For example, 4001 is magnanimous because the numbers 4+001=5, 40+01=41 and 400+1=401 are all prime numbers.

Since all the prime numbers are odd, except for 2, all the magnanimous numbers, except for 11, 20, 101, and 1001, are either a sequence of odd digits followed by an even digit, or a sequence of even digits followed by an odd digits. The fact that 1001 is composite prevents other larger numbers with the same structure like 10001, 100001, etc., to be magnanimous.

It is conjectured that the magnanimous numbers are finite and that probably the largest one is 97393713331910, while the largest one which is also a prime number itself is probably 608844043.

The following table summarizes their frequency as a function of the number of digits, reporting the smallest, the largest and their quantitity.

The first magnanimous numbers are 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, 112, 116, 118, 130, 136, 152, 158, 170, 172, 203 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many magnanimous numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.