My Math Forum Twin Prime Generator

 New Users Post up here and introduce yourself!

May 25th, 2013, 06:14 AM   #1
Newbie

Joined: May 2013

Posts: 3
Thanks: 0

Twin Prime Generator

I'm new to this forum, but I would like to see if I can get some feedback on a Twin Prime Sieve that I developed a few years ago, and an attempt at a proof of the Twin Prime Conjecture.

Thanks,
Dan
Attached Files
 OnComposites.pdf (94.7 KB, 31 views)

 May 25th, 2013, 07:06 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Twin Prime Generator Looks good. I haven't been able to spot any mistakes so far I have read. Welcome, by the way, good to see another combinatorial number theorist around.
 May 25th, 2013, 09:15 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Twin Prime Generator I assume the theorems about compositeness and primality are correct. In the final analysis they're just trial division, presieved for 2 and 3. But the conclusion has the same problem as most attempted proofs of the twin prime conjecture: it shows only that there are infinitely many pairs (n, n+2) not divisible by any prime up to k for some fixed k. This is not the same as the twin prime conjecture! To see why you can't get from one to the other directly, look at how fast the error terms grow.
 May 25th, 2013, 02:20 PM #4 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 Re: Twin Prime Generator I assume you know who Scott Aaronson is and what the Aaronson signs are? Speaking of combinatorial number theory, I hope you won't be too upset when I beat you to the proof!
May 25th, 2013, 02:40 PM   #5
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Twin Prime Generator

Quote:
 Originally Posted by eddybob123 I assume you know who Scott Aaronson is and what the Aaronson signs are?
http://math.crg4.com/breakthrough.html?q=739 in this case. But this particular mistake with the twin prime conjecture is common enough I might want to make a section just for it...

 May 26th, 2013, 07:13 AM #6 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 Re: Twin Prime Generator Thank you to all that reviewed my post. I certainly appreciate the feedback. I am very new to this, and I had not heard of the Aaronson signs. I had sent this paper to some people for feedback at the recommendation of one professor, but never received feedback from the other professors. Now, I think I know why.
 May 26th, 2013, 07:36 AM #7 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 Re: Twin Prime Generator Hi, I do have one question in response to the comment by CRGreathouse: "But the conclusion has the same problem as most attempted proofs of the twin prime conjecture: it shows only that there are infinitely many pairs (n, n+2) not divisible by any prime up to k for some fixed k." My final conclusion was trying to show that, for any integer N, the limit as N goes to infinity of the difference between N and the number of total composite generators would be infinity. (I doubt that I have done this rigorously) I am just wondering if that is a solid approach or if that approach is flawed in itself. I thought what I was doing, was not showing that there are there are infinitely many pairs (n, n+2) not divisible by any prime up to k for some fixed k, but actually showing that the number of integers, K, less than N, such that both 6k-1 and 6K+1 are not composite approaches infinity as N approaches infinity.
May 26th, 2013, 06:39 PM   #8
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Twin Prime Generator

Quote:
 Originally Posted by chibeardan My final conclusion was trying to show that, for any integer N, the limit as N goes to infinity of the difference between N and the number of total composite generators would be infinity.
You didn't, though. You moved away from that when you started measuring the remaining fractions. If you try cutting this off at any finite point you'll see why. Hint: the product of the primes up to x is very large, roughly e^x.

 Tags generator, prime, twin

### prime generator mathe

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mobel Number Theory 10 January 22nd, 2014 09:57 AM billymac00 Number Theory 38 December 21st, 2013 08:29 AM PerAA Number Theory 8 November 11th, 2012 09:29 AM Bogauss Number Theory 7 February 23rd, 2012 11:52 AM ogajajames Number Theory 4 April 26th, 2010 05:51 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top