Re:Do we have negative prime numbers?
by giomasce on Saturday January 16, 2021 @01:47PM
(#25804327)
Hey, didn't notice the nick! Hi!
Well, if you're speaking about non-negative integers, you don't have the problem of the primality of negative numbers.
If you're considering relative integers, still you don't really have a unique factorization property, because negative integers do not have a factorization altogether (in terms of positive primes). So you have to stipulate that a prime factorization is not just a "product of primes", but a "product of primes, perhaps times -1", which is still not the way you usually define it. So I am not totally convinced.
In the end, everybody just pick the definition they like.
Well, if you're speaking about non-negative integers, you don't have the problem of the primality of negative numbers.
If you're considering relative integers, still you don't really have a unique factorization property, because negative integers do not have a factorization altogether (in terms of positive primes). So you have to stipulate that a prime factorization is not just a "product of primes", but a "product of primes, perhaps times -1", which is still not the way you usually define it. So I am not totally convinced.
In the end, everybody just pick the definition they like.