bool, limit) // all false by default
    c[0] = true
    c[1] = true
    // no need to bother with even numbers over 2 for this task
    p := 3 // Start from 3.
    for {
        p2 := p * p
        if p2 >= limit {
            break
        }
        for i := p2; i < limit; i += 2 * p {
            c[i] = true
        }
        for {
            p += 2
            if !c[p] {
                break
            }
        }
    }
    return c
}

func sumDigits(n int) int {
    sum := 0
    for n > 0 {
        sum += n % 10
        n /= 10
    }
    return sum
}

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}

// for big numbers
func countAll(p string, rem, res int) int {
    if rem == 0 {
        b := p[len(p)-1]
        if b == '1' || b == '3' || b == '7' || b == '9' {
            z := new(big.Int)
            z.SetString(p, 10)
            if z.ProbablyPrime(1) {
                res++
            }
        }
    } else {
        for i := 1; i <= min(9, rem); i++ {
            res = countAll(p+fmt.Sprintf("%d", i), rem-i, res)
        }
    }
    return res
}

func commatize(n int) string {
    s := fmt.Sprintf("%d", n)
    if n < 0 {
        s = s[1:]
    }
    le := len(s)
    for i := le - 3; i >= 1; i -= 3 {
        s = s[0:i] + "," + s[i:]
    }
    if n >= 0 {
        return s
    }
    return "-" + s
}

func main() {
    start := time.Now()
    c := sieve(4999)
    var primes25 []int
    for i := 997; i < 5000; i += 2 {
        if !c[i] && sumDigits(i) == 25 {
            primes25 = append(primes25, i)
        }
    }
    fmt.Println("The", len(primes25), "primes under 5,000 whose digits sum to 25 are:")
    fmt.Println(primes25)
    n := countAll("", 25, 0)
    fmt.Println("\nThere are", commatize(n), "primes whose digits sum to 25 and include no zeros.")
    fmt.Printf("\nTook %s\n", time.Since(start))
}

Output:

The 17 primes under 5,000 whose digits sum to 25 are:
[997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993]

There are 1,525,141 primes whose digits sum to 25 and include no zeros.

Took 25.300758564s

Haskell

import Data.Bifunctor (second)
import Data.List (replicate)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (primes)

--------- PRIMES WITH DECIMAL DIGITS SUMMING TO 25 -------

matchingPrimes :: [Int]
matchingPrimes =
  takeWhile
    (< 5000)
    [n | n <- primes, 25 == decimalDigitSum n]

decimalDigitSum :: Int -> Int
decimalDigitSum n =
  snd $
    until
      ((0 ==) . fst)
      (\(n, x) -> second (+ x) $ quotRem n 10)
      (n, 0)

--------------------------- TEST -------------------------
main :: IO ()
main = do
  let w = length (show (last matchingPrimes))
  mapM_ putStrLn $
    ( show (length matchingPrimes)
        <> " primes (< 5000) with decimal digits totalling 25:\n"
    ) :
    ( unwords
        <$> chunksOf
          4
          (justifyRight w ' ' . show <$> matchingPrimes)
    )

justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)

Output:

17 primes (< 5000) with decimal digits totalling 25:

 997 1699 1789 1879
1987 2689 2797 2887
3499 3697 3769 3877
3967 4597 4759 4957
4993

J

   (#~ 25 = +/@("."0@":)"0) p: i. _1 p: 5000
997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Java

Translation of: Kotlin

import java.math.BigInteger;

public class PrimeSum {
    private static int digitSum(BigInteger bi) {
        int sum = 0;
        while (bi.compareTo(BigInteger.ZERO) > 0) {
            BigInteger[] dr = bi.divideAndRemainder(BigInteger.TEN);
            sum += dr[1].intValue();
            bi = dr[0];
        }
        return sum;
    }

    public static void main(String[] args) {
        BigInteger fiveK = BigInteger.valueOf(5_000);
        BigInteger bi = BigInteger.valueOf(2);
        while (bi.compareTo(fiveK) < 0) {
            if (digitSum(bi) == 25) {
                System.out.print(bi);
                System.out.print("  ");
            }
            bi = bi.nextProbablePrime();
        }
        System.out.println();
    }
}

Output:

997  1699  1789  1879  1987  2689  2797  2887  3499  3697  3769  3877  3967  4597  4759  4957  4993

JavaScript

(() => {
    "use strict";

    // ---- PRIMES WITH DECIMAL DIGITS SUMMING TO 25 -----

    // digitSum :: Int -> Int
    const digitSum = n =>
        `${n}`.split("").reduce(
            (a, c) => a + (c.codePointAt(0) - 48),
            0
        );


