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A magnanimous number is an integer where there is no place in the number where a + (plus sign) could be added between any two digits to give a non-prime sum.

E.G.

6425 is a magnanimous number. 6 + 425 == 431 which is prime; 64 + 25 == 89 which is prime; 642 + 5 == 647 which is prime.

3538 is not a magnanimous number. 3 + 538 == 541 which is prime; 35 + 38 == 73 which is prime; but 353 + 8 == 361 which is not prime.

Traditionally the single digit numbers 0 through 9 are included as magnanimous numbers as there is no place in the number where you can add a plus between two digits at all. (Kind of weaselly but there you are...) Except for the actual value 0, leading zeros are not permitted. Internal zeros are fine though, 1001 -> 1 + 001 (prime), 10 + 01 (prime) 100 + 1 (prime).

There are only 571 known magnanimous numbers. It is strongly suspected, though not rigorously proved, that there are no magnanimous numbers above 97393713331910, the largest one known.

Task

Write a routine (procedure, function, whatever) to find magnanimous numbers.

Use that function to find and display, here on this page the first 45 magnanimous numbers.

Use that function to find and display, here on this page the 241st through 250th magnanimous numbers.

Stretch: Use that function to find and display, here on this page the 391st through 400th magnanimous numbers

See also

OEIS:A252996 - Magnanimous numbers: numbers such that the sum obtained by inserting a "+" anywhere between two digits gives a prime.

ALGOL 68

<lang algol68>BEGIN # find some magnanimous numbers - numbers where inserting a + between any #

     # digits ab=nd evaluatinf the sum results in a prime in all cases         #
   # returns the first n magnanimous numbers                                   #
   #         uses global sieve prime which must include 0 and be large enough  #
   #         for all possible sub-sequences of digits                          #
   OP MAGNANIMOUS = ( INT n )[]INT:
      BEGIN
           [ 1 : n ]INT result;
           INT          m count := 0;
           FOR i FROM 0 WHILE m count < n DO
               # split the number into pairs of digit seuences and check the sums of the pairs are all prime #
               INT  divisor   := 1;
               BOOL all prime := TRUE;
               WHILE divisor *:= 10;
                     IF   INT front = i OVER divisor;
                          front = 0
                     THEN FALSE
                     ELSE all prime := prime[ front + ( i MOD divisor ) ]
                     FI
               DO SKIP OD;
               IF all prime THEN result[ m count +:= 1 ] := i FI
           OD;
           result
      END; # MAGNANIMPUS #
   # prints part of a seuence of magnanimous numbers #
   PROC print magnanimous = ( []INT m, INT first, INT last, STRING legend )VOID:
        BEGIN
            print( ( legend, ":", newline ) );
            FOR i FROM first TO last DO print( ( " ", whole( m[ i ], 0 ) ) ) OD;
            print( ( newline ) )
        END ; # print magnanimous #
   # we assume the first 400 magnanimous numbers will be in 0 .. 1 000 000 #
   # so we will need a sieve of 0 up to 99 999 + 9 #
   [ 0 : 99 999 + 9 ]BOOL prime;
   prime[ 0 ] := prime[ 1 ] := FALSE; prime[ 2 ] := TRUE;
   FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE  OD;
   FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
   FOR i FROM 3 BY 2 TO ENTIER sqrt( UPB prime ) DO
       IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI
   OD;
   # construct the sequence of magnanimous numbers #
   []INT m = MAGNANIMOUS 400;
   print magnanimous( m,   1,  45, "First 45 magnanimous numbers" );
   print magnanimous( m, 241, 250, "Magnanimous numbers 241-250"  );
   print magnanimous( m, 391, 400, "Magnanimous numbers 391-400"  )

END</lang>

Output:

First 45 magnanimous numbers:
 0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110
Magnanimous numbers 241-250:
 17992 19972 20209 20261 20861 22061 22201 22801 22885 24407
Magnanimous numbers 391-400:
 486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

ALGOL W

<lang algolw>begin

   % find some Magnanimous numbers - numbers where inserting a "+" between  %
   % any two of the digits and evaluating the sum results in a prime number %
   % implements the sieve of Eratosthenes                                   %
   procedure sieve( logical array s ( * ); integer value n ) ;
   begin
       % start with everything flagged as prime                             % 
       for i := 1 until n do s( i ) := true;
       % sieve out the non-primes                                           %
       s( 1 ) := false;
       for i := 2 until truncate( sqrt( n ) ) do begin
           if s( i ) then for p := i * i step i until n do s( p ) := false
       end for_i ;
   end sieve ;
   % construct an array of magnanimous numbers using the isPrime sieve      %
   procedure findMagnanimous ( logical array magnanimous, isPrime ( * ) ) ;
   begin
       % 1 digit magnanimous numbers                                        %
       for i :=  0 until 9               do magnanimous( i ) := true;
       % initially, the other magnanimous numbers are unknown               %
       for i := 10 until MAGNANIMOUS_MAX do magnanimous( i ) := false;
       % 2 & 3 digit magnanimous numbers                                    %
       for d1 := 1 until 9 do begin
           for d2 := 0 until 9 do begin
               if isPrime( d1 + d2 ) then magnanimous( ( d1 * 10 ) + d2 ) := true
           end for_d2 ;
           for d23 := 0 until 99 do begin
               if isPrime( d1 + d23 ) then begin
                   integer d12, d3;
                   d3  := d23 rem 10;
                   d12 := ( d1 * 10 ) + ( d23 div 10 );
                   if isPrime( d12 + d3 ) then magnanimous( ( d12 * 10 ) + d3 ) := true
               end if_isPrime_d1_plus_d23
           end for_d23
       end for_d1 ;
       % 4 & 5 digit magnanimous numbers                                    %
       for d12 := 10 until 99 do begin
           for d34 := 0 until 99 do begin
               if isPrime( d12 + d34 ) then begin
                   integer d123, d4;
                   d123 := ( d12 * 10 ) + ( d34 div 10 );
                   d4   := d34 rem 10;
                   if isPrime( d123 + d4 ) then begin
                       integer d1, d234;
                       d1   := d12 div 10;
                       d234 := ( ( d12 rem 10 ) * 100 ) + d34;
                       if  isPrime( d1 + d234 ) then magnanimous( ( d12 * 100 ) + d34 ) := true
                   end if_isPrime_d123_plus_d4
               end if_isPrime_d12_plus_d34
           end for_d34 ;
           for d345 := 0 until 999 do begin
               if isPrime( d12 + d345 ) then begin
                   integer d123, d45;
                   d123 := ( d12 * 10 ) + ( d345 div 100 );
                   d45  := d345 rem 100;
                   if isPrime( d123 + d45 ) then begin
                       integer d1234, d5;
                       d1234 := ( d123 * 10 ) + ( d45 div 10 );
                       d5    := d45 rem 10;
                       if isPrime( d1234 + d5 ) then begin
                           integer d1, d2345;
                           d1    := d12 div 10;
                           d2345 := ( ( d12 rem 10 ) * 1000 ) + d345;
                           if isPrime( d1 + d2345 ) then magnanimous( ( d12 * 1000 ) + d345 ) := true
                       end if_isPrime_d1234_plus_d5
                   end if_isPrime_d123_plus_d45
               end if_isPrime_d12_plus_d345
           end for_d234
       end for_d12 ;
       % find 6 digit magnanimous numbers                                   %
       for d123 := 100 until 999 do begin
           for d456 := 0 until 999 do begin
               if isPrime( d123 + d456 ) then begin
                   integer d1234, d56;
                   d1234 := ( d123 * 10 ) + ( d456 div 100 );
                   d56   := d456 rem 100;
                   if isPrime( d1234 + d56 ) then begin
                       integer d12345, d6;
                       d12345 := ( d1234 * 10 ) + ( d56 div 10 );
                       d6     := d56 rem 10;
                       if isPrime( d12345 + d6 ) then begin
                           integer d12, d3456;
                           d12   := d123 div 10;
                           d3456 := ( ( d123 rem 10 ) * 1000 ) + d456;
                           if isPrime( d12 + d3456 ) then begin
                               integer d1, d23456;
                               d1     := d12 div 10;
                               d23456 := ( ( d12 rem 10 ) * 10000 ) + d3456;
                               if isPrime( d1 + d23456 ) then magnanimous( ( d123 * 1000 ) + d456 ) := true
                           end if_isPrime_d12_plus_d3456
                       end if_isPrime_d12345_plus_d6
                   end if_isPrime_d1234_plus_d56
               end if_isPrime_d123_plus_d456
           end for_d456
       end for_d123
   end findMagnanimous ;
   % we look for magnanimous numbers with up to 6 digits, so we need to     %
   % check for primes up to 99999 + 9 = 100008                              %
   integer PRIME_MAX, MAGNANIMOUS_MAX;
   PRIME_MAX       :=  100008;
   MAGNANIMOUS_MAX := 1000000;
   begin
       logical array magnanimous ( 0 :: MAGNANIMOUS_MAX );
       logical array isPrime     ( 1 :: PRIME_MAX       );
       integer mPos;
       integer lastM;
       sieve( isPrime, PRIME_MAX );
       findMagnanimous( magnanimous, isPrime );
       % show some of the magnanimous numbers                               %
       lastM := mPos  := 0;
       i_w := 3; s_w := 1; % output formatting                              %
       for i := 0 until MAGNANIMOUS_MAX do begin
           if magnanimous( i ) then begin
               mPos  := mPos + 1;
               lastM := i;
               if      mPos =   1 then begin
                   write( "Magnanimous numbers 1-45:" );
                   write( i )
                   end
               else if mPos < 46 then begin
                   if mPos rem 15 = 1 then write( i )
                                      else writeon( i )
                   end
               else if mPos = 241 then begin
                   write( "Magnanimous numbers 241-250:" );
                   write( i )
                   end
               else if mPos > 241 and mPos <= 250 then writeon( i )
               else if mPos = 391 then begin
                   write( "Magnanimous numbers 391-400:" );
                   write( i )
                   end
               else if mPos > 391 and mPos <= 400 then writeon( i )
           end if_magnanimous_i
       end for_i ;
       i_w := 1; s_w := 0;
       write( "Last magnanimous number found: ", mPos, " = ", lastM )
   end

end.</lang>

Output:

