# Talk:Calmo numbers

Latest comment: 8 months ago by Tigerofdarkness in topic Edge cases

## Edge cases

Since 0 is divisible by 3, prime numbers (and 1) satisfy the current given constraints for "Calmo numbers". (In the sense that all of the resulting partial sums are prime.) --Rdm (talk) 16:24, 22 March 2023 (UTC)

- The current definition of a Calmo number says the count of divisors (excluding 1 and the number itself) must be divisible by 3.
- Further, these divisors must be split into groups of three and the sum of each group must be prime.
- Primes and 1 have 0 divisors (excluding 1 and the number), so can't be Calmo numbers as the sum of the first three of their 0 divisors must surely be 0, which is not prime.
- 0 has infinite divisors, ecluding 1, they are 2, 3, 4, 5, 6, 7, .... 2 + 3 + 4 is 9 which is not prime, so 0 is not a Calmo Number.
- --Tigerofdarkness (talk) 16:45, 22 March 2023 (UTC)

- To make it absolutely clear, I've changed 'natural number' in the task description to 'positive integer' though, in my view '0' is not a natural number (it's a mathematical invention), even though it's treated as such in some definitions. --PureFox (talk) 16:51, 22 March 2023 (UTC)
- You are correct 0 isn't a natural number - oops! --Tigerofdarkness (talk) 17:33, 22 March 2023 (UTC)

- To make it absolutely clear, I've changed 'natural number' in the task description to 'positive integer' though, in my view '0' is not a natural number (it's a mathematical invention), even though it's treated as such in some definitions. --PureFox (talk) 16:51, 22 March 2023 (UTC)