    // primes :: [Int]
    const primes = function* () {
        // Non finite sequence of prime numbers.
        const dct = {};
        let n = 2;

        while (true) {
            if (n in dct) {
                dct[n].forEach(p => {
                    const np = n + p;

                    dct[np] = (dct[np] || []).concat(p);
                    delete dct[n];
                });
            } else {
                yield n;
                dct[n * n] = [n];
            }
            n = 1 + n;
        }
    };


    // ---------------------- TEST -----------------------
    // main :: IO ()
    const main = () =>
        unlines(
            chunksOf(5)(
                takeWhileGen(n => 5000 > n)(
                    filterGen(n => 25 === digitSum(n))(
                        primes()
                    )
                ).map(str)
            ).map(unwords)
        );


    // --------------------- GENERIC ---------------------

    // chunksOf :: Int -> [a] -> [[a]]
    const chunksOf = n => {
        // xs split into sublists of length n.
        // The last sublist will be short if n
        // does not evenly divide the length of xs .
        const go = xs => {
            const chunk = xs.slice(0, n);

            return 0 < chunk.length ? (
                [chunk].concat(
                    go(xs.slice(n))
                )
            ) : [];
        };

        return go;
    };


    // filterGen :: (a -> Bool) -> Gen [a] -> Gen [a]
    const filterGen = p => xs => {
        // Non-finite stream of values which are
        // drawn from gen, and satisfy p
        const go = function* () {
            let x = xs.next();

            while (!x.done) {
                const v = x.value;

                if (p(v)) {
                    yield v;
                }
                x = xs.next();
            }
        };

        return go(xs);
    };


    // str :: a -> String
    const str = x =>
        x.toString();


    // takeWhileGen :: (a -> Bool) -> Gen [a] -> [a]
    const takeWhileGen = p =>
        // Values drawn from xs until p matches.
        xs => {
            const ys = [];
            let
                nxt = xs.next(),
                v = nxt.value;

            while (!nxt.done && p(v)) {
                ys.push(v);
                nxt = xs.next();
                v = nxt.value;
            }

            return ys;
        };


    // unlines :: [String] -> String
    const unlines = xs =>
        // A single string formed by the intercalation
        // of a list of strings with the newline character.
        xs.join("\n");


    // unwords :: [String] -> String
    const unwords = xs =>
        // A space-separated string derived
        // from a list of words.
        xs.join(" ");

    return main();
})();

997 1699 1789 1879 1987
2689 2797 2887 3499 3697
3769 3877 3967 4597 4759
4957 4993

jq

Works with jq
Works with gojq, the Go implementation of jq

The stretch goal is currently beyond the practical capabilities of both the C and Go-based implementations of jq, so only a simple solution to the primary task is shown here.

A suitable definition of `is_prime` may be found at Erdős-primes#jq and is therefore not repeated here.

Preliminaries

def digits: tostring | explode | map( [.]|implode|tonumber);

def emit_until(cond; stream): label $out | stream | if cond then break $out else . end;

The Task

# Output: primes whose decimal representation has no 0s and whose sum of digits is $sum > 2
def task($sum):
  # Input: array of digits
  def nozeros: select(all(.[]; . != 0));
  range(3;infinite;2)
  | select(digits | (.[-1] != 5 and nozeros and (add == $sum)) )
  | select(is_prime);
     
emit_until(. >= 5000;  task(25) )

Output:

Julia

using Primes

let
    pmask, pcount = primesmask(1, 5000), 0
    issum25prime(n) = pmask[n] && sum(digits(n)) == 25

    println("Primes with digits summing to 25 between 0 and 5000:")
    for n in 1:4999
        if issum25prime(n)
            pcount += 1
            print(rpad(n, 5))
        end
    end
    println("\nTotal found: $pcount")
end

Output:

Primes with digits summing to 25 between 0 and 5000:
997  1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993 
Total found: 17

Stretch goal

Translation of: Phix

using Primes, Formatting

function sum25(p::String, rm, res)
    if rm == 0
        if p[end] in "1379" && isprime(parse(Int128, p))
            res += 1
        end
    else
        for i in 1:min(rm, 9)
            res = sum25(p * string(i), rm - i, res)
        end
    end
    return res
end

@time println("There are ", format(sum25("", 25, 0), commas=true),
    " primes whose digits sum to 25 without any zero digits.")

