The Great God Pan...

Originally posted by XanthosNZ
I mean I view the definition of a prime as:
"All numbers 4 or less and any number greater than 4 which has only 1 and itself as factors."

Why not? This is about as logical as what the 'professional mathematicians' have done.

Originally posted by dmnelson84
You wish.

Cya next thread.

Originally posted by BigDoggProblem
Cya next thread.

I rarely post in the same threads as you. You're just bitter about your incorrect answer. A real man can admit when he's wrong.

Originally posted by BigDoggProblem
Why not? This is about as logical as what the 'professional mathematicians' have done.

At this point you must be trolling. There is no way you can actually believe what you are saying.
Go back to the 1890s if you want 1 to be a prime.

Originally posted by XanthosNZ
Matters of definition are always Ad Populum if you want to use that logic.

Why isn't 4 a prime number? I mean I view the definition of a prime as:
"All numbers 4 or less and any number greater than 4 which has only 1 and itself as factors."

And if you argue with me you are just appealing to the popular definition of a prime number!

Are you calling yourself popular again!?!?!

Originally posted by dmnelson84
I rarely post in the same threads as you. You're just bitter about your incorrect answer. A real man can admit when he's wrong.

C'mon, don't give up so easily! Just a few posts ago, you had me pegged, remember?

Originally posted by XanthosNZ
At this point you must be trolling. There is no way you can actually believe what you are saying.
Go back to the 1890s if you want 1 to be a prime.

Oh, come off it! Your own sources indicate that it is a matter of definition and convention. 🙄

Here's a counter proposal. Amend the Fundamental Theorem of Arithmetic:
"All natural numbers are either a prime number, or can be written as a unique product of prime numbers (excluding 1 as a factor)." Since the FToA must have a special exception for the number 1 anyway, this is better than than denying 1 its proper status as a prime.

Originally posted by BigDoggProblem
Oh, come off it! Your own sources indicate that it is a matter of definition and convention. 🙄

Here's a counter proposal. Amend the Fundamental Theorem of Arithmetic:
"All natural numbers are either a prime number, or can be written as a unique product of prime numbers (excluding 1 as a factor)." Since the FToA must have a special exception for the number 1 anyway, this is better than than denying 1 its proper status as a prime.

Perhaps it would be if the Fundamental Theorem of Arithmatic were the only theorem that relied on 1 not being a prime.

Originally posted by XanthosNZ
Perhaps it would be if the Fundamental Theorem of Arithmatic were the only theorem that relied on 1 not being a prime.

Perhaps those theorems should have been quoted in support of your argument, instead of FToA, which must have an exception for the number 1 either way (edit: which means I reject the idea that FToA 'relies' on 1 not being prime...)

Originally posted by BigDoggProblem
Perhaps those theorems should have been quoted in support of your argument, instead of FToA, which must have an exception for the number 1 either way (edit: which means I reject the idea that FToA 'relies' on 1 not being prime...)

Well let's start with a classic, the zeta function.

The zeta function is defined for all real s as the infinite product of:
1/(1-(1/p)^s)
for all prime numbers p.
So we have to add a provisio to not include 1 there.

And we can continue with the likes of Euler's Criterion (http://mathworld.wolfram.com/EulersCriterion.html), Carmichael Condition (http://mathworld.wolfram.com/CarmichaelCondition.html) and so on down the list of theorems involving primes. There are one or two that would be slightly simplfied (http://mathworld.wolfram.com/SchnirelmannsTheorem.html could allow for all positive integers rather than all greater than 1) but those are a shorter list.