Magnanimous numbers 1-45:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110
Magnanimous numbers 241-250:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407
Magnanimous numbers 391-400:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081
Last magnanimous number found: 434 = 999994

AWK

syntax: GAWK -f MAGNANIMOUS_NUMBERS.AWK
converted from C

BEGIN {

   magnanimous(1,45)
   magnanimous(241,250)
   magnanimous(391,400)
   exit(0)

} function is_magnanimous(n, p,q,r) {

   if (n < 10) { return(1) }
   for (p=10; ; p*=10) {
     q = int(n/p)
     r = n % p
     if (!is_prime(q+r)) { return(0) }
     if (q < 10) { break }
   }
   return(1)

} function is_prime(n, d) {

   d = 5
   if (n < 2) { return(0) }
   if (!(n % 2)) { return(n == 2) }
   if (!(n % 3)) { return(n == 3) }
   while (d*d <= n) {
     if (!(n % d)) { return(0) }
     d += 2
     if (!(n % d)) { return(0) }
     d += 4
   }
   return(1)

} function magnanimous(start,stop, count,i) {

   printf("%d-%d:",start,stop)
   for (i=0; count<stop; ++i) {
     if (is_magnanimous(i)) {
       if (++count >= start) {
         printf(" %d",i)
       }
     }
   }
   printf("\n")

} </lang>

Output:

1-45: 0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110
241-250: 17992 19972 20209 20261 20861 22061 22201 22801 22885 24407
391-400: 486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

C

Translation of: Go

<lang c>#include <stdio.h>

include <string.h>

typedef int bool; typedef unsigned long long ull;

define TRUE 1
define FALSE 0

/* OK for 'small' numbers. */ bool is_prime(ull n) {

   ull d;
   if (n < 2) return FALSE;
   if (!(n % 2)) return n == 2;
   if (!(n % 3)) return n == 3;
   d = 5;
   while (d * d <= n) {
       if (!(n % d)) return FALSE;
       d += 2;
       if (!(n % d)) return FALSE;
       d += 4;
   }
   return TRUE;

}

void ord(char *res, int n) {

   char suffix[3];
   int m = n % 100;
   if (m >= 4 && m <= 20) {
       sprintf(res,"%dth", n);
       return;
   }
   switch(m % 10) {
       case 1:
           strcpy(suffix, "st");
           break;
       case 2:
           strcpy(suffix, "nd");
           break;
       case 3:
           strcpy(suffix, "rd");
           break;
       default:
           strcpy(suffix, "th");
           break;
   }
   sprintf(res, "%d%s", n, suffix);

}

bool is_magnanimous(ull n) {

   ull p, q, r;
   if (n < 10) return TRUE;
   for (p = 10; ; p *= 10) {
       q = n / p;
       r = n % p;
       if (!is_prime(q + r)) return FALSE;
       if (q < 10) break;
   }
   return TRUE;

}

void list_mags(int from, int thru, int digs, int per_line) {

   ull i = 0;
   int c = 0;
   char res1[13], res2[13];
   if (from < 2) {
       printf("\nFirst %d magnanimous numbers:\n", thru);
   } else {
       ord(res1, from);
       ord(res2, thru);
       printf("\n%s through %s magnanimous numbers:\n", res1, res2);
   }
   for ( ; c < thru; ++i) {
       if (is_magnanimous(i)) {
           if (++c >= from) {
               printf("%*llu ", digs, i);
               if (!(c % per_line)) printf("\n");
           }
       }
   }

}

int main() {

   list_mags(1, 45, 3, 15);
   list_mags(241, 250, 1, 10);
   list_mags(391, 400, 1, 10);
   return 0;

}</lang>

Output:

First 45 magnanimous numbers:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20 
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56 
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110 

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407 

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

C#

<lang csharp>using System; using static System.Console;

class Program {

 static bool[] np; // not-prime array

 static void ms(long lmt) { // populates array, a not-prime is true 
   np = new bool[lmt]; np[0] = np[1] = true;
   for (long n = 2, j = 1; n < lmt; n += j, j = 2) if (!np[n])
       for (long k = n * n; k < lmt; k += n) np[k] = true; }

 static bool is_Mag(long n) { long res, rem;
   for (long p = 10; n >= p; p *= 10) {
     res = Math.DivRem (n, p, out rem);
     if (np[res + rem]) return false; } return true; }

 static void Main(string[] args) { ms(100_009); string mn;
   WriteLine("First 45{0}", mn = " magnanimous numbers:");
   for (long l = 0, c = 0; c < 400; l++) if (is_Mag(l)) {
     if (c++ < 45 || (c > 240 && c <= 250) || c > 390)
       Write(c <= 45 ? "{0,4} " : "{0,8:n0} ", l);
     if (c < 45 && c % 15 == 0) WriteLine();
     if (c == 240) WriteLine ("\n\n241st through 250th{0}", mn);
     if (c == 390) WriteLine ("\n\n391st through 400th{0}", mn); } }

}</lang>

Output:

First 45 magnanimous numbers:
   0    1    2    3    4    5    6    7    8    9   11   12   14   16   20 
  21   23   25   29   30   32   34   38   41   43   47   49   50   52   56 
  58   61   65   67   70   74   76   83   85   89   92   94   98  101  110 

241st through 250th magnanimous numbers:
  17,992   19,972   20,209   20,261   20,861   22,061   22,201   22,801   22,885   24,407 

391st through 400th magnanimous numbers:
 486,685  488,489  515,116  533,176  551,558  559,952  595,592  595,598  600,881  602,081

C++

<lang cpp>#include <iomanip>

include <iostream>

bool is_prime(unsigned int n) {

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

}

bool is_magnanimous(unsigned int n) {

   for (unsigned int p = 10; n >= p; p *= 10) {
       if (!is_prime(n % p + n / p))
           return false;
   }
   return true;

}

int main() {

   unsigned int count = 0, n = 0;
   std::cout << "First 45 magnanimous numbers:\n";
   for (; count < 45; ++n) {
       if (is_magnanimous(n)) {
           if (count > 0)
               std::cout << (count % 15 == 0 ? "\n" : ", ");
           std::cout << std::setw(3) << n;
           ++count;
       }
   }
   std::cout << "\n\n241st through 250th magnanimous numbers:\n";
   for (unsigned int i = 0; count < 250; ++n) {
       if (is_magnanimous(n)) {
           if (count++ >= 240) {
               if (i++ > 0)
                   std::cout << ", ";
               std::cout << n;
           }
       }
   }
   std::cout << "\n\n391st through 400th magnanimous numbers:\n";
   for (unsigned int i = 0; count < 400; ++n) {
       if (is_magnanimous(n)) {
           if (count++ >= 390) {
               if (i++ > 0)
                   std::cout << ", ";
               std::cout << n;
           }
       }
   }
   std::cout << '\n';
   return 0;

}</lang>

Output:

First 45 magnanimous numbers:
  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  11,  12,  14,  16,  20
 21,  23,  25,  29,  30,  32,  34,  38,  41,  43,  47,  49,  50,  52,  56
 58,  61,  65,  67,  70,  74,  76,  83,  85,  89,  92,  94,  98, 101, 110

241st through 250th magnanimous numbers:
17992, 19972, 20209, 20261, 20861, 22061, 22201, 22801, 22885, 24407

391st through 400th magnanimous numbers:
486685, 488489, 515116, 533176, 551558, 559952, 595592, 595598, 600881, 602081

F#

The function

This task uses Extensible Prime Generator (F#) <lang fsharp> // Generate Magnanimous numbers. Nigel Galloway: March 20th., 2020 let rec fN n g = match (g/n,g%n) with

                 (0,_)                    -> true
                |(α,β) when isPrime (α+β) -> fN (n*10) g
                |_                        -> false

let Magnanimous = let Magnanimous = fN 10 in seq{yield! {0..9}; yield! Seq.initInfinite id |> Seq.skip 10 |> Seq.filter Magnanimous} </lang>

The Tasks

First 45

<lang fsharp> Magnanimous |> Seq.take 45 |> Seq.iter (printf "%d "); printfn "" </lang>

Output:

0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110

Magnanimous[241] to Magnanimous[250]

<lang fsharp> Magnanimous |> Seq.skip 240 |> Seq.take 10 |> Seq.iter (printf "%d "); printfn "";; </lang>

Output:

17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

Magnanimous[391] to Magnanimous[400]

<lang fsharp> Magnanimous |> Seq.skip 390 |> Seq.take 10 |> Seq.iter (printf "%d "); printfn "";; </lang>

Output:

486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Factor

Translation of: Julia

Works with: Factor version 0.99 2020-01-23

<lang factor>USING: grouping io kernel lists lists.lazy math math.functions math.primes math.ranges prettyprint sequences ;

magnanimous? ( n -- ? )

   dup 10 < [ drop t ] [
       dup log10 >integer [1,b] [ 10^ /mod + prime? not ] with
       find nip >boolean not
   ] if ;

magnanimous ( n -- seq )

   0 lfrom [ magnanimous? ] lfilter ltake list>array ;

show ( seq from to -- ) rot subseq 15 group simple-table. nl ;