Output:

There are 1,525,141 primes whose digits sum to 25 without any zero digits.
 29.377893 seconds (100.61 M allocations: 4.052 GiB, 0.55% gc time)

Kotlin

import java.math.BigInteger

fun digitSum(bi: BigInteger): Int {
    var bi2 = bi
    var sum = 0
    while (bi2 > BigInteger.ZERO) {
        val dr = bi2.divideAndRemainder(BigInteger.TEN)
        sum += dr[1].toInt()
        bi2 = dr[0]
    }
    return sum
}

fun main() {
    val fiveK = BigInteger.valueOf(5_000)

    var bi = BigInteger.valueOf(2)
    while (bi < fiveK) {
        if (digitSum(bi) == 25) {
            print(bi)
            print("  ")
        }

        bi = bi.nextProbablePrime()
    }
    println()
}

Output:

997  1699  1789  1879  1987  2689  2797  2887  3499  3697  3769  3877  3967  4597  4759  4957  4993

Ksh

#!/bin/ksh

# Primes which sum of digits is 25

#	# Variables:
#
integer MAXN=5000 SUM=25

#	# Functions:
#
#	# Function _sumdigits(n, sum) - return 1 if sum of n's digits = sum
#
function _sumdigits {
	typeset _n ; integer _n=$1
	typeset _sum ; integer _sum=$2
	typeset _i _dsum ; integer _i _dsum=0

	for ((_i=0; _i<${#_n}; _i++)); do
		(( _dsum+=${_n:_i:1} ))
	done
	return $(( _dsum == _sum ))
}

#	# Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
	typeset _n ; integer _n=$1
	typeset _i ; integer _i

	(( _n < 2 )) && return 0
	for (( _i=2 ; _i*_i<=_n ; _i++ )); do
		(( ! ( _n % _i ) )) && return 0
	done
	return 1
}

 ######
# main #
 ######

for ((i=3; i<$MAXN; i++)); do
	_isprime ${i} || _sumdigits ${i} $SUM || printf "%d " ${i}
done
echo

Output:


997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Mathematica /Wolfram Language

Select[Prime[Range@PrimePi[4999]], IntegerDigits /* Total /* EqualTo[25]]

Output:

{997, 1699, 1789, 1879, 1987, 2689, 2797, 2887, 3499, 3697, 3769, 3877, 3967, 4597, 4759, 4957, 4993}

Nanoquery

// find primes using the sieve of eratosthenes
// https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Pseudocode
def find_primes(upper_bound)
    a = {true} * (upper_bound + 1)
    for i in range(2, int(sqrt(upper_bound)))
        if a[i]
            for j in range(i ^ 2, upper_bound, i)
                a[j] = false
            end for
        end if
    end for

    primes = {}
    for i in range(2, len(a) - 1)
        if a[i]
            primes.append(i)
        end if
    end for
    return primes
end find_primes

def sum_digits(num)
    digits = str(num)
    digit_sum = 0

    for i in range(0, len(digits) - 1)
        digit_sum += int(digits[i])
    end for

    return digit_sum
end sum_digits

primes_to_check = find_primes(5000)
for prime in primes_to_check
    if sum_digits(prime) = 25
        print prime + " "
    end if
end for
println

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Nim

Task

import strutils, sugar

func isPrime(n: Natural): bool =
  if n < 2: 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
  result = true

func digitSum(n: Natural): int =
  var n = n
  while n != 0:
    result += n mod 10
    n = n div 10

let result = collect(newSeq):
               for n in countup(3, 5000, 2):
                 if digitSum(n) == 25 and n.isPrime: n

for i, n in result:
  stdout.write ($n).align(4), if (i + 1) mod 6 == 0: '\n' else: ' '
echo()

Output:

 997 1699 1789 1879 1987 2689
2797 2887 3499 3697 3769 3877
3967 4597 4759 4957 4993

Stretch goal

Translation of: Julia

Library: bignum

import std/monotimes, strformat, strutils
import bignum

func sum25(p: string; rm, res: Natural): Natural =
  result = res
  if rm == 0:
    if p[^1] in "1379" and probablyPrime(newInt(p), 25) != 0:
      inc result
  else:
    for i in 1..min(rm, 9):
      result = sum25(p & chr(i + ord('0')), rm - i, result)

let t0 = getMonoTime()
let count = $sum25("", 25, 0)
echo &"There are {count.insertSep()} primes whose digits sum to 25 without any zero digits."
echo "\nExecution time: ", getMonoTime() - t0

Output:

There are 1_525_141 primes whose digits sum to 25 without any zero digits.

