this post was submitted on 26 Apr 2024
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submitted 4 months ago by [email protected] to c/[email protected]
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[–] [email protected] 3 points 4 months ago (3 children)

Presumably if they're the product of exactly two factors then those factors would have to be prime, otherwise it wouldn't be exactly two.

[–] [email protected] 2 points 4 months ago* (last edited 4 months ago) (2 children)

Well primes themselves are the product of exactly two (natural) factors, only one of which is prime, so we need to specify semi primes as having exactly two prime factors.

[–] [email protected] 1 points 4 months ago (1 children)

The definitions often exclude 1. In the case where you include it you could then say a semi prime has exactly three factors.

[–] [email protected] 2 points 4 months ago

I have seen 1 called a trivial factor, but I have never seen it excluded entirely from a factor list: perhaps it's a cultural thing like how 0 is/isn't a natural number depending on where you are from.

On further research it seems like my earlier critique about requiring exactly two prime factors is a little off in any case, as it would exclude e.g. 4 (which only has one prime factor). It seems like semi primes must be a product of exactly two prime numbers so I think any definition based on number of factors is doomed to over- or under- define these semi primes as they could have either three or four factors.