400 magnanimous [ "First 45 magnanimous numbers" print 0 45 show ] [ "241st through 250th magnanimous numbers" print 240 250 show ] [ "391st through 400th magnanimous numbers" print 390 400 show ] tri</lang>

Output:

First 45 magnanimous numbers
0  1  2  3  4  5  6  7  8  9  11 12 14 16  20
21 23 25 29 30 32 34 38 41 43 47 49 50 52  56
58 61 65 67 70 74 76 83 85 89 92 94 98 101 110

241st through 250th magnanimous numbers
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

391st through 400th magnanimous numbers
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Go

<lang go>package main

import "fmt"

// OK for 'small' numbers. func isPrime(n uint64) bool {

   switch {
   case n < 2:
       return false
   case n%2 == 0:
       return n == 2
   case n%3 == 0:
       return n == 3
   default:
       d := uint64(5)
       for d*d <= n {
           if n%d == 0 {
               return false
           }
           d += 2
           if n%d == 0 {
               return false
           }
           d += 4
       }
       return true
   }

}

func ord(n int) string {

   m := n % 100
   if m >= 4 && m <= 20 {
       return fmt.Sprintf("%dth", n)
   }
   m %= 10
   suffix := "th"
   if m < 4 {
       switch m {
       case 1:
           suffix = "st"
       case 2:
           suffix = "nd"
       case 3:
           suffix = "rd"
       }
   }
   return fmt.Sprintf("%d%s", n, suffix)

}

func isMagnanimous(n uint64) bool {

   if n < 10 {
       return true
   }
   for p := uint64(10); ; p *= 10 {
       q := n / p
       r := n % p
       if !isPrime(q + r) {
           return false
       }
       if q < 10 {
           break
       }
   }
   return true

}

func listMags(from, thru, digs, perLine int) {

   if from < 2 {
       fmt.Println("\nFirst", thru, "magnanimous numbers:")
   } else {
       fmt.Printf("\n%s through %s magnanimous numbers:\n", ord(from), ord(thru))
   }
   for i, c := uint64(0), 0; c < thru; i++ {
       if isMagnanimous(i) {
           c++
           if c >= from {
               fmt.Printf("%*d ", digs, i)
               if c%perLine == 0 {
                   fmt.Println()
               }
           }
       }
   }

}

func main() {

   listMags(1, 45, 3, 15)
   listMags(241, 250, 1, 10)
   listMags(391, 400, 1, 10)

}</lang>

Output:

First 45 magnanimous numbers:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20 
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56 
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110 

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407 

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Java

<lang java> import java.util.ArrayList; import java.util.List;

public class MagnanimousNumbers {

   public static void main(String[] args) {
       runTask("Find and display the first 45 magnanimous numbers.", 1, 45);
       runTask("241st through 250th magnanimous numbers.", 241, 250);
       runTask("391st through 400th magnanimous numbers.", 391, 400);
   }
   
   private static void runTask(String message, int startN, int endN) {
       int count = 0;
       List<Integer> nums = new ArrayList<>();
       for ( int n = 0 ; count < endN ; n++ ) {
           if ( isMagnanimous(n) ) {
               nums.add(n);
               count++;
           }
       }
       System.out.printf("%s%n", message);
       System.out.printf("%s%n%n", nums.subList(startN-1, endN));
   }
   
   private static boolean isMagnanimous(long n) {
       if ( n >= 0 && n <= 9 ) {
           return true;
       }
       long q = 11;
       for ( long div = 10 ; q >= 10 ; div *= 10 ) {
           q = n / div;
           long r = n % div;
           if ( ! isPrime(q+r) ) {
               return false;
           }
       }
       return true;
   }
   
   private static final int MAX = 100_000;
   private static final boolean[] primes = new boolean[MAX];
   private static boolean SIEVE_COMPLETE = false;
   
   private static final boolean isPrimeTrivial(long test) {
       if ( ! SIEVE_COMPLETE ) {
           sieve();
           SIEVE_COMPLETE = true;
       }
       return primes[(int) test];
   }
   
   private static final void sieve() {
       //  primes
       for ( int i = 2 ; i < MAX ; i++ ) {
           primes[i] = true;            
       }
       for ( int i = 2 ; i < MAX ; i++ ) {
           if ( primes[i] ) {
               for ( int j = 2*i ; j < MAX ; j += i ) {
                   primes[j] = false;
               }
           }
       }
   }

   //  See http://primes.utm.edu/glossary/page.php?sort=StrongPRP
   public static final boolean isPrime(long testValue) {
       if ( testValue == 2 ) return true;
       if ( testValue % 2 == 0 ) return false;
       if ( testValue <= MAX ) return isPrimeTrivial(testValue);
       long d = testValue-1;
       int s = 0;
       while ( d % 2 == 0 ) {
           s += 1;
           d /= 2;
       }
       if ( testValue < 1373565L ) {
           if ( ! aSrp(2, s, d, testValue) ) {
               return false;
           }
           if ( ! aSrp(3, s, d, testValue) ) {
               return false;
           }
           return true;
       }
       if ( testValue < 4759123141L ) {
           if ( ! aSrp(2, s, d, testValue) ) {
               return false;
           }
           if ( ! aSrp(7, s, d, testValue) ) {
               return false;
           }
           if ( ! aSrp(61, s, d, testValue) ) {
               return false;
           }
           return true;
       }
       if ( testValue < 10000000000000000L ) {
           if ( ! aSrp(3, s, d, testValue) ) {
               return false;
           }
           if ( ! aSrp(24251, s, d, testValue) ) {
               return false;
           }
           return true;
       }
       //  Try 5 "random" primes
       if ( ! aSrp(37, s, d, testValue) ) {
           return false;
       }
       if ( ! aSrp(47, s, d, testValue) ) {
           return false;
       }
       if ( ! aSrp(61, s, d, testValue) ) {
           return false;
       }
       if ( ! aSrp(73, s, d, testValue) ) {
           return false;
       }
       if ( ! aSrp(83, s, d, testValue) ) {
           return false;
       }
       //throw new RuntimeException("ERROR isPrime:  Value too large = "+testValue);
       return true;
   }

   private static final boolean aSrp(int a, int s, long d, long n) {
       long modPow = modPow(a, d, n);
       //System.out.println("a = "+a+", s = "+s+", d = "+d+", n = "+n+", modpow = "+modPow);
       if ( modPow == 1 ) {
           return true;
       }
       int twoExpR = 1;
       for ( int r = 0 ; r < s ; r++ ) {
           if ( modPow(modPow, twoExpR, n) == n-1 ) {
               return true;
           }
           twoExpR *= 2;
       }
       return false;
   }
   
   private static final long SQRT = (long) Math.sqrt(Long.MAX_VALUE);
   
   public static final long modPow(long base, long exponent, long modulus) {
       long result = 1;
       while ( exponent > 0 ) {
           if ( exponent % 2 == 1 ) {
               if ( result > SQRT || base > SQRT ) {
                   result = multiply(result, base, modulus);
               }
               else {
                   result = (result * base) % modulus;
               }
           }
           exponent >>= 1;
           if ( base > SQRT ) {
               base = multiply(base, base, modulus);
           }
           else {
               base = (base * base) % modulus;
           }
       }
       return result;
   }

   //  Result is a*b % mod, without overflow.
   public static final long multiply(long a, long b, long modulus) {
       long x = 0;
       long y = a % modulus;
       long t;
       while ( b > 0 ) {
           if ( b % 2 == 1 ) {
               t = x + y;
               x = (t > modulus ? t-modulus : t);
           }
           t = y << 1;
           y = (t > modulus ? t-modulus : t);
           b >>= 1;
       }
       return x % modulus;
   }

} </lang>

Output:

Find and display the first 45 magnanimous numbers.
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101, 110]

241st through 250th magnanimous numbers.
[17992, 19972, 20209, 20261, 20861, 22061, 22201, 22801, 22885, 24407]

391st through 400th magnanimous numbers.
[486685, 488489, 515116, 533176, 551558, 559952, 595592, 595598, 600881, 602081]

J

   write_sum_expressions=: ([: }: ]\) ,"1 '+' ,"1 ([: }. ]\.)   NB. combine prefixes with suffixes
   interstitial_sums=: ".@write_sum_expressions@":
   primeQ=: 1&p:
   magnanimousQ=: 1:`([: *./ [: primeQ interstitial_sums)@.(>&9)
   A=: (#~ magnanimousQ&>) i.1000000       NB. filter 1000000 integers
   #A
434

   strange=: ({. + [: i. -~/)@:(_1 0&+) NB. produce index ranges for output
   I=: _2 <@strange\ 1 45 241 250 391 400
   I (":@:{~ >)~"0 _ A
0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407                                                                   
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

jq

Works with: jq

Works with gojq, the Go implementation of jq

For a suitable definition of `is_prime`, see Erdős-primes#jq.

