35388067 is done up to 1M and no prime found yet.
i'm sieving this k from 1M to 5M: actually there are 679 n up to 2M and 2663 up to 5M in all. sieved till 13B and further. 353437897 is tested to 773k. no new prime. 352744289 tested up to 247k and no prime. sieved till 22B and 968 n's left up to 1M. 20141 tested till 847k, 27253 up to 801k and 31511 up to 787k. no primes. 50227 tested up to 283k > no new primes 57943 up to 268k: new primes nor n=52287,62475 and 76335! thats's all for now. 
k=1515 tested till n=500000, I'm still working on it :smile:

475977645*2^3385861 is prime (101934 digits)

475977645*2^1664791 and 475977645*2^1639981 are prime

Reserving 686701125 from 50k
Cedric 
Reserving 857996205 and 1693514745

Reserving 3645 from the original stats page. Will start at the last known prime (35772).
I'll try to get that page updated with the info from this thread soon.. sorry for falling behind. curtis 
[QUOTE=VBCurtis;98058]Reserving 3645 from the original stats page. Will start at the last known prime (35772).
I'll try to get that page updated with the info from this thread soon.. sorry for falling behind. [/QUOTE] Curtis, I have been working on 3645 for a long time now  currently at n=760k. If you search the Top5000 site you will see that I have already found quite a few primes, although non since n=470k. For info, if anyone does see that I have found Top5000 primes for a particular k, they can see my current status by following the website link on my home page. This will tell you where I have got to and whether I am still working on the k. I am keeping my own record because [url]www.15k.org[/url] is not updated often enough. 
Thanks for letting me know it's marked reserved for you on the next update. can you PM me the list of primes you found? Did you search from 35k on up, or is there a hole? If there's a hole, I'll fill it, since I have a sieve file to 200G or so.
Curtis edit: I'll check your website shortly, and add your data to the 15k stats page. 
Reserving 19217385
Reserving 19217385 from 300k

I've updated the page with your reservation nuggetprime  good luck

What finding chances have I in this k?
Can I expect a prime in the range 300k350k? 
Reserving: 228461805

On average you can expect a prime between 300350k, but individual
results can vary quite a lot. In the typical best case, there could be 3 primes, and in the typical worst case, there may not be a prime until 500k or so. Because of this, it's usually good to sieve a larger range like 300500k in case you go beyond 350k. 
How far should I sieve?

You should sieve until candidates are being removed at the rate LLR
would remove them. You can test this out by stopping the sieve at some point and running LLR on the first (or last) candidate to see how long it will take. On my machine a candidate around n=280k takes about 240 seconds. Using this data you can continue the sieve and sieve until candidates are being removed at about that rate (or a little longer than that since the higher n gets, the longer LLR takes and due to randomness, the rate will fluctuate up and down). My guess would be that for a range of n=300k500k, you'd need to sieve up to p=300Bn as a minimum and up to 500 or 600Bn would be better. 
Where should I post the current status of my k?

You can post it in this thread or if you find primes under the top5000 there
is a thread called "report small primes...". It doesn't have to be too frequent. Oftentimes, I'll just post the primes found as a status indicator :whistle: 
Status update on k=228461805,
228461805*2^4024181 is prime! (121,149 digits) Sieved and LLRing n=300,000500,000 Others are free to test by others. This is my first TOP 5000 prime :) Overall, my second prime found. Ok, off to the TOP Primes submission :) 
Congrats on your first prime! :smile: It was just confirmed on Top5000.

