Next steps for TPS after Primegrid's record twin discovery

[axn]

http://www.primegrid.com/forum_thread.php?id=3873

[Puzzle-Peter]

It's time for Operation Megabit Twin now...

[odicin]

Yeah, I think the variable-n search can retired now. There is no need to search at primes any longer at this low search space.

Regards Odi

[Oddball]

Wow, what a week. It seems that all the interesting things happen when the project leaders are on vacation. (George, are you there?)

The news of the new twin literally came at the lowest point in my life. While driving to visit some family members over the holidays, I took a slight detour and visited Death Valley. On the day the twin was found, I was hiking in Badwater Basin, the lowest point in North America at an elevation of -282 feet. Strangely enough, the n=195000 twin was found by TPS on a high point, when MooMoo was on a ski trip somewhere in the mountains. Interesting coincidence.

But when you've hit rock bottom, the only way you can go is up. So both the Megabit twin and the variable-n efforts will continue as usual. Although a variable n range twin would not be the largest found, the Prime Pages keeps a list of the largest 20 twin primes, and it is highly unlikely that a find at ~150,000 digits will be off that list in any of our lifetimes. Besides, a considerable amount of effort was put into sieving the variable n range, and it would be a shame to let it go to waste. But I also recognize that some crunchers want a record, so there's no pressure here - you can pick whichever subproject you want.

Primegrid is welcome to join our Megabit Twin effort, provided that both projects share credit for primes found. On further thought, it would be ironic if the n=666666 Sophie search only finds twins and the Megabit Twin search finds only Sophies. Not likely, but well within the realm of possibility.

[R. Gerbicz]

Originally Posted by Oddball

Strangely enough, the n=195000 twin was found by TPS on a high point, when MooMoo was on a ski trip somewhere in the mountains.

Spelling of the name is incorrect.

Originally Posted by Oddball

Although a variable n range twin would not be the largest found, the Prime Pages keeps a list of the largest 20 twin primes, and it is highly unlikely that a find at ~150,000 digits will be off that list in any of our lifetimes.

You are really don't plan a long life. The current top twenty twin primes are from 2001-2011. That's eleven years.

[mdettweiler]

Originally Posted by R. Gerbicz

You are really don't plan a long life. The current top twenty twin primes are from 2001-2011. That's eleven years.

I'm not so sure that this is an accurate metric of how quickly new primes will accumulate on the list; probably the biggest reason the list is populated by primes from 2001-2011 is that the rise of the Internet prompted better coordination in the search for them. Prior to 2000-2001 or so, if you wanted to search for k*2^n-1 primes, you had to either a) write an LLR testing program yourself, or b) have a connection to one of the few people in the world who had done such a thing. Once the original PRP program (and later LLR) became widely available online, everyone and his proverbial brother began searching for primes, and so the list was quickly populated with increasingly large primes. At some point, however, the growth rate slowed quite a bit; it's worth noting that it's been a few years since the twin-prime record was last topped. At that rate, the current largest prime won't drop off the list for another 15-20 years at the least, barring incredible advances in computing technology.

[gd_barnes]

Originally Posted by mdettweiler

I'm not so sure that this is an accurate metric of how quickly new primes will accumulate on the list; probably the biggest reason the list is populated by primes from 2001-2011 is that the rise of the Internet prompted better coordination in the search for them. Prior to 2000-2001 or so, if you wanted to search for k*2^n-1 primes, you had to either a) write an LLR testing program yourself, or b) have a connection to one of the few people in the world who had done such a thing. Once the original PRP program (and later LLR) became widely available online, everyone and his proverbial brother began searching for primes, and so the list was quickly populated with increasingly large primes. At some point, however, the growth rate slowed quite a bit; it's worth noting that it's been a few years since the twin-prime record was last topped. At that rate, the current largest prime won't drop off the list for another 15-20 years at the least, barring incredible advances in computing technology.

I mostly disagree. Oddball was talking about when ~150000 digit twins would drop off the list. Now that we have such advances, there's no reason to think that the current twins won't keep dropping off at quick rates. The main issue here is that projects have been looking to shatter records instead of working their way up the list. If, instead of searching for twins that shatter the record, projects take an approach that they just want to search for twins at ~150000-200000 digits, than a ~150000 digit twin will be gone in far less than 20 years.

Since Oddball is young; early 20s if my impression from other postings is correct; then I believe that R. Gerbicz is correct. He doesn't plan on living a very long life.

Edit: BTW, the title of this thread makes little sense. It would probably get more attention if it was changed to something meaningful.


Gary

[Oddball]

Originally Posted by gd_barnes

I mostly disagree. Oddball was talking about when ~150000 digit twins would drop off the list. Now that we have such advances, there's no reason to think that the current twins won't keep dropping off at quick rates. The main issue here is that projects have been looking to shatter records instead of working their way up the list.

Good observation. I based my earlier statement on the assumption that nothing will change; projects will continue to focus on breaking records by a large amount. A ~150,000 digit twin find by a lone individual is highly unlikely - it would require a lot of luck or the patience and resources to tie up dozens of fast cores for over a decade.

But speaking of working up the list, would anybody be interested in looking for twins of the form k*2^n+/-1, where k<n? The largest known twin of that form was found by Flatlander and is still on the top 20 list. AFAIK, all n<48000 have been searched.

Since Oddball is young; early 20s if my impression from other postings is correct; then I believe that R. Gerbicz is correct. He doesn't plan on living a very long life.

Yup, I'm in my early 20s. But I did say that a ~150,000 digit twin (if found) won't be off the list in "any of our lifetimes", so my longevity shouldn't be too big of an issue

Edit: BTW, the title of this thread makes little sense. It would probably get more attention if it was changed to something meaningful.


Gary

I agree. Title changed.