Preliminaries <lang jq># To take advantage of gojq's arbitrary-precision integer arithmetic: def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);

def divrem($x; $y):

 [$x/$y|floor, $x % $y];

</lang> The Task <lang jq> def ismagnanimous:

 . as $n
 | if $n < 10 then true
   else first(range( 1; tostring|length) as $i

| divrem($n; (10|power($i))) as [$q, $r]

              | if ($q + $r) | is_prime == false then 0 else empty end)
        // true
   | . == true
   end;

An unbounded stream ...

def magnanimous:

 range(0; infinite)
 | select(ismagnanimous);

[limit(400; magnanimous)] | "First 45 magnanimous numbers:", .[:45],

 "\n241st through 250th magnanimous numbers:", .[241:251],
 "\n391st through 400th magnanimous numbers:", .[391:]</lang>

Output:

First 45 magnanimous numbers:
[0,1,2,3,4,5,6,7,8,9,11,12,14,16,20,21,23,25,29,30,32,34,38,41,43,47,49,50,52,56,58,61,65,67,70,74,76,83,85,89,92,94,98,101,110]

241st through 250th magnanimous numbers:
[19972,20209,20261,20861,22061,22201,22801,22885,24407,26201]

391st through 400th magnanimous numbers:
[488489,515116,533176,551558,559952,595592,595598,600881,602081]

Julia

<lang julia>using Primes

function ismagnanimous(n)

   n < 10 && return true
   for i in 1:ndigits(n)-1
       q, r = divrem(n, 10^i)
       !isprime(q + r) && return false
   end
   return true

end

function magnanimous(N)

   mvec, i = Int[], 0
   while length(mvec) < N
       if ismagnanimous(i)
           push!(mvec, i)
       end
       i += 1
   end
   return mvec

end

const mag400 = magnanimous(400) println("First 45 magnanimous numbers:\n", mag400[1:24], "\n", mag400[25:45]) println("\n241st through 250th magnanimous numbers:\n", mag400[241:250]) println("\n391st through 400th magnanimous numbers:\n", mag400[391:400])

</lang>

Output:

First 45 magnanimous numbers:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41]
[43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101, 110]

241st through 250th magnanimous numbers:
[17992, 19972, 20209, 20261, 20861, 22061, 22201, 22801, 22885, 24407]

391st through 400th magnanimous numbers:
[486685, 488489, 515116, 533176, 551558, 559952, 595592, 595598, 600881, 602081]

Mathematica/Wolfram Language

<lang Mathematica>Clear[MagnanimousNumberQ] MagnanimousNumberQ[Alternatives @@ Range[0, 9]] = True; MagnanimousNumberQ[n_Integer] := AllTrue[Range[IntegerLength[n] - 1], PrimeQ[Total[FromDigits /@ TakeDrop[IntegerDigits[n], #]]] &] sel = Select[Range[0, 1000000], MagnanimousNumberQ]; sel;; 45 sel241 ;; 250 sel391 ;; 400</lang>

Output:

{0,1,2,3,4,5,6,7,8,9,11,12,14,16,20,21,23,25,29,30,32,34,38,41,43,47,49,50,52,56,58,61,65,67,70,74,76,83,85,89,92,94,98,101,110}
{17992,19972,20209,20261,20861,22061,22201,22801,22885,24407}
{486685,488489,515116,533176,551558,559952,595592,595598,600881,602081}

Nim

<lang Nim>func isPrime(n: Natural): bool =

 if n < 2: return
 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 isMagnanimous(n: Natural): bool =

 var p = 10
 while true:
   let a = n div p
   let b = n mod p
   if a == 0: break
   if not isPrime(a + b): return false
   p *= 10
 return true

iterator magnanimous(): (int, int) =

 var n, count = 0
 while true:
   if n.isMagnanimous:
     inc count
     yield (count, n)
   inc n

for (i, n) in magnanimous():

 if i in 1..45:
   if i == 1: stdout.write "First 45 magnanimous numbers:\n  "
   stdout.write n, if i == 45: '\n' else: ' '

 elif i in 241..250:
   if i == 241: stdout.write "\n241st through 250th magnanimous numbers:\n  "
   stdout.write n, if i == 250: "\n" else: "  "

 elif i in 391..400:
   if i == 391: stdout.write "\n391st through 400th magnanimous numbers:\n  "
   stdout.write n, if i == 400: "\n" else: "  "

 elif i > 400:
   break</lang>

Output:

First 45 magnanimous numbers:
  0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110

241st through 250th magnanimous numbers:
  17992  19972  20209  20261  20861  22061  22201  22801  22885  24407

391st through 400th magnanimous numbers:
  486685  488489  515116  533176  551558  559952  595592  595598  600881  602081

Pascal

Works with: Free Pascal

Version nearly like on Talk. Generating the sieve for primes takes most of the time.
On TIO.RUN found all til 569 84448000009 in 19.171 s <lang pascal>program Magnanimous; //Magnanimous Numbers //algorithm find only numbers where all digits are even except the last //or where all digits are odd except the last //so 1,11,20,101,1001 will not be found //starting at 100001 "1>"+x"0"+"1" is not prime because of 1001 not prime {$IFDEF FPC}

 {$MODE DELPHI}
 {$Optimization ON}
 {$CODEALIGN proc=16}

{$ELSE}

 {$APPTYPE CONSOLE}

{$ENDIF} {$DEFINE USE_GMP} uses

 //strUtils, // commatize Numb2USA
 {$IFDEF USE_GMP}  gmp,{$ENDIF}
 SysUtils;

const

 MaxLimit = 100*1000*1000 +10;// 1e8  == MAXHIGHIDX = 7 
 MAXHIGHIDX = 11;

type

  tprimes = array of byte;
  tBaseType = word;
  tpBaseType = pWord;
  tBase =array[0..31] of tBaseType;

  tNumType = NativeUint;
  tSplitNum  =array[0..15] of tNumType;
  tMagList = array[0..1000] of Uint64;

var

 {$ALIGN 32}
 dgtBase5,
 dgtEvenBase10,
 dgtOddBase10: tbase;
 MagList : tMagList;
 primes : tprimes;
 {$IFDEF USE_GMP} z : mpz_t;gmp_count :NativeUint;{$ENDIF}
 pPrimes0 : pByte;
 T0: int64;
 HighIdx,lstIdx, cnt,num,MagIdx: NativeUint;

 procedure InsertSort(pMag:pUint64; Left, Right : NativeInt );
 var
   I, J: NativeInt;
   Pivot : Uint64;
 begin
   for i:= 1 + Left to Right do
   begin
     Pivot:= pMag[i];
     j:= i - 1;
     while (j >= Left) and (pMag[j] > Pivot) do
     begin
       pMag[j+1]:=pMag[j];
     Dec(j);
   end;
   pMag[j+1]:= pivot;
 end;

end;

function isprime(n: NativeUint):boolean; var

 k,flipflop: NativeUint;

Begin

 if Not(odd(n)) then
   EXIT(false);
 if n mod 3 = 0 then
   EXIT(false);
 k := 5;
 flipflop := 2;
 while k*k<=n do
 Begin
   if n mod k = 0 then
     EXIT(false);
   inc(k,flipflop);
   flipflop := 6-flipflop;
 end;
 EXIT(true);

end;

 procedure InitPrimes;
 const
   smallprimes :array[0..5] of byte = (2,3,5,7,11,13);
 var
   pPrimes : pByte;
   p,i,j,l : NativeUint;
 begin
   l := 1;
   for j := 0 to High(smallprimes) do
     l*= smallprimes[j];
   //scale primelimit to be multiple of l
   i :=((MaxLimit-1) DIV l+1)*l+1;//+1 should suffice
   setlength(primes,i);
   pPrimes := @primes[0];

   for j := 0 to High(smallprimes) do
   begin
     p := smallprimes[j];
     i := p;
     if j <> 0 then
       p +=p;
     while i <= l do
     begin
       pPrimes[i] := 1;
       inc(i,p)
     end;
   end;
   //turn the prime wheel
   for p := length(primes) div l -1 downto 1 do
     move(pPrimes[1],pPrimes[p*l+1],l);

   l := High(primes);
   //reinsert smallprimes
   for j := 0 to High(smallprimes) do
     pPrimes[smallprimes[j]] := 0;
   pPrimes[1]:=1;
   pPrimes[0]:=1;

   p := smallprimes[High(smallprimes)];
   repeat
     repeat
       inc(p)
     until pPrimes[p] = 0;
     j :=  l div p;
     while (pPrimes[j]<> 0) AND (j>=p) do
       dec(j);
     if j<p then
       BREAK;
     //delta  going downwards no factor 2,3 :-2 -4 -2 -4
     i := (j+1) mod 6;
     if i = 0 then
       i :=4;
     repeat
       while (pPrimes[j]<> 0) AND (j>=p) do
       begin
         dec(j,i);
         i := 6-i;
       end;
       if j<p then
         BREAK;
       pPrimes[j*p] := 1;
       dec(j,i);
       i := 6-i;
     until j<p;
   until false;

   pPrimes0 := pPrimes;
 end;

 procedure OutBase5;
 var
   pb: tpBaseType;
   i : NativeUint;
 begin
   pb:= @dgtBase5[0];
   write(num:15);
   for i := HighIdx downto 0 do
     write(pB[i]:2);
   write(#13);
 end;

 function IncDgtBase5:nativeUint;
 var
   pb: tpBaseType;
   num: nativeint;
 begin
   pb:= @dgtBase5[0];
   result := 0;
   repeat
     num := pb[result] + 1;
     if num < 5 then
     begin
       pb[result] := num;
       break;
     end;
     pb[result] := 0;
     Inc(result);
   until False;
   if HighIdx < result then
   begin
     HighIdx := result;
     pb[result] := 0;
   end;
 end;

 procedure CnvEvenBase10(lastIdx:NativeInt);
 var
   pdgt : tpBaseType;
   idx: nativeint;
 begin
   pDgt := @dgtEvenBase10[0];
   for idx := lastIdx downto 1 do
     pDgt[idx] := 2 * dgtBase5[idx];
   pDgt[0] := 2 * dgtBase5[0]+1;
 end;

 procedure CnvOddBase10(lastIdx:NativeInt);
 var
   pdgt : tpBaseType;
   idx: nativeint;
 begin
   pDgt := @dgtOddBase10[0];
   for idx := lastIdx downto 1 do
     pDgt[idx] := 2 * dgtBase5[idx] + 1;
   pDgt[0] := 2 * dgtBase5[0];
 end;

 function Base10toNum(var dgtBase10: tBase):NativeUint;
 var
   i : NativeInt;
 begin
   Result := 0;
   for i := HighIdx downto 0 do
     Result := Result * 10 + dgtBase10[i];
 end;

 procedure CheckMagn(var dgtBase10: tBase);
 //split number into sum of all "partitions" of digits
 //check if sum is always prime
 //1234 -> 1+234,12+34 ;123+4
 var
   LowSplitNum :tSplitNum;
   i,fac,n: NativeInt;
   isMagn : boolean;
 Begin
   n := 0;
   fac := 1;
   For i := 0 to HighIdx-1 do
   begin
     n := fac*dgtBase10[i]+n;
     fac *=10;
     LowSplitNum[HighIdx-1-i] := n;
   end;

   n := 0;
   fac := HighIdx;
   isMagn := true;

