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May 25th, 2013, 06:14 AM   #1
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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.

Please see the attached file.

Thanks,
Dan
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File Type: pdf OnComposites.pdf (94.7 KB, 31 views)
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May 25th, 2013, 07:06 AM   #2
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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.
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May 25th, 2013, 09:15 AM   #3
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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.
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May 25th, 2013, 02:20 PM   #4
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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!
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May 25th, 2013, 02:40 PM   #5
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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...
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May 26th, 2013, 07:13 AM   #6
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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.
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May 26th, 2013, 07:36 AM   #7
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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.
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May 26th, 2013, 06:39 PM   #8
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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.
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