Euclid's proof of the infinite number of primes

[troels munkner]

How to understand Euclid's proof of the infinite number of primes.

[drew]

Originally Posted by troels munkner

How to understand Euclid's proof of the infinite number of primes.

Euclid's proof is very straightforward.

Let's say there is a finite number of primes. (2, 3 and 5, for example). 2n+1 is never divisible by 2. 3n+1 is never divisible by 3. 5n+1 is never divisible by 5.

Now, from the above, 2*3*5+1 is not divisible by 2, 3 or 5, so it must either be:

a. Prime
b. Divisible by other prime factors which are not 2, 3 or 5

In either case, there are more primes than simply 2, 3 and 5.

Which means that whenever you have a finite number of primes, you can find 1 more and repeat the process.

Drew

[troels munkner]

Thanks for your reply. Unfortunately the three attachments were missing.
I try again to submit the (new) thread.

All the best,

troels

[troels munkner]

Unfortunally the three attachments were missing.
I will try to submit them in separate threads.

All the best,


troels

[troels munkner]

The next attachment

[troels munkner]

The final attachment,

All the best,

troels

[Jens K Andersen]

How fortunate I already understood the proof. Otherwise I would be very confused now.

The 3 zip files are Word documents. The last 2 are diagrams. A quote from the 1st:
"Euclid (and most other mathematicians) have assumed that 2 and 3 are primes.
But I claim, that 2 and 3 are not possible primes and should not be considered as
“primes”."

In the words of Paul: Humpty-Dumpty alert!

[Patrick123]

(6*m +1) [one third of all integers]

Definitely a Humpty-Dumpty alert is required.

[troels munkner]

Originally Posted by Jens K Andersen

How fortunate I already understood the proof. Otherwise I would be very confused now.

The 3 zip files are Word documents. The last 2 are diagrams. A quote from the 1st:
"Euclid (and most other mathematicians) have assumed that 2 and 3 are primes.
But I claim, that 2 and 3 are not possible primes and should not be considered as
“primes”."

In the words of Paul: Humpty-Dumpty alert!

You have better read the original publication, - and be more polite.

troels munkner

[troels munkner]

Originally Posted by drew

Euclid's proof is very straightforward.

Let's say there is a finite number of primes. (2, 3 and 5, for example). 2n+1 is never divisible by 2. 3n+1 is never divisible by 3. 5n+1 is never divisible by 5.

Now, from the above, 2*3*5+1 is not divisible by 2, 3 or 5, so it must either be:

a. Prime
b. Divisible by other prime factors which are not 2, 3 or 5

In either case, there are more primes than simply 2, 3 and 5.

Which means that whenever you have a finite number of primes, you can find 1 more and repeat the process.

Drew

I know of course Euclid's "proof". But I went behind the statement and
studied it in more details. Please, look up the attachments which were not
in the first thread (unfortunately).
If you can read the attachments, you will see a new view of integers.

Y.s.

troels

[R.D. Silverman]

Originally Posted by troels munkner

I know of course Euclid's "proof". But I went behind the statement and
studied it in more details. Please, look up the attachments which were not
in the first thread (unfortunately).
If you can read the attachments, you will see a new view of integers.

Y.s.

troels

Just what we need. Another clueless crank.