   For i := 0 to fac-1 do
   begin
     //n = HighSplitNum[i]
     n := n*10+dgtBase10[fac-i];
     LowSplitNum[i] += n;
     //test if not isMagn as soon as possible
     if LowSplitNum[i]<=MAXLIMIT then
     begin
       isMagn := isMagn AND (pPrimes0[LowSplitNum[i]] = 0);
       if NOT(isMagn) then
         EXIT;
     end;
   end;
   {$IFDEF USE_GMP}
   For i := 0 to fac-1 do
   begin
     n := LowSplitNum[i];
     if n >MAXLIMIT then
     Begin
       mpz_set_ui(z,n);
       gmp_count +=1;
       isMagn := isMagn AND (mpz_probab_prime_p(z,1) >0);
       if NOT(isMagn) then
         EXIT;
     end;
   end;
  {$ENDIF}
   //insert magnanimous numbers
   num := Base10toNum(dgtBase10);
   MagList[MagIdx] := num;
   inc(MagIdx);
   //OutBase5;
 end;

BEGIN

 {$IFDEF USE_GMP}mpz_init_set_ui(z,0);{$ENDIF}
 T0 := Gettickcount64;
 InitPrimes;
 T0 -= Gettickcount64;
 writeln('getting primes ',-T0 / 1000: 0: 3, ' s');
 T0 := Gettickcount64;
 fillchar(dgtBase5,SizeOf(dgtBase5),#0);
 fillchar(dgtEvenBase10,SizeOf(dgtEvenBase10),#0);
 fillchar(dgtOddBase10,SizeOf(dgtOddBase10),#0);

//Magnanimous Numbers that can not be found by this algorithm

 MagIdx := 0;
 MagList[MagIdx] := 1;inc(MagIdx);
 MagList[MagIdx] := 11;inc(MagIdx);
 MagList[MagIdx] := 20;inc(MagIdx);
 MagList[MagIdx] := 101;inc(MagIdx);
 MagList[MagIdx] := 1001;inc(MagIdx);

 {$IFDEF USE_GMP} mpz_init_set_ui(z,0);{$ENDIF}

 HighIdx := 0;
 lstIdx := 0;
 repeat
   if dgtBase5[highIdx] <> 0 then
   begin
     CnvEvenBase10(lstIdx);
     CheckMagn(dgtEvenBase10);
   end;
   CnvOddBase10(lstIdx);
   CheckMagn(dgtOddBase10);
   lstIdx := IncDgtBase5;
 until HighIdx > MAXHIGHIDX;
 writeln;
 InsertSort(@MagList[0],0,MagIdx-1);
 {$IFDEF USE_GMP} mpz_clear(z);writeln('Count of gmp tests ',gmp_count);{$ENDIF}
 For cnt := 0 to MagIdx-1 do
   writeln(cnt+1:3,'   ',MagList[cnt]);

 T0 -= Gettickcount64;
 writeln(-T0 / 1000: 0: 3, ' s');
 {$IFDEF WINDOWS}
   readln;
 {$ENDIF}

end. </lang>

Output:

TIO.RUN
getting primes 0.311 s

Count of gmp tests 102061
  1   0
  2   1
  3   2
  4   3
  5   4
  6   5
  7   6
  8   7
  9   8
 10   9
 11   11
 12   12
 13   14
 14   16
 15   20
 16   21
 17   23
 18   25
 19   29
 20   30
 21   32
 22   34
 23   38
 24   41
 25   43
 26   47
 27   49
 28   50
 29   52
 30   56
 31   58
 32   61
 33   65
 34   67
 35   70
 36   74
 37   76
 38   83
 39   85
 40   89
 41   92
 42   94
 43   98
 44   101
 45   110
 46   112
 47   116
 48   118
 49   130
 50   136
 51   152
 52   158
 53   170
 54   172
 55   203
 56   209
 57   221
 58   227
 59   229
 60   245
 61   265
 62   281
 63   310
 64   316
 65   334
 66   338
 67   356
 68   358
 69   370
 70   376
 71   394
 72   398
 73   401
 74   403
 75   407
 76   425
 77   443
 78   449
 79   467
 80   485
 81   512
 82   518
 83   536
 84   538
 85   554
 86   556
 87   574
 88   592
 89   598
 90   601
 91   607
 92   625
 93   647
 94   661
 95   665
 96   667
 97   683
 98   710
 99   712
100   730
101   736
102   754
103   772
104   776
105   790
106   794
107   803
108   809
109   821
110   845
111   863
112   881
113   889
114   934
115   938
116   952
117   958
118   970
119   974
120   992
121   994
122   998
123   1001
124   1112
125   1130
126   1198
127   1310
128   1316
129   1598
130   1756
131   1772
132   1910
133   1918
134   1952
135   1970
136   1990
137   2209
138   2221
139   2225
140   2249
141   2261
142   2267
143   2281
144   2429
145   2447
146   2465
147   2489
148   2645
149   2681
150   2885
151   3110
152   3170
153   3310
154   3334
155   3370
156   3398
157   3518
158   3554
159   3730
160   3736
161   3794
162   3934
163   3974
164   4001
165   4027
166   4063
167   4229
168   4247
169   4265
170   4267
171   4427
172   4445
173   4463
174   4643
175   4825
176   4883
177   5158
178   5176
179   5374
180   5516
181   5552
182   5558
183   5594
184   5752
185   5972
186   5992
187   6001
188   6007
189   6067
190   6265
191   6403
192   6425
193   6443
194   6485
195   6601
196   6685
197   6803
198   6821
199   7330
200   7376
201   7390
202   7394
203   7534
204   7556
205   7592
206   7712
207   7934
208   7970
209   8009
210   8029
211   8221
212   8225
213   8801
214   8821
215   9118
216   9172
217   9190
218   9338
219   9370
220   9374
221   9512
222   9598
223   9710
224   9734
225   9752
226   9910
227   11116
228   11152
229   11170
230   11558
231   11930
232   13118
233   13136
234   13556
235   15572
236   15736
237   15938
238   15952
239   17716
240   17752
241   17992
242   19972
243   20209
244   20261
245   20861
246   22061
247   22201
248   22801
249   22885
250   24407
251   26201
252   26285
253   26881
254   28285
255   28429
256   31370
257   31756
258   33118
259   33538
260   33554
261   35116
262   35776
263   37190
264   37556
265   37790
266   37930
267   39158
268   39394
269   40001
270   40043
271   40049
272   40067
273   40427
274   40463
275   40483
276   42209
277   42265
278   44009
279   44443
280   44447
281   46445
282   48089
283   48265
284   51112
285   53176
286   53756
287   53918
288   55516
289   55552
290   55558
291   55576
292   55774
293   57116
294   57754
295   60007
296   60047
297   60403
298   60443
299   60667
300   62021
301   62665
302   64645
303   66667
304   66685
305   68003
306   68683
307   71536
308   71572
309   71716
310   71752
311   73156
312   75374
313   75556
314   77152
315   77554
316   79330
317   79370
318   80009
319   80029
320   80801
321   80849
322   82265
323   82285
324   82825
325   82829
326   84265
327   86081
328   86221
329   88061
330   88229
331   88265
332   88621
333   91792
334   93338
335   93958
336   93994
337   99712
338   99998
339   111112
340   111118
341   111170
342   111310
343   113170
344   115136
345   115198
346   115772
347   117116
348   119792
349   135158
350   139138
351   151156
352   151592
353   159118
354   177556
355   193910
356   199190
357   200209
358   200809
359   220021
360   220661
361   222245
362   224027
363   226447
364   226681
365   228601
366   282809
367   282881
368   282889
369   311156
370   319910
371   331118
372   333770
373   333994
374   335156
375   339370
376   351938
377   359794
378   371116
379   373130
380   393554
381   399710
382   400049
383   404249
384   408049
385   408889
386   424607
387   440843
388   464447
389   484063
390   484445
391   486685
392   488489
393   515116
394   533176
395   551558
396   559952
397   595592
398   595598
399   600881
400   602081
401   626261
402   628601
403   644485
404   684425
405   686285
406   711512
407   719710
408   753316
409   755156
410   773554
411   777712
412   777776
413   799394
414   799712
415   800483
416   802061
417   802081
418   804863
419   806021
420   806483
421   806681
422   822265
423   864883
424   888485
425   888601
426   888643
427   911390
428   911518
429   915752
430   931130
431   975772
432   979592
433   991118
434   999994
435   1115756
436   1137770
437   1191518
438   1197370
439   1353136
440   1379930
441   1533736
442   1593538
443   1711576
444   1791110
445   1795912
446   1915972
447   1951958
448   2000221
449   2008829
450   2442485
451   2604067
452   2606647
453   2664425
454   2666021
455   2828809
456   2862445
457   3155116
458   3171710
459   3193198
460   3195338
461   3195398
462   3315358
463   3373336
464   3573716
465   3737534
466   3751576
467   3939118
468   4000483
469   4408603
470   4468865
471   4488245
472   4644407
473   5115736
474   5357776
475   5551376
476   5579774
477   5731136
478   5759594
479   5959774
480   6462667
481   6600227
482   6600443
483   6608081
484   6640063
485   6640643
486   6824665
487   6864485
488   6866683
489   7113710
490   7133110
491   7139390
492   7153336
493   7159172
494   7311170
495   7351376
496   7719370
497   7959934
498   7979534
499   8044009
500   8068201
501   8608081
502   8844449
503   9171170
504   9777910
505   9959374
506   11771992
507   13913170
508   15177112
509   17115116
510   19337170
511   19713130
512   20266681
513   22086821
514   22600601
515   22862885
516   26428645
517   28862465
518   33939518
519   37959994
520   40866083
521   44866043
522   48606043
523   48804809
524   51137776
525   51513118
526   53151376
527   53775934
528   59593574
529   60402247
530   60860603
531   62202281
532   64622665
533   66864625
534   66886483
535   71553536
536   77917592
537   82486825
538   86842265
539   91959398
540   95559998
541   117711170
542   222866845
543   228440489
544   244064027
545   280422829
546   331111958
547   400044049
548   460040803
549   511151552
550   593559374
551   606202627
552   608844043
553   622622801
554   622888465
555   773719910
556   844460063
557   882428665
558   995955112
559   1777137770
560   2240064227
561   2444402809
562   5753779594
563   6464886245
564   9151995592
565   22226226625
566   31993717930
567   39393115598
568   46884486265
569   84448000009
19.171 s

