2
votes
2answers
89 views

definition of primes for higher hyperoperations

I was reading yesterday when I came across the history of counting. There was some evidence of an early understanding of prime numbers. I thought that I would try changing the definition of primality ...
2
votes
0answers
65 views

Should $0$ be considered a prime?

Typically, a prime is defined as follows: $p$ is prime iff $(p \mid xy \implies p \mid x$ or $p \mid y)$ and $p$ is not a unit or zero. But for ideals, we say the zero ideal is prime. There is a ...
3
votes
3answers
148 views

Is $0$ a composite number and $-1$ a prime number?

If in the set of natural numbers, all prime numbers $p$ have only two divisors, $1$ and $p$, and all composite numbers have at least three divisors, then can we also use these definitions for the set ...
7
votes
4answers
1k views

Alternate definition of prime number

I know the definition of prime number when dealing with integers, but I can't understand why the following definition also works: A prime is a quantity $p$ such that whenever $p$ is a factor of ...