686701125
Sieved to 200G Currently @ 122k Primes found: [code] 686701125*2^59037  1 is prime! 17781 digits 686701125*2^61564  1 is prime! 18542 digits 686701125*2^61743  1 is prime! 18596 digits 686701125*2^71904  1 is prime! 21655 digits 686701125*2^77984  1 is prime! 23485 digits 686701125*2^82487  1 is prime! 24840 digits 686701125*2^85355 1 is prime! 25704 digits 686701125*2^86208 1 is prime! 25961 digits 686701125*2^92474 1 is prime! 27847 digits 686701125*2^101321 1 is prime! 30510 digits 686701125 106669 686701125 117433 686701125 118513 [/code] 
99311355
don't know if i reserve this k, think not so i do this here.
the first 100 primes are: 3, 5, 10, 12, 14, 24, 25, 30, 38, 40, 41, 46, 75, 85, 88, 106, 113, 133, 156, 163, 179, 190, 218, 238, 250, 259, 276, 287, 297, 340, 378, 391, 408, 415, 432, 464, 469, 472, 529, 543, 588, 597, 629, 655, 675, 689, 833, 851, 1114, 1313, 1580, 1680, 1841, 1859, 1904, 2194, 2201, 2521, 2763, 3110, 3797, 3819, 4140, 4799, 5044, 5159, 5962, 6701, 7331, 7932, 9220, 9373, 11064, 11109, 11621, 12056, 13894, 14918, 16493, 18071, 19557, 20360, 21217, 21382, 24062, 25045, 25996, 26422, 27803, 32142, 33579, 34076, 36918, 77713, 108615, 111785, 120458, 124695, 128145, 133176(100th prime) (134k) (max n first search area) 99311355*2^1565811 was found by Burt. the second search area starts at 285k: no prime yet 
status update: 687218805 still crunching.

Reserving k=15015
I haven't seen k=15015 mentioned anywhere including the 15K site for this effort so I'd like to reserve it if no one has worked on it. I was surprised that no one had it because it is the product of the first 5 noneven primes, 3x5x7x11x13. And since the initial effort on this was directed towards 15k's, I like the fact that it has two 15's in the value. :smile:
I've sieved and tested this k to n=100K and have found it to be a good mediumweight k. So far, it has been very consistent in its generation of primes. There were primes in every range of 10K up to this point for a total of 61, broken down by # of digits of n as follows: n=1 to <100; 10 n=100 to <1K; 18 n=1K to <10K; 16 n=10K to <100K; 17 The highest prime was 15015*2^945881. I'll list them all on the 'smaller primes' thread. For now, I plan to test this k to n=500K. Gary 
A good place to check if anybody has worked on a k is by searching at:
[url]http://primes.utm.edu/primes/search.php[/url] That lists 8 primes up to n=356533. You can try to contact the submitter to see how far he searched. 
Unreserving K=15015
I guess I jumped the gun. I now see that K=15015 has been heavily researched, with several entries in the top5000 list. So obviously I can't 'reserve' it here. I searched this entire site and the 15K site and didn't find it. :yucky:
If there is a comprehensive list of all K's, their status, how far they've been tested, and whether they have been reserved, that would be really helpful. All I could find was a smattering here and there on this forum. Thanks, Gary 
Reserving K=102765 and K=19437
After my last effort at K=15015 that had already been heavily tested, I did some additional checking this time around and found two interesting K's that I'd like to reserve and test...102765 and 19437. 19437 should be an interesting effort for a K that is not a 15K.
I checked several sites including the top5000 site and didn't find that these had been tested at any point. If anyone knows that they have been, please let me know. Thanks, Gary 
I reported 19437 *2^2113571 in April 2005. When searching the top5000
site, there is a box to check: all (under the Type section). If you don't check that box, you only get primes currently on the top5000. I searched my directories and, unfortunately, can't find how far I went on 19437 :blush: 
Here are the top20 or so in terms of weight for 1000 < K < 1000000
K, Weight/100 624195, 67 (primes up to n=128008 on top5000 site, searched by Shane) 980265, 66 (primes up to n=188537 on top5000 site, searched by Thomas) 542685, 65 810810, 63 405405, 62 (primes up to n=220242 on top5000 site, searched by Thomas) 998910, 61 (didn't check the top5000 here or below) 916110, 61 870870, 61 861735, 61 743910, 61 684255, 61 666735, 61 663465, 61 607815, 61 529815, 61 499455, 61 486540, 61 458055, 61 435435, 61 371955, 61 243270, 61 1059630, 61 (oops, overshot 1M by a bit) 
to gd_barnes
k=15015 is on the site [url]http://www.15k.org/SummaryKvalues.htm[/url] too but this site is not reachable from [url]www.15k.org[/url] directly at the moment.
so try to the upper link for now. i'm preparing a new menu for this site and uptodate information of all k mentioned in this thread and the archived thread too. you're not the first one who have done work for 'nothing', so i decided to collect more data about these special primes. be patient! i hope i have a new layout next week. for your reservations: lsoule had tested 102765 to n=10k with 60 primes but no primes reported. look here [url]http://www.mersenneforum.org/showpost.php?p=51331&postcount=9[/url] 
to lsoule
i inserted your k's in my datacollection but i 'normalized' your candidates
so 810810 divisible by 2 makes 405405 and therefore i used only odd k's! the new data page is available next week. 
Ah yes, divisible by 2. Guess I checked everything twice!

