6 ms·

No notable mathematician has considered one prime since the early 20th century (of course, I'm oversimplifying, see [1] for more information). [1]: https://cs.

• btilly 13y ago
  You are oversimplifying more than you know. In a number theory course around 1990, I remember reading papers from the 60s which would explicitly note whether the counts of primes that they were using were starting from 1 or 2. You can define them as not notable mathematicians, but working mathematicians in number theory still had not completely standardized 50 years ago. Now for more fun, sit down with a group of mathematicians and ask whether they consider 0 to be a natural number. :-) (The answer you get will vary by field. But none will consider it a particularly important question.)
  • tel 13y ago
    cperciva answered this according to the modern algebraic understanding in response to the parent. 1 is definitely not prime when you more fully categorize the elements of sets by their algebraic properties: the existence of units is a less singular phenomenon in other algebraic structures.
    • btilly 13y ago
      Yes. More abstractly, prime numbers are those that generate prime ideals. This is a definition which generalizes to much more complex algebraic structures. However the last vestiges of the question about what definition was most natural didn't get settled until surprisingly recently.
      • tel 13y ago
        Oh, sorry for being presumptuous then. I'm not aware of the recent history.