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-   -   Euclid's proof of the infinite number of primes (https://www.mersenneforum.org/showthread.php?t=6090)

troels munkner 2006-07-10 14:34

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

drew 2006-07-10 14:49

[QUOTE=troels munkner]How to understand Euclid's proof of the infinite number of primes.[/QUOTE]
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 2006-07-11 08:32

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

All the best,

troels

troels munkner 2006-07-11 08:51

Euclid's proof
 
1 Attachment(s)
Unfortunally the three attachments were missing.
I will try to submit them in separate threads.

All the best,


troels

troels munkner 2006-07-11 09:00

Euclid's proof (II)
 
1 Attachment(s)
The next attachment

troels munkner 2006-07-11 09:36

Euclid (III)
 
1 Attachment(s)
The final attachment,

All the best,

troels

Jens K Andersen 2006-07-12 00:52

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 [URL="http://mersenneforum.org/showpost.php?p=81325&postcount=2"]words of Paul[/URL]: Humpty-Dumpty alert!

Patrick123 2006-07-12 08:12

[QUOTE](6*m +1) [one third of all integers][/QUOTE]:no:

Definitely a Humpty-Dumpty alert is required.

troels munkner 2006-07-13 12:20

[QUOTE=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 [URL="http://mersenneforum.org/showpost.php?p=81325&postcount=2"]words of Paul[/URL]: Humpty-Dumpty alert![/QUOTE]


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

troels munkner

troels munkner 2006-07-13 12:26

[QUOTE=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[/QUOTE]


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 2006-07-13 14:30

[QUOTE=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[/QUOTE]

Just what we need. Another clueless crank.


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