Execution time: (seconds: 12, nanosecond: 182051288)

Pascal

added only strechted goal.Generating the combination of the digits for the numbers and afterwards generating the Permutations with some identical elements
Now seting one digit out of 1,3,7,9 to the end and permute the rest of the digits in front.
So much less numbers have to be tested.10.5e6 instead of 16.4e6.Generating of the numbers is reduced in the same ratio.

program Perm5aus8;
//formerly roborally take 5 cards out of 8
{$IFDEF FPC}
  {$mode Delphi}
  {$Optimization ON,All}
{$ELSE}
  {$APPTYPE CONSOLE}
{$ENDIF}
uses
  sysutils,
  gmp;
const
  cTotalSum = 31;

  cMaxCardsOnDeck = cTotalSum;//8
  CMaxCardsUsed   = cTotalSum;//5

type
  tDeckIndex     = 0..cMaxCardsOnDeck-1;
  tSequenceIndex = 0..CMaxCardsUsed-1;

  tDiffCardCount = 0..9;

  tSetElem     = record
                      Elem  : tDiffCardCount;
                      Elemcount : tDeckIndex;
                 end;

  tSet          =  record
                      RemSet : array [low(tDiffCardCount)..High(tDiffCardCount)] of tSetElem;
                      MaxUsedIdx,
                      TotElemCnt   : byte;
                    end;

  tRemainSet      = array [low(tSequenceIndex)..High(tSequenceIndex)+1] of tSet;

  tCardSequence   = array [low(tSequenceIndex)..High(tSequenceIndex)] of tDiffCardCount;

var
  ManifoldOfDigit : array[tDiffCardCount] of Byte;
  TotalUsedDigits : array[tDeckIndex] of Byte;
  RemainSets     : tRemainSet;

  CardString    : AnsiString;

  PrimeCount : integer;
  PermCount  : integer;

//*****************************************************************************
var
  CS : pchar;
  z : mpz_t;

procedure SetInit(var ioSet:tSet);
var
  i : integer;
begin
  with ioSet do
    begin
    MaxUsedIdx := 0;
    For i := Low(tDiffCardCount) to High(tDiffCardCount) do
      with RemSet[i] do
        begin
        ElemCount := 0;
        Elem      := 0;
        end;
    end;
end;

procedure CheckPrime;inline;
begin
  mpz_set_str(z,CS,10);
  inc(PrimeCount,ORD(mpz_probab_prime_p(z,3)>0));
end;

procedure Permute(depth,MaxCardsUsed:NativeInt);
var
  pSetElem : ^tSetElem;
  i : NativeInt;
begin
  i := 0;
  pSetElem := @RemainSets[depth].RemSet[i];
  repeat
    if pSetElem^.Elemcount <> 0 then begin
      //take one of the same elements of the stack
      //insert in result here string
      CS[depth] := chr(pSetElem^.Elem+Ord('0'));
       //done one permutation
      IF depth = MaxCardsUsed then
      begin
        inc(permCount);
        CheckPrime;
      end
      else
      begin
        dec(pSetElem^.ElemCount);
        RemainSets[depth+1]:= RemainSets[depth];
        Permute(depth+1,MaxCardsUsed);
        //re-insert that element
        inc(pSetElem^.ElemCount);
      end;
    end;
    //move on to the next digit
    inc(pSetElem);
    inc(i);
  until i >=RemainSets[depth].MaxUsedIdx;
end;

procedure Check(n:nativeInt);
var
  i,dgtCnt,cnt,dgtIdx : NativeInt;
Begin
  SetInit(RemainSets[0]);
  dgtCnt := 0;
  dgtIdx := 0;
  //creating the start set.
  with RemainSets[0] do
  Begin
    For i in tDiffCardCount do
    Begin
      cnt := ManifoldOfDigit[i];
      if cnt > 0 then
      Begin
        with RemSet[dgtIdx] do
        Begin
          Elemcount := cnt;
          Elem  := i;
        end;
        inc(dgtCnt,cnt);
        inc(dgtIdx);
      end;
    end;
    TotElemCnt := dgtCnt;
    MaxUsedIdx := dgtIdx;

