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Old 2009-10-20, 13:52   #1
Mini-Geek
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"Tim Sorbera"
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Default idea for twin prime searching

Has anybody tried taking a list of primes from the top 5000, or other lists of primes, and searching the opposite side for a prime? (e.g. #500 is currently 2951*2^852818-1, so sieve and if necessary LLR 2951*2^852818+1; in this case it has small factors, just an example) It could potentially be a very easy way to find a twin prime pair where one side is already known.

Last fiddled with by Mini-Geek on 2009-10-20 at 13:54
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Old 2009-10-20, 15:55   #2
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I tried that a couple of years ago and got part way through the list. (From the bottom up.)

edit:
Check out the "Other Primes" thread at NPLB, from post 20.

Last fiddled with by Flatlander on 2009-10-20 at 16:08
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Old 2009-10-20, 17:59   #3
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thought of this earlier in the year,but came to the conclusion that someone would of done this already.thought it would be logical for someone that's searching for a twin prime to test the opposite side of known primes.
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Old 2009-10-21, 14:53   #4
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Quote:
Originally Posted by Flatlander View Post
I tried that a couple of years ago and got part way through the list. (From the bottom up.)
The primes you checked are probably all off the list by now, then. Do you happen to know the limit you checked?
Quote:
Originally Posted by Flatlander View Post
edit:
Check out the "Other Primes" thread at NPLB, from post 20.
Interesting...As noted there, I'm checking the drive 9 prime's +1 sides for primes. (going very fast, should be done within fifteen minutes at worst) Edit: I just realized I eliminated n != 0 mod 3, instead of k != 0 mod 3. Restarting...
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thought of this earlier in the year,but came to the conclusion that someone would of done this already.thought it would be logical for someone that's searching for a twin prime to test the opposite side of known primes.
I'd think that too, but you never know unless you ask. Maybe everybody who's thought of this ignored it for the same reasons, and so an easy twin prime is still hiding in plain sight!

Last fiddled with by Mini-Geek on 2009-10-21 at 15:01
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Old 2009-10-21, 17:05   #5
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I'mm 99% sure anything I tested would be off the list now. I think it was longer than 2 years ago; I don't think I got near k*2^400000-1.
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Old 2009-10-22, 04:13   #6
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You might also go to the -3 and not just the opposite side?

ie

253*2^5000-1 and
253*2^5000-3 or some such thing

Still a twin!
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Old 2009-10-23, 17:40   #7
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The problem with the -3 is I don't think there's an easy primality test for k2^n-3. That's why all our searches are for +1 and -1 is people have figured out "easy" tests to show whether those are prime. For numbers of random form the best we can do is show it's probably prime.
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Old 2009-10-23, 19:46   #8
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The ones on the list are way to big for primo as well. It still would be an interesting project to show they are prp's though.
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Old 2011-01-30, 00:18   #9
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Quote:
Originally Posted by wolfemancs View Post
The problem with the -3 is I don't think there's an easy primality test for k2^n-3. That's why all our searches are for +1 and -1 is people have figured out "easy" tests to show whether those are prime. For numbers of random form the best we can do is show it's probably prime.
Can't we extend the PRP test to turn it into a true primality prover?
I have an idea, but it's just germinating.
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