20030401, 14:22  #1 
Feb 2003
40_{8} Posts 
twin prime generator
while toying with twin primes, i noticed that following:
if p and p+2 are twin primes, then there exists an integer B such that if q = (B^2  p)^2  B, then q and q+2 are also twin primes greater than p. i have also noticed that in some cases, if r=q mod p, then r and r+2 are also twin primes. does a proof for this already exist or are there counterexamples? 
20030401, 17:11  #2  
∂^{2}ω=0
Sep 2002
República de California
2×11×13×41 Posts 
Re: twin prime generator
Quote:
Even saying there exists at least ONE such value of B for any twinprime pair (p,p+2) is a very strong statement, since it implies that the twin prime conjecture is true. While this is generally believed to be the case, it has never been proven, and some of the best mathematicians in history have worked on it. Are you saying you have a proof, or just some numerical examples? 

20030402, 11:14  #3  
Feb 2003
40_{8} Posts 
Quote:
Quote:
Yes, I only intended q to be positve. The following are some negative values of B for p=3. [code:1] B q 10 9419 28 609989 223 2472675299[/code:1] Quote:


20030404, 05:40  #4 
Aug 2002
Ann Arbor, MI
433 Posts 
I don't think a distributed effort would necessarily lead to a proof, but it may give us an idea on where to start one. I've taken up interest in this, and have been doing some work on. Due to a small error in my program, I have a list of all positive B up to around a million for p=11 that make q and q+2 prime. I don't plan to go this far for the rest of the numbers, I'll probably restrict it to about B=1000. I'll try and get as much done as I can now, since I'm on Spring Break. Once I get back to school, I can set up a small cluster of TI82's to do some work during Doc Block (AP Physics C followed AP Calculus BC, 3 hours long). I'm going to intentionally avoid B being negative, partially because it doesn't seem right to include negative numbers for this kinda thing, and I also see it more at positive values of B for q=(B^2p)+B. Another interesting thing to look at might be to see how often B and B both yield twin primes.
P.S. My only programming experience is with TI calculators ops: . Running stuff on a TI89 emulator at full throttle my computer works good, but if anyone makes a better program, I'd like to know about it. 
20030406, 22:42  #5 
Feb 2003
37_{10} Posts 
Off topic, but do you have any links/info on this cluster of ti82s u talk about? I have a couple 82/83 sitting around, and if i could get them working together it could help on some of my progs that ive got crunching during class while i sleep.

20030406, 23:43  #6 
Aug 2002
Ann Arbor, MI
433 Posts 
Oh, i didn't mean a cluster working together at once. I meant you'd have the 1st one testing for B with p= 11, then the second testing for B with p=17...etc. I probably misused "cluster" ops: .

20030407, 02:36  #7 
Feb 2003
37 Posts 
Dang I got all excited about nothing heh. Oh well, guess I still have something to dream about.

20030414, 11:02  #8 
Feb 2003
32_{10} Posts 
Here's another thing I've noticed:
If the equation is rearranged like this: (B^2  p)^2 = B + q then let A be another integer such that: A^2 = B + q A = B^2  p then: B = A^2  q B^2 = A + p resulting in: (A^2  p)^2 = A + p They look symmetric but I haven't found a case where A = B. I've also noticed that A  B = 0 mod 3. 
20030423, 12:55  #9 
Feb 2003
2^{5} Posts 
Anyone interested in breaking the world twin prime record?
According to Chris Caldwell (http://www.utm.edu/research/primes/l...op20/twin.html) the largest twin prime pair to date is 33218925*2^169690+1, found in 2002 by Papp using Proth.exe. Let p=33218925*2^1696901. then (B^2  p)^2  B is another twin prime greater than p. Can anyone try B for 11 to 100? or 1 to 100? I'm presently testing B for 1 to 10 using PFGW (PrimeForm). Does anyone know of other programs (windowsbased) that can test an expression for primality? Is there a version of PRP that implements this? (I guess, I should have asked this in The Software section.) 
20030610, 04:23  #10 
Feb 2003
2^{5} Posts 
I tested B for values from 1999 to 2000 and didn't find any twin primes. I guess, its larger than 2000 or smaller than 1999.
By the way, B is always of the form 3n  1 where n is any integer. 
20030613, 07:44  #11  
5×11×13 Posts 
Quote:


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