20060710, 14:34  #1 
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.

20060710, 14:49  #2  
Jun 2005
2×191 Posts 
Quote:
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 20060710 at 14:50 

20060711, 08:32  #3 
May 2006
35_{8} Posts 
Thanks for your reply. Unfortunately the three attachments were missing.
I try again to submit the (new) thread. All the best, troels 
20060711, 08:51  #4 
May 2006
35_{8} Posts 
Euclid's proof
Unfortunally the three attachments were missing.
I will try to submit them in separate threads. All the best, troels 
20060711, 09:00  #5 
May 2006
11101_{2} Posts 
Euclid's proof (II)
The next attachment

20060711, 09:36  #6 
May 2006
29 Posts 
Euclid (III)
The final attachment,
All the best, troels 
20060712, 00:52  #7 
Feb 2006
Denmark
2×5×23 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: HumptyDumpty alert! 
20060712, 08:12  #8  
Jan 2006
JHB, South Africa
157 Posts 
Quote:
Definitely a HumptyDumpty alert is required. 

20060713, 12:20  #9  
May 2006
29 Posts 
Quote:
You have better read the original publication,  and be more polite. troels munkner 

20060713, 12:26  #10  
May 2006
11101_{2} Posts 
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 

20060713, 14:30  #11  
"Bob Silverman"
Nov 2003
North of Boston
1110101001000_{2} Posts 
Quote:


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