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magnanimous numbers
A number (which we assume of at least 2 digits) such that the sum obtained inserting a "+" among its digit in any position gives a prime.

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, are either a sequence of odd digits followed by an even digit, or a sequence of even digits followed by an odd digits.

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.

d#m. minm. max
2 33 11 98
3 79 101 998
4 104 1001 9910
5 112 11116 99998
6 96 111112 999994
7 71 1115756 9959374
8 35 11771992 95559998
9 18 117711170 995955112
10 6 1777137770 9151995592
11 5 22226226625 84448000009
12 0 none
13 1 5391391551358
14 1 97393713331910
15 0 none

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

Magnanimous numbers can also be... (you may click on names or numbers and on + to get more values)