Real time: 19.793 s User time: 19.520 s Sys. time: 0.095 s CPU share: 99.09 %

Perl

Translation of: Raku

Library: ntheory

<lang perl>use strict; use warnings; use feature 'say'; use ntheory 'is_prime';

sub magnanimous {

   my($n) = @_;
   my $last;
   for my $c (1 .. length($n) - 1) {
       ++$last and last unless is_prime substr($n,0,$c) + substr($n,$c)
   }
   not $last;

}

my @M; for ( my $i = 0, my $count = 0; $count < 400; $i++ ) {

   ++$count and push @M, $i if magnanimous($i);

}

say "First 45 magnanimous numbers\n".

   (sprintf "@{['%4d' x 45]}", @M[0..45-1]) =~ s/(.{60})/$1\n/gr;

say "241st through 250th magnanimous numbers\n" .

   join ' ', @M[240..249];

say "\n391st through 400th magnanimous numbers\n".

   join ' ', @M[390..399];</lang>

Output:

First 45 magnanimous numbers
   0   1   2   3   4   5   6   7   8   9  11  12  14  16  20
  21  23  25  29  30  32  34  38  41  43  47  49  50  52  56
  58  61  65  67  70  74  76  83  85  89  92  94  98 101 110

241st through 250th magnanimous numbers
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

391st through 400th magnanimous numbers
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Phix

with javascript_semantics 
function magnanimous(integer n)
    integer p = 1, r = 0
    while n>=10 do
        r += remainder(n,10)*p
        n = floor(n/10)
        if not is_prime(n+r) then return false end if
        p *= 10
    end while
    return true
end function
 
sequence mag = {}
integer n = 0
while length(mag)<400 do
    if magnanimous(n) then mag &= n end if
    n += 1
end while
puts(1,"First 45 magnanimous numbers: ") pp(mag[1..45],{pp_Indent,30,pp_IntCh,false,pp_Maxlen,100})
printf(1,"magnanimous numbers[241..250]: %v\n", {mag[241..250]})
printf(1,"magnanimous numbers[391..400]: %v\n", {mag[391..400]})

Output:

First 45 magnanimous numbers: {0,1,2,3,4,5,6,7,8,9,11,12,14,16,20,21,23,25,29,30,32,34,38,41,43,
                               47,49,50,52,56,58,61,65,67,70,74,76,83,85,89,92,94,98,101,110}
magnanimous numbers[241..250]: {17992,19972,20209,20261,20861,22061,22201,22801,22885,24407}
magnanimous numbers[391..400]: {486685,488489,515116,533176,551558,559952,595592,595598,600881,602081}

PicoLisp

<lang PicoLisp>(de **Mod (X Y N)

  (let M 1
     (loop
        (when (bit? 1 Y)
           (setq M (% (* M X) N)) )
        (T (=0 (setq Y (>> 1 Y)))
           M )
        (setq X (% (* X X) N)) ) ) )

(de isprime (N)

  (cache '(NIL) N
     (if (== N 2)
        T
        (and
           (> N 1)
           (bit? 1 N)
           (let (Q (dec N)  N1 (dec N)  K 0  X)
              (until (bit? 1 Q)
                 (setq
                    Q (>> 1 Q)
                    K (inc K) ) )
              (catch 'composite
                 (do 16
                    (loop
                       (setq X
                          (**Mod
                             (rand 2 (min (dec N) 1000000000000))
                             Q
                             N ) )
                       (T (or (=1 X) (= X N1)))
                       (T
                          (do K
                             (setq X (**Mod X 2 N))
                             (when (=1 X) (throw 'composite))
                             (T (= X N1) T) ) )
                       (throw 'composite) ) )
                 (throw 'composite T) ) ) ) ) ) )

(de numbers (N)

  (let (P 10  Q N)
     (make
        (until (> 10 Q)
           (link
              (+
                 (setq Q (/ N P))
                 (% N P) ) )
           (setq P (* P 10)) ) ) ) )

(de ismagna (N)

  (or 
     (> 10 N)
     (fully isprime (numbers N)) ) )

(let (C 0 N 0 Lst)

  (setq Lst
     (make
        (until (== C 401)
           (when (ismagna N)
              (link N)
              (inc 'C) )
           (inc 'N) ) ) )
  (println (head 45 Lst))
  (println (head 10 (nth Lst 241)))
  (println (head 10 (nth Lst 391))) )</lang>

Output:

(0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110)
(17992 19972 20209 20261 20861 22061 22201 22801 22885 24407)
(486685 488489 515116 533176 551558 559952 595592 595598 600881 602081)

PL/M

This sample can be compiled with the original 8080 PL/M compiler and run under CP/M (or a clone/emulator).
THe original 8080 PL/M only supports 8 and 16 bit quantities, so this only shows magnanimous numbers up to the 250th. <lang plm>100H: /* FIND SOME MAGNANIMOUS NUMBERS - THOSE WHERE INSERTING '+' BETWEEN */

  /* ANY TWO OF THE DIGITS AND EVALUATING THE SUM RESULTS IN A PRIME       */
  BDOS: PROCEDURE( FN, ARG ); /* CP/M BDOS SYSTEM CALL */
     DECLARE FN BYTE, ARG ADDRESS;
     GOTO 5;
  END BDOS;
  PRINT$CHAR:   PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C );    END;
  PRINT$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
  PRINT$NL:     PROCEDURE; CALL PRINT$STRING( .( 0DH, 0AH, '$' ) );   END;
  PRINT$NUMBER: PROCEDURE( N );
     DECLARE N ADDRESS;
     DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
     V = N;
     W = LAST( N$STR );
     N$STR( W ) = '$';
     N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
     DO WHILE( ( V := V / 10 ) > 0 );
        N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
     END;
     IF N < 100 THEN DO;
        IF N < 10 THEN CALL PRINT$CHAR( ' ' );
        CALL PRINT$CHAR( ' ' );
     END;
     CALL PRINT$STRING( .N$STR( W ) );
  END PRINT$NUMBER;
  /* INTEGER SQUARE ROOT: BASED ON THE ONE IN THE PL/M FROBENIUS NUMBERS */
  SQRT: PROCEDURE( N )ADDRESS;
     DECLARE ( N, X0, X1 ) ADDRESS;
     IF N <= 3 THEN DO;
         IF N = 0 THEN X0 = 0; ELSE X0 = 1;
         END;
     ELSE DO;
        X0 = SHR( N, 1 );
        DO WHILE( ( X1 := SHR( X0 + ( N / X0 ), 1 ) ) < X0 );
           X0 = X1;
        END;
     END;
     RETURN X0;
  END SQRT;

  DECLARE MAGNANIMOUS (251)ADDRESS; /* MAGNANIMOUS NUMBERS              */
  DECLARE FALSE           LITERALLY '0';
  DECLARE TRUE            LITERALLY '0FFH';
  /* TO FIND MAGNANIMOUS NUMBERS UP TO 30$000, WE NEED TO FIND PRIMES   */
  /* UP TO 9$999 + 9 = 10$008                                           */
  DECLARE MAX$PRIME       LITERALLY '10$008';
  DECLARE DCL$PRIME       LITERALLY '10$009';
  /* SIEVE THE PRIMES TO MAX$PRIME */
  DECLARE ( I, S ) ADDRESS;
  DECLARE PRIME ( DCL$PRIME )BYTE;
  PRIME( 1 ) = FALSE; PRIME( 2 ) = TRUE;
  DO I = 3 TO LAST( PRIME ) BY 2; PRIME( I ) = TRUE;  END;
  DO I = 4 TO LAST( PRIME ) BY 2; PRIME( I ) = FALSE; END;
  DO I = 3 TO SQRT( MAX$PRIME );
     IF PRIME( I ) THEN DO;
        DO S = I * I TO LAST( PRIME ) BY I + I;PRIME( S ) = FALSE; END;
     END;
  END;