    CS := @CardString[1];
    //Check only useful end-digits
    For i := 0 to dgtIdx-1 do
    Begin
      if RemSet[i].Elem in[1,3,7,9]then
      Begin
        CS[dgtCnt-1] := chr(RemSet[i].Elem+Ord('0'));
        CS[dgtCnt] := #00;

        dec(RemSet[i].ElemCount);
        permute(0,dgtCnt-2);
        inc(RemSet[i].ElemCount);
      end;
    end;
  end;
end;

procedure AppendToSum(n,dgt,remsum:NativeInt);
var
  i: NativeInt;
begin
  inc(ManifoldOfDigit[dgt]);
  IF remsum > 0 then
    For i := dgt to 9 do
      AppendToSum(n+1,i,remsum-i)
  else
  Begin
    if remsum = 0 then
    Begin
      Check(n);
      //n is 0 based PrimeCount combinations of length n
      inc(TotalUsedDigits[n+1]);
    end;
  end;
  dec(ManifoldOfDigit[dgt]);
end;

procedure CheckAll(SumGoal:NativeInt);
var
  i :NativeInt;
begin
  setlength(CardString,SumGoal);
  IF sumGoal>cTotalSum then
    EXIT;
  fillchar(ManifoldOfDigit[0],SizeOf(ManifoldOfDigit),#0);
  permcount:=0;
  PrimeCount := 0;

  For i := 1 to 9 do
    AppendToSum(0,i,SumGoal-i);

  writeln('PrimeCount of generated numbers with digits sum of ',SumGoal,' are ',permcount);
  writeln('Propably primes ',PrimeCount);
  writeln;
end;
var
  T1,T0 : Int64;
  SumGoal: NativeInt;
BEGIN
  writeln('GMP-Version ',gmp.version);
  mpz_init_set_ui(z,0);
  T0 := GetTickCount64;
  For SumGoal := 25 to 25 do
  Begin
    CheckAll(SumGoal);
    T1 := GetTickCount64;Writeln((T1-T0)/1000:7:3,' s');
    T0 := T1;
  end;
  mpz_clear(z);
END.

Output:

//Runnning on TIO.RUN
GMP-Version 6.1.2
PrimeCount of generated numbers with digits sum of 25 are 10488498
Propably primes 1525141

  9.932 s
....
Free Pascal Compiler version 3.0.4 [2018/07/13] for x86_64
Copyright (c) 1993-2017 by Florian Klaempfl and others
Target OS: Linux for x86-64
Compiling .code.tio.pp
Linking .bin.tio
/usr/bin/ld: warning: link.res contains output sections; did you forget -T?
204 lines compiled, 0.2 sec

Real time: 10.135 s
User time: 10.027 s
Sys. time: 0.052 s
CPU share: 99.45 %
Exit code: 0

Perl

Library: ntheory

use strict;
use warnings;
use feature 'say';
use List::Util 'sum';
use ntheory 'is_prime';

my($limit, @p25) = 5000;
is_prime($_) and 25 == sum(split '', $_) and push @p25, $_ for 1..$limit;
say @p25 . " primes < $limit with digital sum 25:\n" . join ' ', @p25;

Output:

17 primes < 5000 with digital sum 25:
997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Phix

function sum25(integer p) return sum(sq_sub(sprint(p),'0'))=25 end function
sequence res = filter(get_primes_le(5000),sum25)
string r = join(shorten(apply(res,sprint),"",4))
printf(1,"%d sum25 primes less than 5000 found: %s\n",{length(res),r})

Output:

17 sum25 primes less than 5000 found: 997 1699 1789 1879 ... 4597 4759 4957 4993

Stretch goal

Library: Phix/mpfr

without js
include mpfr.e
atom t0 = time(), t1 = time()+1
mpz pz = mpz_init(0)

function sum25(string p, integer rem, res=0)
    if rem=0 then
        if find(p[$],"1379") then -- (saves 13s)
            mpz_set_str(pz,p)
            if mpz_prime(pz) then
                res += 1
                if platform()!=JS and time()>t1 then
                    progress("%d, %s...",{res,p})
                    t1 = time()+1
                end if
            end if
        end if
    else
        for i=1 to min(rem,9) do
            res = sum25(p&'0'+i,rem-i,res)
        end for
    end if
    return res
end function
 
printf(1,"There are %,d sum25 primes that contain no zeroes\n",sum25("",25))
?elapsed(time()-t0)

Output:

There are 1,525,141 sum25 primes that contain no zeroes
"1 minute and 27s"

Note this works under pwa/p2js but you would get to stare at a blank screen for 8½ minutes with 100% cpu, hence it has been marked "without js".

