[QUOTE=kar_bon;108713]
the primesearch site is not coordinated to RPS for 251<n<300 so there are reservations or done ranges not marked at primesearch. at the beginning of my search for primes i found primesearch-site first and did some work for nothing 'cause the range was already done not mentioned there. my suggestion is everyone on RPS should mark these ranges in primesearch too.
[/QUOTE]
The PrimeSearch site appears to go down as far as k=101 and, presumably, isn't co-ordinated with RPS for 101 - 249 either.

Reserving k=289 from n=260K to n=520K
 

Thanks for the speedy response Kar_bon and Kosmaj. Since there's no easy way to contact Bo and the PrimeSearch site has no reservations beyond n=260K, I'm going to reserve the range of n=260K to 520K at this site AND the PrimeSearch site. :smile:

Even though Jeffrey tested it up to n=300K, this way I can correctly tell the people at the PrimeSearch site that I've consecutively tested their unreserved ranges up to 520K. I'll also report the 2 primes between n=500K and 520K to them and let them know that Bo previously found them.

I am your official gap filler! :flex:




Gary

I mistakenly thought that Karsten asked those questions :smile: Sorry about my comment about "replying to your own questions" :blush:

[QUOTE]I am your official gap filler! [/QUOTE]
Gary, that's cool, but I wonder can you possibly deploy one of your machines at n>333,333 using a previously untested k (like one of those heavy weight ones you are working on in other threads) because we are rapidly losing primes on the Top-5000 due to the flood of by-product primes posted by TPS. Later you can work on the gap created by skipping to 333,333 :geek:

Hi Kosmaj,

I am favor of working up to the higher n's and not leaving gaps instead of just going after top-5000 primes.

I almost consider the whole n=333333 twin prime search to be kind of a joke. No offense intended to anyone involved in the effort, which I know is huge. The problem that I have with it is that they've innundated the top-5000 list with all of these primes that really aren't very big and just as soon as n=333333 hits #5000 on the list, which it will in the next few months, then we will start knocking them off en masse. But the main reason I don't like the effort is because it's too high of an n for a decent twin-prime search and too low of an n to stay on the top-5000 list for long. Even with the huge effort involved, I calculated that it will almost definitely be many months and could be several years before they find twin primes that are so large. They've already spent a very long time at it.

If I was going after the twin-prime record (which happens to be at n=195000 at the moment), I would reserve an n somewhere between 200K and 225K. And if I was concerned about getting top-5000 primes that stay there for a long time, I would not be reserving k's. I'd reserve single n's instead (!) somewhere between 500K and 1M.

But wasn't the original intent of the 15k prime search site to find all of the primes for particular k's? It seems like we've gotten away from that in the search for glory on the top-5000 site. I think that things should be done in a systematic manner first, closely checked for errors, and then go after the big primes. The <300 site is a beautiful piece of work because it has all of the k's listed and almost all of the primes listed for each k with only a few gaps here and there. In my opinion, that is the way that it should be done and we can still get plenty of top-5000 primes that way.

On another note...This might be something for another forum but kind of fits in with the above here...I am going after a top-10 twin prime. I'd love to beat the n=333333 TPS at their own game by beating the current record before they do but I calculated that I don't have near the CPU resources needed to try an n=200K for a TPS. Even though I chose a specific n for this effort, I feel that it is OK because the primes aren't big enough to make the top-5000 list and I won't even bother posting such small riesel primes found from the effort so there won't be gaps to fill on the particular k's except for when I really find a twin. When and if that happens, I'll do another search on the k where the twin was hit to list all of its primes.

On another, more interesting, note, I have an entire list of all twin primes of the form k * 2 ^ n +/- 1 for all k's and n's listed on our site, the prime search site, and the proth search site that matched up with one another. It only goes up to k=600 because that's all that is shown on the proth site and of course it is only good for n's up to whatever have been searched by anyone for the k's in question. I kind of cheated :smile: because I ran no programs to get this list. I was able to manually extract all of the data from on all 3 sites into an Excel spreadsheet and then used formulas to match up the k's and n's that were the same. It's nice to have the information and I will eventually post it somewhere here after double-checking some things. The largest twin primes that I found from this effort were 459 * 2 ^ 8529 +/- 1. They are quite small, but alas, it was an interesting exercise and only took a few hours time to put all of it together. I was hoping to 'get lucky' and find a gargantuan twin-prime with n > 100K.

I now have one machine working on k=289 (will be done sieveing to 400G today), one going after a top-10 twin prime, and one working on one of my high-weight k's that I have reserved here.