Reserving k=405 from 260k to 600k. I also reserved it on Primesearch.
260 is too low to make top5000, but I prefer to have a k fully searched. Curtis 
19437 now tested to 100K
Hi Isoule,
I got your note about finding 19437x2^2113571 as prime back in 2005. But I'm going ahead and testing it anyway since there doesn't appear to be a list of primes on it up to that point that I could find anywhere. I've now completed it to 100K and will continue at least to 250K to 'fill in the gap' below your find. I'll post the primes on the 'low primes' thread. Gary 
102765 now tested to 100K
I have completed testing up to 100K on k=102765 and will continue at least up until the 250K300K range. The primes will be posted on the 'small primes' thread.
Gary 
Reserving k=290499495 and k=968911515
I'd like to reserve k=290499495 and k=968911515 and test them to n=250K or 300K or so. I see that they both have been previously tested to a certain extent and there were a number of primes on the top5000 list back in 2002 or 2003 for k=290499495 up to about n=170K, which are now below 11,000th place. But there appeared to be many gaps in its testing and no complete list that I could find of all of its primes so I'd like to get them filled in. 968911515 appears to have been only tested to n=50K a long time ago and it looks like a good one for further testing.
If anyone is currently working on them, please let me know. Also, if there's anywhere else where I should be posting a reservation for Riesel k's, please let me know. Thanks, Gary 
Reserving k=3545685
I'd like to reserve k=3545685. I don't see where this one has ever been tested so I'll test it up to about n=250K to n=300K.
Gary 
Reserving k=775784295 and k=3428677395
I'd like to reserve k=775784295 and k=3428677395 and test them to n=250K or 300K or so. Both are highweight k's and I see that they were both previously lightly tested but are currently unreserved so I'll fill in some gaps, report them, and continue on from there.
If anyone is currently working on them, please let me know. Thanks, Gary 
unreserved 686701125
file available @ [url]http://users.skynet.be/bk261068/686701125.zip[/url] containing input, prime & results 
Reserving k=1019370495
I'd like to reserve k=1019370495 to fill in a large gap only.
This one was previously tested from 2003 to 2005 up to n=42K and from about n=135K to n=150K and appears unreserved right now. At this point, I only plan on testing it to n=150K to fill in the gap and confirm prior testing. But if it performs very well, I may continue further. Gary 
Reserving k=686701125 if OK
Cedric,
That is a very nice sieve file that you attached to your results for k=686701125. Since you're unreserving it, if you or no one else has an objection, I'd like to reserve this one and use your sieve file to run with it starting from your ending point around n=173.3K. I've kind of had my eye on it since you reserved it. I think it's a great k. :smile: Thanks, Gary 
Knock yourself out! :)
But a good advice, sieve further, the numbers are eliminated very quickly! Regards C. 
Reserving k=111546435
I'd like to reserve k=111546435 to fill in some gaps.
This one was previously tested in 1999, 2002, 2006 and originally had many primes in the top 5000 but there appears to have been several gaps in the testing. Gary 
Big gap in k=289? If so, reserving gap.
To whom it may concern and can answer some questions:
k=289 is confusing to me for the range of n=90201 to n=501991. This appears to be a gap that is at least partially untested. I say this because of the density of primes both before and after this range. I did some research and found the following: 1. Our n<300 site shows: 77391, 90201 [300k Jeffrey], 501991, 509401. Question: What does this mean? 3 possibilities come to mind: a. A gap from n=90201 to n=300K. b. A gap from n=300K to n=501991. c. No gap at all. Previous primes were found by someone else and primes > then 300K were found by Jeffrey. Comments: The n<300 is a wonderful site. Unfortunately, it has several examples like the above where it shows something like [Lsoule at 804k] right in between all of the listed primes and it is not clear where testing might have stopped and/or restarted and/or if there is/was a gap in between. The k's of 1, 3, 181, and 289 are some examples of this. Suggested change: I think there needs to be something like the notation of (..) to indicate if and where there is a gap on the n<300 site, similiar to the way our summary site shows it. 2. The Primesearch site shows: 77391, 90201... with no more primes listed. I then went and checked the ranges reserved on the site and it only showed that ranges were completed up thru n=260K and that the ranges from n=260K to n=600K are "available". This is funny since our site has already found 2 primes between n=500K and 600K. But what it did do is narrow down the possible gap but not completely. Obviously the Primesearch site doesn't keep up with the primes found on our site. 3. The top5000 site shows primes for k=289 of n=55693, 60243, 501991, 509401, and several higher. This only confirmed some of the primes shown on our < 300 site but didn't help in determing if a gap existed. If anyone can say what gap, if any, remains on k=289, I would be interested in hearing it. Regardless, it seems very unlikely that the entire range of n=90201 thru n=501991 contains no primes so I would like to reserve the entire range for testing and/or checking. That is unless someone can say for sure that parts of it have been tested, in which case I won't check those ranges. Unless somoeone thinks this would be a waste of CPU time, I will dedicate my new highspeed dual core laptop on it. A quick look at preliminary sieves on the entire range show that I could complete it in about 2030 days, while leaving my other 2 machines to work on other reserved k's. Thanks, Gary 
k=289
to 1.
... [300k Jeffrey], 501991, 509401... means: Jeffrey has llrtested this k up to n=300k (without gaps) and other higher prime n are also known/found by someone not with RPS and limit is unknown (here all higher n found by Bo Xiao since 2005). to 2. 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 primesearchsite 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. to 3. see 1. (would help to contact Xiao) on the other hand 289 is reserved by Xiao (see riesellist on [url]www.15k.org[/url]) so it make no sense to work on this k. try another unreserved k. i'm now working on the summayk for 251<k<1001 to include all informations of primesearch or [url]www.prothsearch.net/riesel2.html[/url]. karsten 
Karsten
You replied correctly to your questions :smile:
k=289 was tested to 300k by Jeffrey. From there on we know nothing about tested ranges, only primes posted by Bo to Top5000. I'd also like to talk to Bo but his email address on his bio page on Top5000 is unpublished, so I guess he doesn't want to be contacted that way. Besides prof Caldwell I know one more person who possibly knows his eaddress but I never asked. Maybe one day he will appear to tell us, maybe not. Obviously he started at least at 500k, maybe lower. Maybe indeed there is a gap 300400k, or 300500k (?) LLR tests to about 400k (while the FFT length is 24k) will be very fast so you can try. Also because 289 is a square, sr1sieve will be also very fast. 
[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 primesearchsite 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 coordinated 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 Top5000 due to the flood of byproduct 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 top5000 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 top5000 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 twinprime search and too low of an n to stay on the top5000 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 twinprime 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 top5000 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 top5000 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 top5000 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 top10 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 top5000 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 doublechecking 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 twinprime with n > 100K. I now have one machine working on k=289 (will be done sieveing to 400G today), one going after a top10 twin prime, and one working on one of my highweight 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 top5000 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, 200225k 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 top5000 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 nonstop day and night...probably 1015 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 top5000. If you want REAL glory, you have to go after the BIG monsters...i.e. the first 10,000,000digit 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 twinprime 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 11001200 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 highspeed machine looking for twins, I only have a very slowspeed 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 5050 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 fixedk searches are more "complete" than fixedn searches? :unsure:

