Reply to: Things I learnt yesterday.....

[DaveB]

Decomposing Composers

Henry Purcell The baroque composer died suddenly at the age of 36, one theory being that he caught a chill after being locked out by his wife

Beethoven's gone, but his music lives on,
And Mozart don't go shopping no more.
You'll never meet Lizst or Brahms again,
And Elgar doesn't answer the door.

Schubert and Chopin used to chuckle and laugh,
Whilst composing a long symphony.
But one hundred and fifty years later,
There's very little of them left to see.

The decomposing composers,
There's not much anyone can do.
You can still hear Beethoven,
But Beethoven cannot hear you.

Handel and Haydn and Rachmaninoff
Enjoyed a nice drink with their meal.
But nowadays no one will serve them,
And their gravy is left to congeal.

Verdi and Wagner delighted the crowds
With their highly original sounds.
The pianos they play are still working,
But they're both six feet underground.

The decomposing composers,
There's less of them every year.
You can say what you like to
But there's not much of them left to hear.

Claude Akil Debussy. Died, 1918.
Christof Viliborg Kralk. Died, 1787.
Carl Maria von Weber. Not at all well, 1825. Died, 1826.
Giacommo Meiabier. Still alive, 1863. Not still alive, 1864.
Modest Mussorgsky. 1880, going to parties. No fun anymore, 1881.
Johann Neopok Hummel. Chattin' away 19 'an a dozen with his friends down at the Pub every evenin', 1836. 1837, nothing.

[AlfredJPruffock]

Decomposing Composers

Henry Purcell The baroque composer died suddenly at the age of 36, one theory being that he caught a chill after being locked out by his wife

[expat]

It's quite simple: IF you start off with a list that you claim is a complete list of all primes, THEN in short order you arrive at a new prime that was not on your list. (It doesn't matter whether that new prime is p*q*r*.... +1, or a factor of that: the point is that you have found a new prime not on the list).

THEREFORE any supposed list of all primes is no such thing, there is always at least 1 more.


The logic of this proof is that IF you assume the number of primes is finite, THEN you get more primes, therefore that assumption is false, therefore the opposite is true.

--------------------------------------------------------
Part 2: It's actually quite complicated. The proof above assumes that "finite" = "able to be listed". It also assumes that if A is false, then "not A" is true. And it assumes that if A implies B, but B is false, then A is false.

[Pogle]

02/04/09

The petrol symbol on your fuel meter on your car dashboard has the nozzle pointing to the side of the car your petrol cap is on.

[original PM]

a good point

but surely this means the theorem is wrong?

or was the theorum put forward last night not complete?

i did not understand it too much then either tbh!

[DaveB]

I also watched Horizon re the prime numbers and I think what they are getting at is that if you add up all the numbers you know are prime and then add 1 you will get a prime.

So if the only prime numbers you know of are 1,2,3,7 you will be able to get a prime.

so 1*2*3*7 = 42 + 1 = 43

However this only works if you know of every prime number in between your first and last number - so for example if you know 1, 2 and 7 are primes and you did not know 3 was then 1*2*7 = 14 +1 = 15 - which is not a prime simply because we know it is divisible by 3.

So lets assume we know 1 and 2 are primes

1*2=2 + 1 = 3 which is a prime

So now we now 1,2 and 3 are primes

1*2*3 =6 + 1 = 7 which is a prime - now we can continue this indefinetly (if we have enough time and computing power)

But yes all it will prove is that if you know all the primes between 1 and x (where x is the largest prime discovered) then you multiply them together and add 1 you therefore have another prime.

So yes this proves that there are an infinte number of primes.

No, not nessecerily.

(2*3*5*7*11*13)+1 = 30031 which is divisible by 59 and 509.

However factors of the number you have generated may be prime which does prove there are an infinite number of primes. For very large primes calculating these factors is a job in itself and is part of the process of identifying a suspected prime number.

[Badger]

I've got Ham, but I'm not a Hamster.

I've got a badge but I'm not a, oh hang on.

[original PM]

I also watched Horizon re the prime numbers and I think what they are getting at is that if you add up all the numbers you know are prime and then add 1 you will get a prime.

So if the only prime numbers you know of are 1,2,3,7 you will be able to get a prime.

so 1*2*3*7 = 42 + 1 = 43

However this only works if you know of every prime number in between your first and last number - so for example if you know 1, 2 and 7 are primes and you did not know 3 was then 1*2*7 = 14 +1 = 15 - which is not a prime simply because we know it is divisible by 3.

So lets assume we know 1 and 2 are primes

1*2=2 + 1 = 3 which is a prime

So now we now 1,2 and 3 are primes

1*2*3 =6 + 1 = 7 which is a prime - now we can continue this indefinetly (if we have enough time and computing power)

But yes all it will prove is that if you know all the primes between 1 and x (where x is the largest prime discovered) then you multiply them together and add 1 you therefore have another prime.

So yes this proves that there are an infinte number of primes.

[NickNick]

I've got soul but....I'm not a soldier

I've got Ham, but I'm not a Hamster.

[expat]

He probably meant/said the resulting number must be divisible only by primes other than the ones you used (and the same applies to the sum or difference of any two products of those primes).

Also, +-1 are not considered prime these days, although they fit the usual loose definition of a prime number ("divisible only by 1 and itself").

spot-on. So you have found a new prime (but it is not necessarily the result of your calculation). Therefore if you start with the supposition that there is a finite list of primes, you find a new prime not in that list: therefore your supposition is false.

[OwlHoot]

According to the maths proff on Horizon,
If you multiply prime numbers in order from 1 ( so 1,2,3,5,7, etc..) and add 1 the resulting number will be a prime number.
And if thats wrong dont blame me, blame Euclid! or Horizon or blame my hard of understanding brain

He probably meant/said the resulting number must be divisible only by primes other than the ones you used (and the same applies to the sum or difference of any two products of those primes).

Also, +-1 are not considered prime these days, although they fit the usual loose definition of a prime number ("divisible only by 1 and itself").

[Pogle]

2*3*5*7*11*13 = 30,031 which is divisible by 59 and 509.

I sat here and tried to write a meaningfull explanation of the thoerem behind it but it's been so long since I had anything to do with maths like this I can't remember in enough detail to avoid being shot down in flames by those who do

I didn't see it but what I think the program was getting at is that multiplying known primes and adding 1 is part of the proof that there are an infinite number of primes, not that the results will always be prime.

I think that may be so - well at least it gave you something to think about for a bit

[DaveB]

According to the maths proff on Horizon,
If you multiply prime numbers in order from 1 ( so 1,2,3,5,7, etc..) and add 1 the resulting number will be a prime number.
And if thats wrong dont blame me, blame Euclid! or Horizon or blame my hard of understanding brain

2*3*5*7*11*13 = 30,031 which is divisible by 59 and 509.

I sat here and tried to write a meaningfull explanation of the thoerem behind it but it's been so long since I had anything to do with maths like this I can't remember in enough detail to avoid being shot down in flames by those who do

I didn't see it but what I think the program was getting at is that multiplying known primes and adding 1 is part of the proof that there are an infinite number of primes, not that the results will always be prime.

[Pogle]

According to the maths proff on Horizon,
If you multiply prime numbers in order from 1 ( so 1,2,3,5,7, etc..) and add 1 the resulting number will be a prime number.
And if thats wrong dont blame me, blame Euclid! or Horizon or blame my hard of understanding brain

[DaveB]

If you muliply a bunch of prime numbers together and then add 1 the resulting number will also be a prime number.

Not true, otherwise finding very large primes would not be as complicated as it is.

Hmmmm, just noticed the date this was posted on......