Aspies For Freedom

Is 1 a prime number? have your say!

Yes, it is a prime number.  If it isn't, it is like saying that 2+2=Fish!

B"H

1 is no longer considered a prime number.  There are too many paradoxes involved.  Has anyone read "Prime Obsession" by John Derbyshire>

God, I love you people

Ah, lovely zero.  No, zero finds common ground because at it's heart lies chaos, the mother of all and the end of all. A delicious book you might enjoy is "Zero: The Biography of a Dangerous Idea," by Charles Seife. One, on the other hand, is order. Here is something rather than nothing. A discrete thing that can be manipulated, perhaps coddled in one hand if it is small enough. With one begins all measurable things.

B"H

It is tricky.  1 *seems* to be a prime.  However, if we were to use the Sieve of Eratosthenes to eliminate composite numbers, we would have to start with 2 or we would eliminate all numbers above one.  That, and other logical paradoxes, lead us to leave 1 aside as neither prime nor composite.  (Calling 1 composite also leads to logical paradoxes, since it has no other factors among natural numbers).

Why be enslaved by an ancient sieve? Shall we claim that the sun orbits the earth simply because it is ancient wisdom? Here's the deal -- 1 used to be considered prime, but 2 wasn't. Now it is the opposite.  It is a matter of definition rather than proof, and the definitions are adjusted for mathematical expediency.  It is just easier to exclude 1 from the primes since it messes up so many theories that are true for all prime numbers except 1.  There is no truth here, only convenience. It is pragmatic at best and lazy at worst. 1 is the unit. 1 is the identity. (though I'm actually partial to 6 )

Let me ask a favor.  Do you know the basis upon which 2 was once excluded as a prime?  That would be interesting to know.  The reason I stick with the Sieve is because it is the basis of so much of Riemann and modern prime number theory.  It is also very logical, in my opinion.  Expediency perhaps, but I rather think it "fits."

I *HAVE* heard that some mathematicians deny that 2 is a prime today.  I am less familiar with past views on 2.  My sense is that we can honestly call 2 a prime because, even though it is even, it still only factors in to itself and one on the natural number line.  However, I would like to know about past thought on 2.  Do you know where to go on the web?  Perhaps I'll ask "Dr. Math," as I so often do!

Honestly, that little tidbit of random information was in one of the many books I've read just for the hang of it. I don't precisely remember which one.  It was rejected due to being 'different,' much as 1 is today. I understand the argument against 1, but there is some small bit of messiness to the whole affair that I can't quite put my finger on.  Might help if I were actually a mathematician rather than a groupie.