Python

'''Primes with a decimal digit sum of 25'''

from itertools import takewhile


# primesWithGivenDigitSum :: Int -> Int -> [Int]
def primesWithGivenDigitSum(below, n):
    '''Primes below a given value with
       decimal digits sums equal to n.
    '''
    return list(
        takewhile(
            lambda x: below > x,
            (
                x for x in primes()
                if n == sum(int(c) for c in str(x))
            )
        )
    )


# ------------------------- TEST -------------------------
# main :: IO ()
def main():
    '''Test'''
    matches = primesWithGivenDigitSum(5000, 25)
    print(
        str(len(matches)) + (
            ' primes below 5000 with a decimal digit sum of 25:\n'
        )
    )
    print(
        '\n'.join([
            ' '.join([str(x).rjust(4, ' ') for x in xs])
            for xs in chunksOf(4)(matches)
        ])
    )


# ----------------------- 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


# primes :: [Int]
def primes():
    ''' Non-finite sequence of prime numbers.
    '''
    n = 2
    dct = {}
    while True:
        if n in dct:
            for p in dct[n]:
                dct.setdefault(n + p, []).append(p)
            del dct[n]
        else:
            yield n
            dct[n * n] = [n]
        n = 1 + n


# MAIN ---
if __name__ == '__main__':
    main()

Output:

17 primes below 5000 with a decimal digit sum of 25:

 997 1699 1789 1879
1987 2689 2797 2887
3499 3697 3769 3877
3967 4597 4759 4957
4993

Quackery

eratosthenes and isprime are defined at Sieve of Eratosthenes#Quackery.

  5000 eratosthenes
  
  [ 0
    [ over while
      swap 10 /mod
      rot + again ]
    nip  ]          is digitsum ( n --> n )

  [] 5000 times
    [ i^ isprime not if done
      i^ digitsum 25 = if
        [ i^ join ] ]
  echo

Output:

[ 997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993 ]

Raku

unit sub MAIN ($limit = 5000);
say "{+$_} primes < $limit with digital sum 25:\n{$_».fmt("%" ~ $limit.chars ~ "d").batch(10).join("\n")}",
    with ^$limit .grep: { .is-prime and .comb.sum == 25 }

Output:

17 primes < 5000 with digital sum 25:
 997 1699 1789 1879 1987 2689 2797 2887 3499 3697
3769 3877 3967 4597 4759 4957 4993

REXX

This REXX version allows the following to be specified on the command line:

the high number (HI)
the number of columns shown per line (COLS)
the target sum (TARGET)

/*REXX pgm finds and displays primes less than  HI  whose decimal digits sum to  TARGET.*/
parse arg hi cols target .                       /*obtain optional argument from the CL.*/
if     hi=='' |     hi==","  then     hi= 5000   /*Not specified?  Then use the default.*/
if   cols=='' |   cols==","  then   cols=   10   /* "      "         "   "   "     "    */
if target=='' | target==","  then target=   25   /* "      "         "   "   "     "    */
call genP                                        /*build array of semaphores for primes.*/
w= 10                                            /*width of a number in any column.     */
title= ' primes that are  < '  commas(hi)  " and whose decimal digits sum to " ,
                               commas(target)
if cols>0  then say ' index │'center(title,   1 + cols*(w+1)      )
if cols>0  then say '───────┼'center(""   ,   1 + cols*(w+1),  '─')
found= 0;                      idx= 1            /*define # target primes found and IDX.*/
$=                                               /*list of target primes found (so far).*/
     do j=1  for #                               /*examine all the primes generated.    */
     if sumDigs(@.j)\==target  then iterate      /*Is sum≡target sum?  No, then skip it.*/
     found= found + 1                            /*bump the number of target primes.    */
     if cols<1                 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 a prime ──► list,  allow big #'s.*/
     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),  '─')
say
say 'Found '      commas(found)      title
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?;  do jc=length(?)-3  to 1  by -3; ?=insert(',', ?, jc); end;  return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: !.= 0                                      /*placeholders for primes' semaphores. */
      @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13 /*define some  low primes.             */
      !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; @.13=1 /*   "     "   "   primes' semaphores. */
                           #= 6;  sq.#= @.# ** 2 /*number of primes so far;     prime². */
                                                 /* [↓]  generate more  primes  ≤  high.*/
        do j=@.#+2  by 2  to hi                  /*find odd primes from here on.        */
        parse var   j    ''  -1  _               /*obtain the last decimal digit of  J. */
        if    _==5  then iterate;  if j// 3==0  then iterate   /*J ÷ by 5?   J ÷ by  3? */
        if j//7==0  then iterate;  if j//11==0  then iterate   /*" "  " 7?   " "  " 11? */
               do k=6  while sq.k<=j             /* [↓]  divide by the known odd primes.*/
               if j // @.k == 0  then iterate j  /*Is  J ÷ X?  Then not prime.     ___  */
               end   /*k*/                       /* [↑]  only process numbers  ≤  √ J   */
        #= #+1;    @.#= j;    sq.#= j*j;  !.j= 1 /*bump # of Ps; assign next P;  P²; P# */
        end          /*j*/;               return
/*──────────────────────────────────────────────────────────────────────────────────────*/
sumDigs: parse arg x 1 s 2 '' -1 z;   L= length(x);    if L==1  then return s;    s= s + z
                   do m=2  for L-2;   s= s + substr(x, m, 1);  end;  return s