Gary

Gary--

I see things somewhat the same way you do. I'm more interested in continuous ranges and expanding the body of knowledge on our stats pages (and primesearch's) than I am solely in top-5000 primes. I have a few k>2000 numbers currently running, with LLR complete to 160k and sieve from 160 to 600k. While I could have started at 333333, I wanted to have the small primes completed also.

I also started a twin prime search on my own; I chose my zip code, figuring an n in the 90,000's was a size I could tackle on my own, while still producing a meaningful result if I do find a twin. I sieved to k=1G to p=65T, and have LLR'ed to a few million (too many projects going, so this is on back burner). I have about 620,000 candidates to test.

TPS put thought and effort into choosing their k. After 190,000 (or whatever exact value they last chose), they wanted a significant leap to the next target. They wanted the primes to make top 5000, and a majority liked the idea of finding a 100,000 digit twin, which led to 333333 as far the most popular choice. Clearly, 200-225k would be a much faster project for the record, but they had just set the record, and that would be a nearly identical project to what they had just completed.

We all have our priorities and subinterests in prime searching-- I guess this wordy reply is my way of saying thanks for your efforts to fill gaps and remove doubts about our completed work. It is appreciated.
-Curtis

Curtis,

Thanks for the thinking on the n=333333 for the TPS. Sorry if I seemed a little krass there. Though it does seem like a monster effort to go after such a high n for twin primes and those 100's of 'regular' primes have knocked out such a large block of primes on the top-5000 that I'm sure took others far longer to find. I can't help but wonder how many I would have if I just chose n=400000 for a 'regular' prime search and put all 3 of my machines on them non-stop day and night...probably 10-15 or more by now and I've only been at this about 2 months. But you are correct, if they find one, it will make one BIG splash and it will be a record for a long time I think.

You have stated my feelings exactly. To me the glory is the search to find all primes of certain forms and have the lists exactly correct, not to get the most in the top-5000. If you want REAL glory, you have to go after the BIG monsters...i.e. the first 10,000,000-digit prime! Good luck with that! :-)

I do have a thread in the TPS where I've posted all small twins with k<600 of the form k * 2 ^ n +/- 1 up to the limit that all k's have been searched on the Riesel and Proth 'regular' prime search sights. I just simply extracted the info. from the various sites and matched them up using Excel formulas. One person has already expanded on it and I hope to expand it further in the next few days. Eventually I'd like to see a comprehensive list of Riesel/Proth twin primes we have for 'regular' Riesel and Proth primes now. Once I get a little bigger list, I'll probably submit it to Karsten or Kosmaj and ask if they'd like to create another site or link just to list all of the twin primes of this form. I think that would be excellent.

It's interesting that you mentioned using your zip code in the 90,000's as a value for n in your twin-prime search. I'm in almost the exact same place. I chose an n between 100K and 110K. It just seemed like a reasonable starting place where I wouldn't have to have multitudes of machines working on it. You did sieve FAR further than I did and your forsight was better on how many k's needed to be started with. My initial effort only involved k's from 1 to 100M so I only sieved to about 4.5T. LLR is just past testing to k=80M now...34 Riesel's but no matching Proth's yet. :mad: I'm now computing the odds at around 1 in 1100-1200 on finding a matching Proth each time a Riesel is found so it's clear that I didn't sieve enough k's to start with. Although I have a high-speed machine looking for twins, I only have a very slow-speed machine available for sieving them and I'm now sieving from k=100M to 500M. With a much wider range of k, it will probably make sense to sieve to at least 10T. I won't know for a while until it gets up a little closer. Alas, it is such a slow machine! :yucky: Regardless, my estimate is that I have a slightly better than 50-50 chance of finding one by k=3G so I'm almost 1/30th of the way there! Based on that, I guess I should really be sieving k's from 100M to 3G in one big chunk, but I'm not patient enough to wait so long. :-) Maybe if I don't find one by k=500M, then I'll sieve the rest in one chunck.


Gary

I'm just curious: why do we assume that fixed-k searches are more "complete" than fixed-n searches? :unsure:

[QUOTE=Cruelty;108942]I'm just curious: why do we assume that fixed-k searches are more "complete" than fixed-n searches? :unsure:[/QUOTE]

What do you mean by complete?

Fixed-k has a few features that make it more interesting for a cooperative search:
First, each chosen k can be worked on as deep or not-so-deep as one likes, while still contributing to the group's work. A fixed-n search is pretty much worthless to report progress on, as nobody is going to bother to record which n's have had searches done and which haven't.