[QUOTE=Cruelty;108942]I'm just curious: why do we assume that fixedk searches are more "complete" than fixedn searches? :unsure:[/QUOTE]
What do you mean by complete? Fixedk has a few features that make it more interesting for a cooperative search: First, each chosen k can be worked on as deep or notsodeep as one likes, while still contributing to the group's work. A fixedn 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 5000thprime 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 top5000) 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 searchspace of k/n combos. What possible completed searchspacerange would a group of fixedn 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 100500M block, if you even possibly might do another block later.
fixedk sieves scale with the square root of nrange; fixedn (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 counterargument 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 2diminensional 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)? 
[QUOTE=Cruelty;108963]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)?[/QUOTE]
About 70%. Expected # of primes: 1.2 
[QUOTE=axn1;108988]About 70%. Expected # of primes: 1.2[/QUOTE]How do one get those numbers? :unsure:

[QUOTE=Cruelty;108991]How do one get those numbers? :unsure:[/QUOTE]
Probability of a random number N being prime = 1/ln(N). For k*2^1234567+/1, you can approximate it to 1/(1234567*ln(2)). Probability after sieving upto p = (e^gamma*ln(p))/ln(N) Here, gamma is Euler's constant. You can take e^gamma = 1.781. So, the probability of one of your candidates to be prime = (1.781*ln(82T))/(1234567 * ln(2)) = 57.06/855736 = 1/14997 = 6.67e5 The prob that /none/ of your 18283 surviving candidates is prime is (11/14997)^18283 = 29.5%. So, prob that at least one prime is present is 70.5% Expected number of primes = 18283 * 1/14997 = 1.22 
Thanks! :smile:

Probability of prime after sieve, nicely stated!
Nicely stated and calculated, axn1! The only part that really lost me was the e^gamma part. Sounds like part of a calucation for the area under the bellshaped curve. How was the e^gamma constant arrived at?
I enjoy the math and have done a fair amount of statistical analysis but I'm no highermath whiz so if the exaplanation involves too much calculus differenciation or integration, then it may be above my head. But I figured I'd ask anyway. Thanks for the analogy on the chances of a number being prime after being sieved to a certain amount. I'll use it a lot in the future to decide how to divide up work on my machines. Gary 
Thanks, axn, for the formula. Very much fun to "predict" the number of primes left in a candidate pool.
Curtis 
reserving k=2145
I've freed up a machine from twinprime searching so I'm going to reserve another, most interesting, k, that is k=2145, to fill a gap and then continue from the highest found prime.
Being the 'base' factor for many highweight k's, I'm amazed that it has not been tested more than it has. It has a gap from n=50K to 115899 and there is no indication that it has been tested higher than its highest prime of n=214994. Gary 
Gary
2145 has 7 primes from 50k to 160k, the limit of my current search. A few months ago I got interested in k>2000, and began working on 2055, 2085, 2115, 2145, 2175. I have them LLR'ed to 160k so far, with the sieve to n=600k approaching p=4T. I neglected to reserve them for no good reason you'll find a thread well down the list about k>1000 started by me; I began sieving back then, and just never posted the reservation. I guess I thought it unimportant until I got above top5000 cutoff, but we didn't have anyone like you working on small numbers back then. I can send you the primes and sieve if you'd like to work higher; you can just tell me your new limit when you tire of the work, and I'll pick it back up from there. You're welcome to work as high as you please. I have 160210k ready for work now, 210+ still sieving. Please, allow me to send you at least this chunk! Curtis p.s. reserving the other 4 now, please 2055, 2085, 2115, 2175. 
Sharing the glory on k=2145
I sure am good at stepping all over others people k's! :wink: I guess I shouldn't be surprised that someone was working on this one at some point...sorry about that.
