|Re: When was 1 a prime number?|
Message #37 Posted by Mike on 1 Sept 2010, 9:25 a.m.,
in response to message #35 by John Mosand
I must be in a disagreeable mood today.
How does 1 violate the Fundamental Theory of Arithmetic? If what you say is true, then making 1 a prime number would violate that theorem. But if 1 was prime, it fits perfectly with the definition of Fundamental Theory of Arithmetic.
Fundamental Theory of Arithmetic
"In number theory and algebraic number theory, the Fundamental Theorem of Arithmetic (or Unique-Prime-Factorization Theorem) states that any integer greater than 1 can be written as a unique product of prime numbers."
In fact, in my view if that is the definition, you it is flawed without 1 being a prime.
For instance, according to that theory, what is the factors of 2?
2 must have uniquie product of prime numbers.
2 = 2 * 1
According to the theory, those factors must be prime. In order for that theory to hold, 1 must be a prime. If 1 is not a prime number, then there is no product of factors at all for 2. Product implies multiplication of 2 numbers.
The problem I see, is that all of these definitions are designed to exclude 1 from the list of primes, for no particularly good reason. The definitions are flawed. 1 being a prime voilates no rules of mathematics that I know of, unless it's related to a flawed definition.
So here is a test
1) What is the oldest known list showing 1 as a prime? (no definitions please; just lists of numbers)
2) What is the oldest known list showing 2 as the first prime? (no definitions please; just lists of numbers)
3) Which is older?
I know "todays" answer as to whether or not 1 is prime.
I know when I was going to school, many, many moons ago 1 was prime.
I also know that when I was going to school, Pluto was a planet.
From where I sit now; nothing has changed but definitions.
Edited: 1 Sept 2010, 9:43 a.m.