Talk:Calmo numbers: Difference between revisions
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(→Edge cases: Oops 1 isn't one of the divisors of 0 (exclusing 1) but 0 still isn't Calmo) |
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: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. |
: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. |
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:--[[User:Tigerofdarkness|Tigerofdarkness]] ([[User talk:Tigerofdarkness|talk]]) 16:45, 22 March 2023 (UTC) |
:--[[User:Tigerofdarkness|Tigerofdarkness]] ([[User talk:Tigerofdarkness|talk]]) 16:45, 22 March 2023 (UTC) |
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;;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. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 16:51, 22 March 2023 (UTC) |
Revision as of 16:51, 22 March 2023
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)