It's really just been in the last 2 weeks that I've looked at lower k's with gaps. For the first 67 weeks of my primefinding existence, I was looking for very highweight k's with gaps or that just looked extremely good to me. But I just decided that I wanted to fill all gaps, regardless of the size of k, and it is the lower k's that are more visible. I'm aware of 4 of the 7 primes that you found between n=50K and 160K because they are posted on the summary site. I'm guessing that Thomas previously found them. Since you have the entire range searched with all of its primes, I'd just suggest posting the primes to fill the gap in the 'small primes found' forum and Karsten can post them all. There's no reason to send them to me since you found them and I don't see a reason for me to doublecheck them since we would all know for sure that you've tested the entire range. That's a heck of a sieve file! This is a bit awkward. Tell you what...I'd really like a crack at taking this one higher if your OK with providing me your sieved file. If I find a top5000 prime, we can share in the glory. I think that's the way it usually works on the big projects...that is the coordinator, top siever, top searcher, and the finder all get credit for the find. Personally, it's doesn't make much difference to me. As you know the glory to me is just having complete and accurate lists of primes but I wouldn't mind having a prime or two in the top5000 just for grins. :smile: I will just start from the last prime found of n=214994. The sieved file to n=600K to P=4T :surprised is probably more than I'd be willing to test but I'll have to see what my machine situation is in the next couple of months. I have a friend who's going to lend me an 850Mhz machine tomorrow for several months so that will help. I'll use it for some of my 'side projects' like twin prime searches that don't need highspeed processors but that have been taking time away from my speedy machines at different times lately. Oh, and speaking of side projects...I have the ultimate gapfilling file that I will be sending on to Karsten / Kosmaj in the next couple of days. I'll create a separate thread for it. You'll probably want to see it when I post it. Karsten, I'm going to keep you really busy! But I'll be nice and warn you a little while ahead of time. :smile: Thanks a bunch. Gary 
There is no need to share in the glory if you find a 2145 prime big enough for the top 5000, it's all yours. You have done plenty of work for our project, and deserve some fame and fortune.
PM me your email, and I'll send the the sieve from where I stopped (162k or so) to 240k; n>240k is still sieving, so I'll send the rest when you get up to 240k. My trusty old celeron566@850 sieves at just over a trillion a month on this file. Curtis 
gd_barnes:
"... Karsten, I'm going to keep you really busy! But I'll be nice and warn you a little while ahead of time. " oh. no problem! i'm hunger for new informations to put them in the summary pages, to fill gaps and kill errors!!! keep our summary for all k*2^n1 the best, actual and completest on net is my purpose! i'll keep an eye on this forum (and quite many other pages like Top5000) every day and all new info i obtain i put in the summary. so sending your ultimate gapfilling file is like christmas and easter at one day for me :grin: 
Also reserving k=923. Looks like a very highweight for a non3*k value.
Curtis 
BIG file coming today and more error checking
[quote=kar_bon;109710]
oh. no problem! i'm hunger for new informations to put them in the summary pages, to fill gaps and kill errors!!! keep our summary for all k*2^n1 the best, actual and completest on net is my purpose! i'll keep an eye on this forum (and quite many other pages like Top5000) every day and all new info i obtain i put in the summary. so sending your ultimate gapfilling file is like christmas and easter at one day for me :grin:[/quote] OK, you asked for it. :smile: I'll send my very big file your way later today. But first, I've analyzed and checked all k's where 1000 < k < 10000 on the summary site that have primes listed where n <= 10000. This was a comprehensive check on the entire range, not just a spot check. I found 4 problems. (Quite excellent really!) After the corrections are made, I can personally guarantee that every prime shown that is n<=10000 will be correct for that range of k on the summary pages. I may do this for k < 1000 at some point also but I feel that the primes for k > 1000 would be far more prone to error because the smaller k's have had much more coordinated efforts. I seriously doubt that there are any errors on small n's on the k < 300 site. I anticipate maybe 12 errors for small n's for the Prime Search range of 300 < k < 1000. I'll post the problems in the 'new data page' forum where you ask for error checking and that I've posted some problems before. Gary 
k=1000065
Reserving: 1000065.
First primes from 1 to 50k: 3, 5, 7, 14, 19, 20, 26, 81, 82, 113, 117, 146, 190, 268, 298, 308, 341, 391, 526, 979, 1122, 1221, 1310, 1454, 2146, 2468, 2564, 2938, 3047, 3119, 3791, 4395, 6303, 6439, 7117, 7635, 8165, 10082, 10357, 12532, 22597, 25263, 25411, 25713, 32663, 35845, 46340 
1000065
to arminius:
1000065 is also prime for n=3, 5 and 7! (inserted in Summary) Karsten 
Ah  thank you!