Second, we can choose a k and even working slowly, easily stay ahead of the 5000th-prime cutoff. It doesn't really matter which k one picks, in a sense. If you choose an n, you must put some thought into what n and range of k will finish before the primes you might find are too small for anyone (read top-5000) to care about.

Third, since small k's LLR much faster than large k's, we have reason to search every small k, making a completed search-space of k/n combos. What possible completed search-space-range would a group of fixed-n searchers build? For example, it appears we'll have every k<100 complete to 1M or more by the end of 2007. Proth stats pages note a similar level of completeness of entire ranges. This is *my* definiton of more complete, and the one that makes this method better for organizational purposes.

-Curtis

Gary-- if you play with the sieving program a bit, you'll note that the sieve is roughly the same speed no matter how large a range of k you choose. I chose 1G because I was sieving on an old 128mb machine, and that was the biggest range that sieved at full speed. You may wish to reconsider doing the 100-500M block, if you even possibly might do another block later.

fixed-k sieves scale with the square root of n-range; fixed-n (including twin) sieves hardly scale at all.

-Curtis

Fixed n vs. k 'completeness' and bias of n values?
 

Great point, Cruelty. And one that has crossed my mind at different times also. Namely because, as you know, it's much faster to sieve by n then by k so why not try to complete n's instead of k's? Because of this, I have a spreadsheet of very small Riesel primes by n instead of by k. When I compiled it, I was looking to see if there is some bias for prime n's, even n's, odd n's, n's divisible by 3, n's divisible by 5, n's that are powers of 2, powers of 3, etc., etc. in the number of primes that they produce. Alas, I could fine none.

I mention this lack of bias (by my analysis anyway) of n's because I think part of the reason that we prefer to search by k's instead of n's is frankly because n's are quite boring in their distribution of primes. They are really very random in their total # of primes for similiar values of n so this makes n's far less interesting. There may be some n's that have quite a few more primes than others within a similiar range of n but by my testing at lower values so n, I can only conclude that its just random fluctuations in their numbers. For instance if you choose to search n=333333 for values of k from 1 to 1G, you're likely to find about the same number of primes as if you searched n=333334 for the same range of k. Obviously they slowly become less the higher the value of n but it is a very controlled and most likely logarithmic reduction.

The same as the above cannot be said of k's. k's are very interesting and people have spent much time determining their 'weights' and other factors to determine the density of their potential primes. Some are extremely heavy weight and others are so light weight that they have no primes at all or their primes are so hidden that extensive searches by mankind so far on them have not found any primes for them yet even though there's not a proof that says they shouldn't be there.

But I think the main reason is history. History started out searching for Mersenne primes, which obviously is a fixed value of k=1 simply because that was the easiest equation to compute the primality of huge primes. So it was only a natural progression to test k=3 then k=15 etc. because by logic, most of the time, there has to be many more primes when you eliminate the possibility of the answer not being divisible by 3 or 5.

So what happens if someone tests, say, n=333333 up to k=1T or something like that and finds k's along the way that are in the range of k's that we have listed here, technically it leaves gaps in those k's below n=333333.

But you can make the counter-argument to the above that our testing by k's is leaving many gaps in the n's. I agree. That's part of the reason that I started my spreadsheet...that is to 'fill some gaps' in the n's. For instance, there are huge gaps for the simple value of n = 1. Just a sampling...between k=9980 and k=10000, the values of 9981, 9987, 9997, and 9999 are all primes, yet we don't have those values of k anywhere on our summary site. This is not to say that there's anything wrong with our site, it's just that nobody has chosen to test those values of k.

So I can say that also part of the reason is the time involved to compile a list by n and keep it maintained. You could look at it as a 2-diminensional problem that we're choosing to attack from left to right instead of from top to bottom because it is mostly the value of n that determines the magnitude of the number yet it is the value of k that we use to attack it by. Whether that is right or wrong is a matter of opinion depending on whom you ask or what you are after.

At some point when I have completed my list of primes by n a little further, I may forward it on and see if anyone is interested in posting it somewhere or extending it at all.

And finally...if someone is aware of a bias in the distribution of primes for certain values of n based on some condition, I would be very VERY interested in hearing it. I had hoped that there would be a bias for certain n's since only prime values of n work for Mersenne primes but I was unable to conclude it with my analysis across values of n from 1 to 100 and values of k from 1 to 10000. Perhaps I need a larger testing range.


Gary

interesting points :tu:
BTW: sometime ago I have sieved n=1234567 for k<20bit till p=82T. I am wondering what is the porbability that there is a prime among the remaining candidates (18283)?