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.


   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                                                         
