idea for twin prime searching

TimSorbet · 2009-10-20, 13:52

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.

Flatlander · 2009-10-20, 15:55

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.

Dougal · 2009-10-20, 17:59

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.

TimSorbet · 2009-10-21, 14:53

Quote:

Originally Posted by Flatlander

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

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...

Quote:

Originally Posted by Dougal

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!

Flatlander · 2009-10-21, 17:05

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.

Skligmund · 2009-10-22, 04:13

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!

wolfemancs · 2009-10-23, 17:40

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.

Joshua2 · 2009-10-23, 19:46

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.

davar55 · 2011-01-30, 00:18

Quote:

Originally Posted by wolfemancs

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.

2009-10-20, 13:52	#1
TimSorbet Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 1000010110111₂ Posts	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 29512^852818-1, so sieve and if necessary LLR 29512^852818+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 TimSorbet on 2009-10-20 at 13:54

2009-10-20, 15:55	#2
Flatlander I quite division it "Chris" Feb 2005 England 31·67 Posts	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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2009-10-20, 17:59	#3
Dougal Jan 2009 Ireland 2·3·31 Posts	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.

2009-10-21, 17:05	#5
Flatlander I quite division it "Chris" Feb 2005 England 31×67 Posts	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.

2009-10-22, 04:13	#6
Skligmund Dec 2006 Anchorage, Alaska 2×3×13 Posts	You might also go to the -3 and not just the opposite side? ie 2532^5000-1 and 2532^5000-3 or some such thing Still a twin!

2009-10-23, 17:40	#7
wolfemancs Jul 2009 2² Posts	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.

2009-10-23, 19:46	#8
Joshua2 Sep 2004 13×41 Posts	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.