mersenneforum.org Euclid's proof of the infinite number of primes
 Register FAQ Search Today's Posts Mark Forums Read

 2006-07-10, 14:34 #1 troels munkner     May 2006 29 Posts Euclid's proof of the infinite number of primes How to understand Euclid's proof of the infinite number of primes.
2006-07-10, 14:49   #2
drew

Jun 2005

38210 Posts

Quote:
 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

Last fiddled with by drew on 2006-07-10 at 14:50

 2006-07-11, 08:32 #3 troels munkner     May 2006 29 Posts Thanks for your reply. Unfortunately the three attachments were missing. I try again to submit the (new) thread. All the best, troels
2006-07-11, 08:51   #4
troels munkner

May 2006

111012 Posts
Euclid's proof

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

All the best,

troels
Attached Files
 troels06072006.zip (4.8 KB, 466 views)

2006-07-11, 09:00   #5
troels munkner

May 2006

29 Posts
Euclid's proof (II)

The next attachment
Attached Files
 troelsPP-OPDELING.zip (3.5 KB, 197 views)

2006-07-11, 09:36   #6
troels munkner

May 2006

29 Posts
Euclid (III)

The final attachment,

All the best,

troels
Attached Files
 troelsOPDELING-AF-HELTAL.zip (3.3 KB, 191 views)

 2006-07-12, 00:52 #7 Jens K Andersen     Feb 2006 Denmark E616 Posts 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!
2006-07-12, 08:12   #8
Patrick123

Jan 2006
JHB, South Africa

15710 Posts

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

Definitely a Humpty-Dumpty alert is required.

2006-07-13, 12:20   #9
troels munkner

May 2006

29 Posts

Quote:
 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

2006-07-13, 12:26   #10
troels munkner

May 2006

29 Posts

Quote:
 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
If you can read the attachments, you will see a new view of integers.

Y.s.

troels

2006-07-13, 14:30   #11
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

164448 Posts

Quote:
 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.

 Similar Threads Thread Thread Starter Forum Replies Last Post flagrantflowers Aliquot Sequences 43 2016-10-22 08:14 Nick Number Theory Discussion Group 5 2016-10-08 09:05 literka Factoring 5 2012-01-30 12:28 CRGreathouse Math 10 2010-07-23 20:47 kayjongsma Math 4 2008-11-29 20:27

All times are UTC. The time now is 00:36.

Thu Jun 30 00:36:42 UTC 2022 up 76 days, 22:38, 0 users, load averages: 1.00, 1.44, 1.58