  /* FIND THE MAGNANIMOUS NUMBERS                                       */
  FIND$MAGNANIMOUS: PROCEDURE;
     DECLARE ( D1, D2, D3, D4, D5
             , D12, D123, D1234
             , D23, D234, D2345
             , D34, D345, D45
             ) ADDRESS;
     DECLARE M$COUNT ADDRESS; /* COUNT OF MAGNANIMOUS NUMBERS FOUND     */
     STORE$MAGNANIMOUS: PROCEDURE( N )BYTE;
        DECLARE N ADDRESS;
        M$COUNT = M$COUNT + 1;
        IF M$COUNT <= LAST( MAGNANIMOUS ) THEN MAGNANIMOUS( M$COUNT ) = N;
        RETURN M$COUNT <= LAST( MAGNANIMOUS );
     END STORE$MAGNANIMOUS;

     M$COUNT = 0;
     /* 1 DIGIT MAGNANIMOUS NUMBERS                                        */
     DO D1 = 0 TO 9; IF NOT STORE$MAGNANIMOUS( D1 ) THEN RETURN; END;
     /* 2 DIGIT MAGNANIMOUS NUMBERS                                        */
     DO D1 = 1 TO 9;
        DO D2 = 0 TO 9;
           IF PRIME( D1 + D2 ) THEN DO;
              IF NOT STORE$MAGNANIMOUS( ( D1 * 10 ) + D2 ) THEN RETURN;
           END;
        END;
     END;
     /* 3 DIGIT MAGNANIMOUS NUMBERS                                        */
     DO D1 = 1 TO 9;
        DO D23 = 0 TO 99;
           IF PRIME( D1 + D23 ) THEN DO;
              D3  = D23 MOD 10;
              D12 = ( D1 * 10 ) + ( D23 / 10 );
              IF PRIME( D12 + D3 ) THEN DO;
                 IF NOT STORE$MAGNANIMOUS( ( D12 * 10 ) + D3 ) THEN RETURN;
              END;
           END;
        END;
     END;
     /* 4 DIGIT MAGNANIMOUS NUMBERS                                     */
     DO D12 = 10 TO 99;
        DO D34 = 0 TO 99;
           IF PRIME( D12 + D34 ) THEN DO;
              D123 = ( D12 * 10 ) + ( D34 / 10 );
              D4   = D34 MOD 10;
              IF PRIME( D123 + D4 ) THEN DO;
                 D1   = D12 / 10;
                 D234 = ( ( D12 MOD 10 ) * 100 ) + D34;
                 IF PRIME( D1 + D234 ) THEN DO;
                    IF NOT STORE$MAGNANIMOUS( ( D12 * 100 ) + D34 )
                       THEN RETURN;
                 END;
              END;
           END;
        END;
     END;
     /* 5 DIGIT MAGNANIMOUS NUMBERS UP TO 30$000                        */
     DO D12 = 10 TO 30;
        DO D345 = 0 TO 999;
           IF PRIME( D12 + D345 ) THEN DO;
              D123 = ( D12 * 10 ) + ( D345 / 100 );
              D45  = D345 MOD 100;
              IF PRIME( D123 + D45 ) THEN DO;
                 D1234 = ( D123 * 10 ) + ( D45 / 10 );
                 D5    = D45 MOD 10;
                 IF PRIME( D1234 + D5 ) THEN DO;
                    D1    = D12 / 10;
                    D2345 = ( ( D12 MOD 10 ) * 1000 ) + D345;
                    IF PRIME( D1 + D2345 ) THEN DO;
                       IF NOT STORE$MAGNANIMOUS( ( D12 * 1000 ) + D345 )
                          THEN RETURN;
                    END;
                 END;
              END;
           END;
        END;
     END;
  END FIND$MAGNANIMOUS ;

  CALL FIND$MAGNANIMOUS;
  DO I = 1 TO LAST( MAGNANIMOUS );
     IF I = 1 THEN DO;
        CALL PRINT$STRING( .'MAGNANIMOUS NUMBERS 1-45:$' ); CALL PRINT$NL;
        CALL PRINT$NUMBER( MAGNANIMOUS( I ) );
        END;
     ELSE IF I < 46 THEN DO;
        IF I MOD 15 = 1 THEN CALL PRINT$NL; ELSE CALL PRINT$CHAR( ' ' );
        CALL PRINT$NUMBER( MAGNANIMOUS( I ) );
        END;
     ELSE IF I = 241 THEN DO;
        CALL PRINT$NL;
        CALL PRINT$STRING( .'MAGANIMOUS NUMBERS 241-250:$' ); CALL PRINT$NL;
        CALL PRINT$NUMBER( MAGNANIMOUS( I ) );
        END;
     ELSE IF I > 241 AND I <= 250 THEN DO;
        CALL PRINT$CHAR( ' ' );
        CALL PRINT$NUMBER( MAGNANIMOUS( I ) );
     END;
  END;
  CALL PRINT$NL;

EOF</lang>

Output:

MAGNANIMOUS NUMBERS 1-45:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110
MAGANIMOUS NUMBERS 241-250:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

Raku

Works with: Rakudo version 2020.02

<lang perl6>my @magnanimous = lazy flat ^10, (10 .. 1001).map( {

   my int $last;
   (1 ..^ .chars).map: -> \c { $last = 1 and last unless (.substr(0,c) + .substr(c)).is-prime }
   next if $last;
   $_

} ),

(1002 .. ∞).map: {

    # optimization for numbers > 1001; First and last digit can not both be even or both be odd
   next if (.substr(0,1) + .substr(*-1)) %% 2;
   my int $last;
   (1 ..^ .chars).map: -> \c { $last = 1 and last unless (.substr(0,c) + .substr(c)).is-prime }
   next if $last;
   $_

}

put 'First 45 magnanimous numbers'; put @magnanimous[^45]».fmt('%3d').batch(15).join: "\n";

put "\n241st through 250th magnanimous numbers"; put @magnanimous[240..249];

put "\n391st through 400th magnanimous numbers"; put @magnanimous[390..399];</lang>

Output:

First 45 magnanimous numbers
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110

241st through 250th magnanimous numbers
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

391st through 400th magnanimous numbers
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

REXX

The majority of the time consumed was in generating a list (sparse array) of suitable primes.
The magna function (magnanimous) was quite simple to code and pretty fast, it includes the 1^st and last digit parity test.
By far, the most CPU time was in the generation of primes. <lang REXX>/*REXX pgm finds/displays magnanimous #s (#s with a inserted + sign to sum to a prime).*/ parse arg bet.1 bet.2 bet.3 highP . /*obtain optional arguments from the CL*/ if bet.1== | bet.1=="," then bet.1= 1..45 /* " " " " " " */ if bet.2== | bet.2=="," then bet.2= 241..250 /* " " " " " " */ if bet.3== | bet.3=="," then bet.3= 391..400 /* " " " " " " */ if highP== | highP=="," then highP= 1000000 /* " " " " " " */ call genP /*gen primes up to highP (1 million).*/

    do j=1  for 3                               /*process three magnanimous "ranges".  */
    parse var   bet.j   LO  '..'  HI            /*obtain the first range (if any).     */
    if HI==  then HI= LO                      /*Just a single number?   Then use LO. */
    if HI==0   then iterate                     /*Is HI a zero?   Then skip this range.*/
    finds= 0;                             $=    /*#:  magnanimous # cnt;  $:  is a list*/
               do k=0  until finds==HI          /* [↓]  traipse through the number(s). */
               if \magna(k)  then iterate       /*Not magnanimous?  Then skip this num.*/
               finds= finds + 1                 /*bump the magnanimous number count.   */
               if finds>=LO  then $= $ k        /*In range►  Then add number ──► $ list*/
               end   /*k*/
    say
    say center(' 'LO       "──►"       HI       'magnanimous numbers ',  126, "─")
    say strip($)
    end        /*j*/

exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ magna: procedure expose @. !.; parse arg x 1 L 2 -1 R /*obtain #, 1st & last digit.*/

      len= length(x);       if len==1  then return 1     /*one digit #s are magnanimous*/
      if x>1001  then if L//2 == R//2  then return 0     /*Has parity?  Not magnanimous*/
               do  s= 1  for  len-1                      /*traipse thru #, inserting + */
               parse var  x   y  +(s)  z;   sum= y + z   /*parse 2 parts of #, sum 'em.*/
               if !.sum  then iterate                    /*Is sum prime? So far so good*/
                         else return 0                   /*Nope?  Then not magnanimous.*/
               end   /*s*/
      return 1                                  /*Pass all the tests, it's magnanimous.*/

/*──────────────────────────────────────────────────────────────────────────────────────*/ genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13 /*assign low primes; # primes.*/

     !.= 0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1   /*   "   semaphores to   "    */
                          #= 6;  sq.#= @.# ** 2          /*# primes so far;  P squared.*/
       do j=@.#+4  by 2  to highP; parse var j  -1 _; if _==5  then iterate /*÷ by 5?*/
       if j// 3==0  then iterate;   if j// 7==0  then iterate    /*÷ by 3?;     ÷ by 7?*/
       if j//11==0  then iterate                                 /*"  " 11?     " " 13?*/
               do k=6  while sq.k<=j            /*divide by some generated odd primes. */
               if j//@.k==0  then iterate j     /*Is J divisible by  P?  Then not prime*/
               end   /*k*/                      /* [↓]  a prime  (J)  has been found.  */
       #= #+1;   @.#= j;   sq.#= j*j;   !.j= 1  /*bump #Ps; P──►@.assign P; P^2; P flag*/
       end     /*j*/;                 return</lang>

output when using the default inputs:

──────────────────────────────────────────────── 1 ──► 45 magnanimous numbers ────────────────────────────────────────────────
0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110
and took 0.00 seconds.


────────────────────────────────────────────── 241 ──► 250 magnanimous numbers ───────────────────────────────────────────────
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407
and took 0.31 seconds.


