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Just because you don't like novel threads doesn't mean you have to mock them.

Yes he does. This is the *internet*

"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

2) øbviously a mîshtakë by PL, as any even number greater than two is divisible by 2 (= 'two'). So, let's correct it to the prime number after 2, i.e., 3. It will have to be Rachmaninoff's Morceaux de fantaisie.

3) Deux kazooræ, Op.2 by A. Kangarøö (1913 - 2013)

4) Prélude à l'après-midi d'un Göldfisch

"I don't play accurately - anyone can play accurately - but I play with wonderful expression. As far as the piano is concerned, sentiment is my forte. I keep science for Life."

Answers:2) øbviously a mishtake by PL, as any even number greater than two is divisible by 2 (=two). So, let's correct it to the prime number after 2, i.e., 3. It will have to be Rachmaninoff's Morceaux de fantaisie.

Can I switch to a prime number less than two? I don't care if it's even or odd or... anything???

1. Mussorgsky's Moustache: A Romantic Tour by Chabrier

2. I am not sure that there are even prime numbers greater than two

3. I'm going to say the piano transcription of Mozart's Bassoon Concerto, as the bassoon is clearly the instrument which most imitates the kazoo aurally. Especially the French "grande kazoo" which is nearly identical to the bassoon for all practical purposes.

4. There's actually a lesser known Bach Variations on the Debussy Variations on the Reger Bach Variations. Then Busoni actually did a variation on that. It just sounded like beeping noises after everyone was done. Then John Cage performed it.

2. I am not sure that there are even prime numbers greater than two

There aren't. I almost made the mistake of correcting him too, until I realized he's a retired math teacher. So it's no mistake. He's simply having fun with us.

Since he has nothing but contempt for emoticons, Plover will never "lead" you to his humor. You either tumble upon it yourself, or you don't.

And the many who "don't" have gotten unjustifiably PO'd at him.

(sorry, just been watching Life of π - great movie! )

"I don't play accurately - anyone can play accurately - but I play with wonderful expression. As far as the piano is concerned, sentiment is my forte. I keep science for Life."

Who knows why 1 is not a prime even though its only divisors are itself and 1(the basic idea of a prime number)? (Seems like a perfectly good question on a piano forum)

Who knows why 1 is not a prime even though its only divisors are itself and 1(the basic idea of a prime number)? (Seems like a perfectly good question on a piano forum)

Because one can arbitrarily include any number of copies of 1 in any factorization - e.g. 5, 5x1, 5x1x1, 5x1x1x1 etc are all valid factorizations of 5. Therefore, 1 has to be uniquely excluded as a prime number.

"I don't play accurately - anyone can play accurately - but I play with wonderful expression. As far as the piano is concerned, sentiment is my forte. I keep science for Life."

Who knows why 1 is not a prime even though its only divisors are itself and 1(the basic idea of a prime number)? (Seems like a perfectly good question on a piano forum)

Because one can arbitrarily include any number of copies of 1 in any factorization - e.g. 5, 5x1, 5x1x1, 5x1x1x1 etc are all valid factorizations of 5. Therefore, 1 has to be uniquely excluded as a prime number.

That is not my understanding of the correct answer although I am only going by what one professor told me a long time ago. (I don't see how it's related to my point about the main idea of a prime number.)

Who knows why 1 is not a prime even though its only divisors are itself and 1(the basic idea of a prime number)? (Seems like a perfectly good question on a piano forum)

Because one can arbitrarily include any number of copies of 1 in any factorization - e.g. 5, 5x1, 5x1x1, 5x1x1x1 etc are all valid factorizations of 5. Therefore, 1 has to be uniquely excluded as a prime number.

That is not my understanding of the correct answer although I am only going by what one professor told me a long time ago. (I don't see how it's related to my point about the main idea of a prime number.)

bennevis's response is basically exactly right.

The question of whether to consider 1 a prime is, in once sense, arbitrary. If we define a prime to be "any integer > 0 whose factors are 1 and itself", then 1 is a prime. If we define a prime to be "any integer > 1 whose factors are 1 and itself", then 1 is not a prime.

Mathematicians have chosen the second definition. Why did they do that?

The answer is that if 1 were a prime, then the Fundamental Theorem of Arithmetic, which states that any positive number can be uniquely decomposed into a product of primes, wouldn't be true. The "unique" part would break. The corrected statement of that theorem would become less elegant.

And the Fundamental Theorem of Arithmetic is so important that mathematicians decided it should have a simple and elegant statement!

(Source: I'm a mathematician! )

-Jason

p.s. the first three google hits under "why isn't 1 a prime number" corroborate this reason; two of them mention the Fundamental Theorem of Arithmetic by name!

Beethoven op.110, Chopin op.27/2, Liszt Vallée d'Obermann

The question of whether to consider 1 a prime is, in once sense, arbitrary. If we define a prime to be "any integer > 0 whose factors are 1 and itself", then 1 is a prime. If we define a prime to be "any integer > 1 whose factors are 1 and itself", then 1 is not a prime.

Mathematicians have chosen the second definition. Why did they do that?

The answer is that if 1 were a prime, then the Fundamental Theorem of Arithmetic, which states that any positive number can be uniquely decomposed into a product of primes, wouldn't be true. The "unique" part would break. The corrected statement of that theorem would become less elegant.

And the Fundamental Theorem of Arithmetic is so important that mathematicians decided it should have a simple and elegant statement!

(Source: I'm a mathematician! )

-Jason

p.s. the first three google hits under "why isn't 1 a prime number" corroborate this reason; two of them mention the Fundamental Theorem of Arithmetic by name!

This sounds much more like(or exactly like) what the professor told me. He said that if 1 was included in the primes than many theorems from number theory(like the one you mentioned, for example)would have to say this is true for all prime numbers except 1.

Are there other relatively basic number theory theorems besides the one you mentioned that would need a disclaimer if 1 was a prime?

Who knows why 1 is not a prime even though its only divisors are itself and 1(the basic idea of a prime number)? (Seems like a perfectly good question on a piano forum)

Because one can arbitrarily include any number of copies of 1 in any factorization - e.g. 5, 5x1, 5x1x1, 5x1x1x1 etc are all valid factorizations of 5. Therefore, 1 has to be uniquely excluded as a prime number.

That is not my understanding of the correct answer although I am only going by what one professor told me a long time ago. (I don't see how it's related to my point about the main idea of a prime number.)

Who knows why 1 is not a prime even though its only divisors are itself and 1(the basic idea of a prime number)? (Seems like a perfectly good question on a piano forum)

Because one can arbitrarily include any number of copies of 1 in any factorization - e.g. 5, 5x1, 5x1x1, 5x1x1x1 etc are all valid factorizations of 5. Therefore, 1 has to be uniquely excluded as a prime number.

That is not my understanding of the correct answer although I am only going by what one professor told me a long time ago. (I don't see how it's related to my point about the main idea of a prime number.)

It's correct - at least that's how I learned it.

Apparently you didn't even read my previous post. Without mentioning that the different factorizations of 5 given would contradict to the Fundamental Theorem of Algebra the example is not particularly relevant or at best unclear.

Didn't John Cleese do a gag about a parrot ... as I remember he nailed the dead bird to the perch in it's cage ... a bit of chicanery to be able to sell the smelly thing.

Didn't John Cleese do a gag about a parrot ... as I remember he nailed the dead bird to the perch in it's cage ... a bit of chicanery to be able to sell the smelly thing.

Alkan came later.

Hahaha, I would LOVE if those two things were related.