Re: Mersenne: interesting theorem
But what about 8? It's factors are 1 and 8 and 2 and 4. That doesn't work too well. 8 = 3 + 5 : 3 is prime 5 is prime. Q. E. D. other examples: 4 = 2 + 2 6 = 3 + 3 8 = 5 + 3 10 = 5 + 5 = 3 + 7 etc . . . I believe what we are talking about here is Goldbach's Conjecture. To date (to my knowledge) it has not been proven. I once read (somewhere) that when Goldbach conjectured this, he mailed the idea (or somehow presented it) to Euler, who never responded. Any book on number theory would probably mention this conjecture, most likely in a section on "Unsolved Problems and Conjectures." Hope this helps, Alex Healy [EMAIL PROTECTED] I ran across an interesting statement on the top of a math paper that I was helping my sister with. It said that every even number greater than 4 is the sum of two primes. I am curious if this has been proven and if anyone knows where I could find more info about this. Thanks.
Re: Mersenne: interesting theorem
At 07:51 PM 11/13/98 -0800, William Stuart wrote: Another interesting thing about this conjecture... If it is correct, then there is no last prime. And if Goldbach's conjecture is incorrect - then there is no last prime! +--+ | Jud McCranie [EMAIL PROTECTED] or @camcat.com | | | | 127*2^96744+1 is prime!(29,125 digits, Oct 20, 1998) | +--+
Re: Mersenne: interesting theorem
At 07:51 PM 11/13/98 -0800, William Stuart wrote: Another interesting thing about this conjecture... If it is correct, then there is no last prime. There's no last prime anyways. This is Euclid's Theorem and was proven thousands of years ago, as follows: Let p1, p2, ... , pn be a finite collection of primes. Let N = (p1p2...pn) + 1. Now N is clearly not divisible by any of the primes. If N is prime, then it is a prime not in the list. If N is not prime, it can be factored as N1N2, neither of which is divisible by any of the ps; and both strictly smaller than N; so eventually by this process you must find a prime factor of N that is not in the collection. Hence any finite collection of primes is incomplete, hence there must be infinitely many primes. -- .*. "Clouds are not spheres, mountains are not cones, coastlines are not -()circles, and bark is not smooth, nor does lightning travel in a `*' straight line."- -- B. Mandelbrot |http://surf.to/pgd.net _ | Paul Derbyshire [EMAIL PROTECTED] Programmer Humanist|ICQ: 10423848|
Mersenne: interesting theorem
I ran across an interesting statement on the top of a math paper that I was helping my sister with. It said that every even number greater than 4 is the sum of two primes. I am curious if this has been proven and if anyone knows where I could find more info about this. Thanks. -- Visit my new and improved home page at http://www.fireantproductions.com/cannona ICQ #: 22773363
Re: Mersenne: interesting theorem
Ok, let's see. 3x2=6 But what about 8? It's factors are 1 and 8 and 2 and 4. That doesn't work too well. Jon I ran across an interesting statement on the top of a math paper that I was helping my sister with. It said that every even number greater than 4 is the sum of two primes. I am curious if this has been proven and if anyone knows where I could find more info about this. Thanks.
Re: Mersenne: interesting theorem
I'm sure that it probably has been done, however, I am considering writing a program to see if I can disprove this theorem. It is my belief that it can be disproven because the higher you go, the less primes you have. Anyway, writing the program will be challenging and give me something to do. -- Visit my new and improved home page at http://www.fireantproductions.com/cannona ICQ #: 22773363 On Fri, 13 Nov 1998 [EMAIL PROTECTED] wrote: In a message dated 11/13/98 6:55:53 PM Eastern Standard Time, [EMAIL PROTECTED] writes: I ran across an interesting statement on the top of a math paper that I was helping my sister with. It said that every even number greater than 4 is the sum of two primes. I am curious if this has been proven and if anyone knows where I could find more info about this. Thanks. I, too, had heard this when in the seventh grade (we did a lot of work with theorems and conjectures). As I recall, this particular one was not or could not be proven. It sure is interesting to consider and who knows in what ways this simple theorem could be useful for us. -Joel
Re: Mersenne: interesting theorem
Try http://www.utm.edu/research/primes/notes/conjectures/ for a list of interesting conjectures including this one. Steve Gardner [EMAIL PROTECTED] Check out 84000 computer products at www.pcavenue.com -Original Message- From: Aaron Cannon [EMAIL PROTECTED] To: [EMAIL PROTECTED] [EMAIL PROTECTED] Date: Friday, November 13, 1998 9:11 PM Subject: Mersenne: interesting theorem I ran across an interesting statement on the top of a math paper that I was helping my sister with. It said that every even number greater than 4 is the sum of two primes. I am curious if this has been proven and if anyone knows where I could find more info about this. Thanks. -- Visit my new and improved home page at http://www.fireantproductions.com/cannona ICQ #: 22773363
Re: Mersenne: interesting theorem
At 8:51 PM -0500 11/13/98, [EMAIL PROTECTED] wrote: No, not factors. The different addends of the number. 4 = 2 + 2 (2 is prime) 6 = 3 + 3 (3 is prime) 8 = 3 + 5 (both prime) 10 = 5+5 12 = 5+7 14=7+7 16=5+11 18=7+11 Well, you get the idea. Another interesting thing to note which is part of the theorem is that it can only be done in one way, and exactly one way. So what ever the two primes are that add to 250...few secs later 163 and 87, no other pair of primes will add to 250 according to the theorem. Joel Not quite. 10= 5 + 5 = 3 + 7, 14 = 7 + 7 = 3 + 11, 34 = 17 + 17 = 31 + 3 = 29 + 5 = 23 + 11. There are many others... Anyway, it's not a theorem, it's a conjecture (Goldbach's conjecture). It's never been proven, nor has anyone found a counterexample. mark snyder mark snyder fitchburg state college
