mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2006-07-10, 14:34   #1
troels munkner
 
troels munkner's Avatar
 
May 2006

1D16 Posts
Default Euclid's proof of the infinite number of primes

How to understand Euclid's proof of the infinite number of primes.
troels munkner is offline   Reply With Quote
Old 2006-07-10, 14:49   #2
drew
 
drew's Avatar
 
Jun 2005

17E16 Posts
Default

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
drew is offline   Reply With Quote
Old 2006-07-11, 08:32   #3
troels munkner
 
troels munkner's Avatar
 
May 2006

29 Posts
Default

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

All the best,

troels
troels munkner is offline   Reply With Quote
Old 2006-07-11, 08:51   #4
troels munkner
 
troels munkner's Avatar
 
May 2006

29 Posts
Default Euclid's proof

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

All the best,


troels
Attached Files
File Type: zip troels06072006.zip (4.8 KB, 454 views)
troels munkner is offline   Reply With Quote
Old 2006-07-11, 09:00   #5
troels munkner
 
troels munkner's Avatar
 
May 2006

111012 Posts
Default Euclid's proof (II)

The next attachment
Attached Files
File Type: zip troelsPP-OPDELING.zip (3.5 KB, 185 views)
troels munkner is offline   Reply With Quote
Old 2006-07-11, 09:36   #6
troels munkner
 
troels munkner's Avatar
 
May 2006

1D16 Posts
Default Euclid (III)

The final attachment,

All the best,

troels
Attached Files
File Type: zip troelsOPDELING-AF-HELTAL.zip (3.3 KB, 180 views)
troels munkner is offline   Reply With Quote
Old 2006-07-12, 00:52   #7
Jens K Andersen
 
Jens K Andersen's Avatar
 
Feb 2006
Denmark

E616 Posts
Default

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!
Jens K Andersen is offline   Reply With Quote
Old 2006-07-12, 08:12   #8
Patrick123
 
Patrick123's Avatar
 
Jan 2006
JHB, South Africa

157 Posts
Default

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


Definitely a Humpty-Dumpty alert is required.
Patrick123 is offline   Reply With Quote
Old 2006-07-13, 12:20   #9
troels munkner
 
troels munkner's Avatar
 
May 2006

2910 Posts
Default

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
troels munkner is offline   Reply With Quote
Old 2006-07-13, 12:26   #10
troels munkner
 
troels munkner's Avatar
 
May 2006

2910 Posts
Default

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
in the first thread (unfortunately).
If you can read the attachments, you will see a new view of integers.

Y.s.

troels
troels munkner is offline   Reply With Quote
Old 2006-07-13, 14:30   #11
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

22×5×373 Posts
Thumbs down

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.
R.D. Silverman is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Number of sequences that merge with any given sequence - infinite? flagrantflowers Aliquot Sequences 43 2016-10-22 08:14
Basic Number Theory 3: gcd, lcm & Euclid's algorithm Nick Number Theory Discussion Group 5 2016-10-08 09:05
Fermat number F6=18446744073709551617 is a composite number. Proof. literka Factoring 5 2012-01-30 12:28
Estimating an infinite product over primes CRGreathouse Math 10 2010-07-23 20:47
Method of Euclid's Proof kayjongsma Math 4 2008-11-29 20:27

All times are UTC. The time now is 22:58.


Mon Dec 6 22:58:36 UTC 2021 up 136 days, 17:27, 1 user, load averages: 2.30, 1.80, 1.70

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.