0

The definition is taken from here. Is

$$\forall y \; \forall z \; y \cdot z = x \rightarrow y = 1 \lor z = 1$$

the correct way to define a prime number? Do you have a link to an article where prime numbers are defined this way?

If you would have to write this as a definition in a book or in an article, how would you write it?

  • 3
    That would make $1$ a prime number, which it isn't. – Gerry Myerson Nov 20 '21 at 11:57
  • 1
    Do you want members of $\Bbb N$ only? – Henno Brandsma Nov 20 '21 at 12:38
  • 1
    "If you would have to write this as a definition in a book or in an article, how would you write it?" You wouldn't. Why don't you just use common language and say "prime numbers"? Is there a specific purpose behind trying to define prime numbers in formal notation? I have clicked the video but I don't understand German. – Adam Rubinson Nov 20 '21 at 12:42
  • 1
    I agree with the comment of @AdamRubinson. On the one hand, yes the posted definition can be remedied to be a valid definition of primes: you simply insist that $y,z \in \Bbb{Z^+}$, and that the candidate prime $x \in \Bbb{Z_{\geq 2}}.$ However, the more natural and more common definition is that $p$ is prime if and only if $p$ is a positive integer $\geq 2$ such that the only positive integer divisors of $p$ are $1$ and $p$ itself. – user2661923 Nov 20 '21 at 15:21

0 Answers0