Things I learnt yesterday.....

[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").

[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.

[NickNick]

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

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

[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.

[Badger]

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

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

[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.

[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!

[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.

[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.

[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