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