output when using the default inputs:

 index │                         primes that are  <  5,000  and whose decimal digits sum to  25
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │        997      1,699      1,789      1,879      1,987      2,689      2,797      2,887      3,499      3,697
  11   │      3,769      3,877      3,967      4,597      4,759      4,957      4,993
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  17  primes that are  <  5,000  and whose decimal digits sum to  25

output when using the input of: 1000000 0

Found  6,198  primes that are  <  1,000,000  and whose decimal digits sum to  25

Ring

load "stdlib.ring"

see "working..." + nl
decimals(0)
row = 0
num = 0
nr = 0
numsum25 = 0
limit1 = 25
limit2 = 5000

for n = 1 to limit2
    if isprime(n)
       bool = sum25(n)
       if bool = 1
          row = row + 1
          see "" + n + " "
          if (row%5) = 0
              see nl
          ok
       ok
    ok
next

see nl + "Found " + row + " sum25 primes below 5000" + nl

time1 = clock()
see nl
row = 0

while true
      num = num + 1
      str = string(num)
      for m = 1 to len(str)
          if str[m] = 0
             loop
          ok
      next
      if isprime(num)
         bool = sum25(num)
         if bool = 1
            nr = num
            numsum25 = numsum25 + 1
          ok
      ok
      time2 = clock()
      time3 = (time2-time1)/1000/60
      if time3 > 30
         exit
      ok
end

see "There are " + numsum25 + " sum25 primes that contain no zeroes (during 30 mins)" + nl
see "The last sum25 prime found during 30 mins is: " + nr + nl
see "time = " + time3 + " mins" + nl
see "done..." + nl

func sum25(n)
     sum = 0
     str = string(n)
     for n = 1 to len(str)
         sum = sum + number(str[n])
     next
     if sum = limit1
        return 1
     ok

Output:

working...
997 1699 1789 1879 1987 
2689 2797 2887 3499 3697 
3769 3877 3967 4597 4759 
4957 4993 
Found 17 sum25 primes below 5000

There are 1753 sum25 primes that contain no zeroes (during 30 mins)
The last sum25 prime found during 30 mins is: 230929
time = 30 mins
done...

RPL

∑DIGITS is defined at Sum digits of an integer

≪ { } 799      @ 799 is the smallest integer whose digits sum equals 25, and is not prime : 799 = 47 * 17
   DO
      NEXTPRIME
      IF DUP ∑DIGITS 25 == THEN SWAP OVER + SWAP END
   UNTIL DUP 5000 > END
   DROP
≫ 'TASK' STO

Output:

1: {997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993}

Ruby

require 'prime'

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

for p in Prime.take_while { |p| p < 5000 }
    if digitSum(p) == 25 then
        print p, "  "
    end
end

Output:

997  1699  1789  1879  1987  2689  2797  2887  3499  3697  3769  3877  3967  4597  4759  4957  4993

Sidef

Simple solution:

5000.primes.grep { .sumdigits == 25 }.say

Generate such primes from digits (asymptotically faster):

func generate_from_prefix(limit, digitsum, p, base, digits, t=p) {

    var seq = [p]

    digits.each {|d|
        var num = (p*base + d)
        num <= limit    || return seq

        var sum = (t + d)
        sum <= digitsum || return seq

        seq << __FUNC__(limit, digitsum, num, base, digits, sum)\
               .grep { .is_prime }...
    }

    return seq
}

func primes_with_digit_sum(limit, digitsum = 25, base = 10, digits = @(^base)) {
    digits.grep { _ > 0 }\
          .map  { generate_from_prefix(limit, digitsum, _, base, digits)... }\
          .grep { .sumdigits(base) == digitsum }\
          .sort
}

say primes_with_digit_sum(5000)

Output:

[997, 1699, 1789, 1879, 1987, 2689, 2797, 2887, 3499, 3697, 3769, 3877, 3967, 4597, 4759, 4957, 4993]