────────────────────────────────────────────── 391 ──► 400 magnanimous numbers ───────────────────────────────────────────────
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Ring

<lang ring> load "stdlib.ring" n = -1 sum = 0 magn = []

while sum < 45

     n = n + 1
     if n < 10
        add(magn,n)
        sum = sum + 1
     else   
        nStr = string(n)
        check = 0
        for m = 1 to len(nStr)-1
            nr1 = number(left(nStr,m))
            nr2 = number(right(nStr,len(nStr)-m))
            nr3 = nr1 + nr2
            if not isprime(nr3)
               check = 1
            ok
         next
         if check = 0
            add(magn,n)
            sum = sum + 1
         ok
      ok

end

see "Magnanimous numbers 1-45:" + nl showArray(magn)

n = -1 sum = 0 magn = []

while sum < 250

     n = n + 1
     if n < 10
        sum = sum + 1
     else   
        nStr = string(n)
        check = 0
        for m = 1 to len(nStr)-1
            nr1 = number(left(nStr,m))
            nr2 = number(right(nStr,len(nStr)-m))
            nr3 = nr1 + nr2
            if not isprime(nr3)
               check = 1
            ok
         next 
         if check = 0
            sum = sum + 1
         ok
         if check = 0 and sum > 240 and sum < 251
            add(magn,n)
         ok
      ok

end

see nl see "Magnanimous numbers 241-250:" + nl showArray(magn)

func showArray array

    txt = ""
    see "["
    for n = 1 to len(array)
        txt = txt + array[n] + ","
    next
    txt = left(txt,len(txt)-1)
    txt = txt + "]"
    see txt

</lang>

Magnanimous numbers 1-45:
[0,1,2,3,4,5,6,7,8,9,11,12,14,16,20,21,23,25,29,30,32,34,38,41,43,47,49,50,52,56,58,61,65,67,70,74,76,83,85,89,92,94,98,101,110]

Magnanimous numbers 241-250:
[17992,19972,20209,20261,20861,22061,22201,22801,22885,24407]

Ruby

Translation of: Sidef

<lang ruby>require "prime"

magnanimouses = Enumerator.new do |y|

 (0..).each {|n| y << n if (1..n.digits.size-1).all? {|k| n.divmod(10**k).sum.prime?} }

end

puts "First 45 magnanimous numbers:" puts magnanimouses.first(45).join(' ')

puts "\n241st through 250th magnanimous numbers:" puts magnanimouses.first(250).last(10).join(' ')

puts "\n391st through 400th magnanimous numbers:" puts magnanimouses.first(400).last(10).join(' ') </lang>

Output:

First 45 magnanimous numbers:
0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Rust

<lang rust>fn is_prime(n: u32) -> bool {

   if n < 2 {
       return false;
   }
   if n % 2 == 0 {
       return n == 2;
   }
   if n % 3 == 0 {
       return n == 3;
   }
   let mut p = 5;
   while p * p <= n {
       if n % p == 0 {
           return false;
       }
       p += 2;
       if n % p == 0 {
           return false;
       }
       p += 4;
   }
   true

}

fn is_magnanimous(n: u32) -> bool {

   let mut p: u32 = 10;
   while n >= p {
       if !is_prime(n % p + n / p) {
           return false;
       }
       p *= 10;
   }
   true

}

fn main() {

   let mut m = (0..).filter(|x| is_magnanimous(*x)).take(400);
   println!("First 45 magnanimous numbers:");
   for (i, n) in m.by_ref().take(45).enumerate() {
       if i > 0 && i % 15 == 0 {
           println!();
       }
       print!("{:3} ", n);
   }
   println!("\n\n241st through 250th magnanimous numbers:");
   for n in m.by_ref().skip(195).take(10) {
       print!("{} ", n);
   }
   println!("\n\n391st through 400th magnanimous numbers:");
   for n in m.by_ref().skip(140) {
       print!("{} ", n);
   }
   println!();

}</lang>

Output:

First 45 magnanimous numbers:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20 
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56 
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110 

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407 

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Sidef

<lang ruby>func is_magnanimous(n) {

   1..n.ilog10 -> all {|k|
       sum(divmod(n, k.ipow10)).is_prime
   }

}

say "First 45 magnanimous numbers:" say is_magnanimous.first(45).join(' ')

say "\n241st through 250th magnanimous numbers:" say is_magnanimous.first(250).last(10).join(' ')

say "\n391st through 400th magnanimous numbers:" say is_magnanimous.first(400).last(10).join(' ')</lang>

Output:

First 45 magnanimous numbers:
0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50 52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 101 110

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Swift

Translation of: Rust

<lang swift>import Foundation

func isPrime(_ n: Int) -> Bool {

   if n < 2 {
       return false
   }
   if n % 2 == 0 {
       return n == 2
   }
   if n % 3 == 0 {
       return n == 3
   }
   var p = 5
   while p * p <= n {
       if n % p == 0 {
           return false
       }
       p += 2
       if n % p == 0 {
           return false
       }
       p += 4
   }
   return true

}

func isMagnanimous(_ n: Int) -> Bool {

   var p = 10;
   while n >= p {
       if !isPrime(n % p + n / p) {
           return false
       }
       p *= 10
   }
   return true

}

let m = (0...).lazy.filter{isMagnanimous($0)}.prefix(400); print("First 45 magnanimous numbers:"); for (i, n) in m.prefix(45).enumerated() {

   if i > 0 && i % 15 == 0 {
       print()
   }
   print(String(format: "%3d", n), terminator: " ")

} print("\n\n241st through 250th magnanimous numbers:"); for n in m.dropFirst(240).prefix(10) {

   print(n, terminator: " ")

} print("\n\n391st through 400th magnanimous numbers:"); for n in m.dropFirst(390) {

   print(n, terminator: " ")

} print()</lang>

Output:

First 45 magnanimous numbers:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20 
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56 
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110 

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407 

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081

Visual Basic .NET

Translation of: C#

<lang vbnet>Imports System, System.Console

Module Module1

   Dim np As Boolean()

   Sub ms(ByVal lmt As Long)
       np = New Boolean(CInt(lmt)) {} : np(0) = True : np(1) = True
       Dim n As Integer = 2, j As Integer = 1 : While n < lmt
           If Not np(n) Then
               Dim k As Long = CLng(n) * n
               While k < lmt : np(CInt(k)) = True : k += n : End While
           End If : n += j : j = 2 : End While
   End Sub

   Function is_Mag(ByVal n As Integer) As Boolean
       Dim res, rm As Integer, p As Integer = 10
       While n >= p
           res = Math.DivRem(n, p, rm)
           If np(res + rm) Then Return False
           p = p * 10 : End While : Return True
   End Function

   Sub Main(ByVal args As String())
       ms(100_009) : Dim mn As String = " magnanimous numbers:"
       WriteLine("First 45{0}", mn) : Dim l As Integer = 0, c As Integer = 0
       While c < 400 : If is_Mag(l) Then
           c += 1 : If c <= 45 OrElse (c > 240 AndAlso c <= 250) OrElse c > 390 Then Write(If(c <= 45, "{0,4} ", "{0,8:n0} "), l)
           If c < 45 AndAlso c Mod 15 = 0 Then WriteLine()
           If c = 240 Then WriteLine(vbLf & vbLf & "241st through 250th{0}", mn)
           If c = 390 Then WriteLine(vbLf & vbLf & "391st through 400th{0}", mn)
       End If : l += 1 : End While
   End Sub

End Module</lang>

Output:

First 45 magnanimous numbers:
   0    1    2    3    4    5    6    7    8    9   11   12   14   16   20 
  21   23   25   29   30   32   34   38   41   43   47   49   50   52   56 
  58   61   65   67   70   74   76   83   85   89   92   94   98  101  110 

241st through 250th magnanimous numbers:
  17,992   19,972   20,209   20,261   20,861   22,061   22,201   22,801   22,885   24,407 

391st through 400th magnanimous numbers:
 486,685  488,489  515,116  533,176  551,558  559,952  595,592  595,598  600,881  602,081

Wren

Library: Wren-fmt

Library: Wren-math

Translation of: Go

<lang ecmascript>import "/fmt" for Conv, Fmt import "/math" for Int

var isMagnanimous = Fn.new { |n|

   if (n < 10) return true
   var p = 10
   while (true) {
       var q = (n/p).floor
       var r = n % p
       if (!Int.isPrime(q + r)) return false
       if (q < 10) break
       p = p * 10
   }
   return true

}

var listMags = Fn.new { |from, thru, digs, perLine|

   if (from < 2) {
       System.print("\nFirst %(thru) magnanimous numbers:")
   } else {
       System.print("\n%(Conv.ord(from)) through %(Conv.ord(thru)) magnanimous numbers:")
   }
   var i = 0
   var c = 0
   while (c < thru) {
       if (isMagnanimous.call(i)) {
           c = c + 1
           if (c >= from) {
               System.write(Fmt.d(digs, i) + " ")
               if (c % perLine == 0) System.print()
           }
       }
       i = i + 1
   }

}

listMags.call(1, 45, 3, 15) listMags.call(241, 250, 1, 10) listMags.call(391, 400, 1, 10)</lang>

Output:

First 45 magnanimous numbers:
  0   1   2   3   4   5   6   7   8   9  11  12  14  16  20 
 21  23  25  29  30  32  34  38  41  43  47  49  50  52  56 
 58  61  65  67  70  74  76  83  85  89  92  94  98 101 110 

241st through 250th magnanimous numbers:
17992 19972 20209 20261 20861 22061 22201 22801 22885 24407 

391st through 400th magnanimous numbers:
486685 488489 515116 533176 551558 559952 595592 595598 600881 602081