Tcl

Library: Tcllib (Package: math::numtheory)

Could be made prettier with the staple helper proc lfilter.

package require Tcl 8.5
package require math::numtheory
namespace path ::tcl::mathop

puts [lmap x [math::numtheory::primesLowerThan 5000] {
    if {[+ {*}[split $x {}]] == 25} {set x} else continue
}]

Output:

997 1699 1789 1879 1987 2689 2797 2887 3499 3697 3769 3877 3967 4597 4759 4957 4993

Wren

Basic

Library: Wren-math

Library: Wren-fmt

import "./math" for Int
import "./fmt" for Fmt

var sumDigits = Fn.new { |n|
    var sum = 0
    while (n > 0) {
        sum = sum + (n % 10)
        n = (n/10).floor
    }
    return sum
}

var primes = Int.primeSieve(4999).where { |p| p >= 997 }
var primes25 = []
for (p in primes) {
    if (sumDigits.call(p) == 25) primes25.add(p)
}
System.print("The %(primes25.count) primes under 5,000 whose digits sum to 25 are:")
Fmt.tprint("$,6d", primes25, 6)

Output:

The 17 primes under 5,000 whose digits sum to 25 are:
   997  1,699  1,789  1,879  1,987  2,689
 2,797  2,887  3,499  3,697  3,769  3,877
 3,967  4,597  4,759  4,957  4,993

Stretch

Translation of: Go

Library: Wren-gmp

Run time is about 25.5 seconds.

import "./gmp" for Mpz
import "./fmt" for Fmt

var z = Mpz.new()

var countAll // recursive
countAll = Fn.new { |p, rem, res|
    if (rem == 0) {
        var b = p[-1]
        if ("1379".contains(b)) {
            if (z.setStr(p).probPrime(15) > 0) res = res + 1
        }
    } else {
        for (i in 1..rem.min(9)) {
            res = countAll.call(p + i.toString, rem - i, res)
        }
    }
    return res
}

var n = countAll.call("", 25, 0)
Fmt.print("There are $,d primes whose digits sum to 25 and include no zeros.", n)

Output:

There are 1,525,141 primes whose digits sum to 25 and include no zeros.

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 sum of digits in N
int  N, Sum;
[Sum:= 0;
repeat  N:= N/10;
        Sum:= Sum + rem(0);
until   N=0;
return Sum;
];

int Cnt, N;
[Cnt:= 0;
for N:= 2 to 5000-1 do
    if IsPrime(N) & SumDigits(N) = 25 then
        [IntOut(0, N);
        Cnt:= Cnt+1;
        if rem(Cnt/5) then ChOut(0, 9\tab\) else CrLf(0);
        ];
CrLf(0);
IntOut(0, Cnt);
Text(0, " primes whose sum of digits is 25.
");
]

Output:

997     1699    1789    1879    1987
2689    2797    2887    3499    3697
3769    3877    3967    4597    4759
4957    4993    
17 primes whose sum of digits is 25.

Zig

Translation of: Nim

const std = @import("std");

fn isPrime(n: u64) bool {
    if (n < 2) return false;
    if (n % 2 == 0) return n == 2;
    if (n % 3 == 0) return n == 3;
    var d: u64 = 5;
    while (d * d <= n) {
        if (n % d == 0) return false;
        d += 2;
        if (n % d == 0) return false;
        d += 4;
    }
    return true;
}

fn digitSum(n_: u64) u16 {
    var n = n_; // parameters are immutable, copy to var
    var sum: u16 = 0;
    while (n != 0) {
        sum += @truncate(u16, n % 10);
        n /= 10;
    }
    return sum;
}

pub fn main() !void {
    var arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);
    defer arena.deinit();

    var result = std.ArrayList(u64).init(arena.allocator());
    defer result.deinit();

    {
        var n: u64 = 3;
        while (n <= 5000) : (n += 2)
            if (digitSum(n) == 25 and isPrime(n))
                try result.append(n);
    }

    const stdout = std.io.getStdOut().writer();
    for (result.items, 0..) |n, i|
        _ = try stdout.print("{d:4}{s}", .{ n, if ((i + 1) % 6 == 0) "\n" else " " });
}

Output:

 997 1699 1789 1879 1987 2689
2797 2887 3499 3697 3769 3877
3967 4597 4759 4957 4993

Stretch Goal

Functional

Idiomatic

Stretch goal

Mathematica /Wolfram Language

Task

Stretch goal

Stretch goal

Basic

Stretch