Reserving k=115029915
After initially doing a little testing on this one to fill some gaps, I realized that it is a HUGE performer for its size!
After completion of gap filling on it, I plan to include it in my arsenal of heavyweights that I am sieving all at once from n=200K to 400K. Gary 
[quote=VBCurtis;108952]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 100500M block, if you even possibly might do another block later.
fixedk sieves scale with the square root of nrange; fixedn (including twin) sieves hardly scale at all. Curtis[/quote] Curtis, This was from a while back so I thought I'd give you an update. Since we exchanged notes about us both doing a TPS in the n=90K to 110K range, I got access to another somewhat highspeed machine so have started up again on it. In doing so, I completed sieving on the k=100500M block and have tested up to about k=200M on it. Since the odds are still well against me finding a twin in that range, last week, I started a sieve for the k=500M to 4G range. The machine has 1G memory so that isn't an issue. The main thing is that fortunately the range is just barely able to fit in NewPGen's max memory allocation of 485M so it is sieving at full speed. I calculated that testing the entire range of k=0 to 4G should give me about a 66% chance of a twin that would be in the top10 (at the current time). Although total testing time on the one machine would be nearly 6 months if a twin isn't found sooner. :yawn: :yucky: I hope it won't take that long and more than that, I hope it won't take a bigger range! If so, I may have to pull a machine off of my heavyweight k search and I don't really want to do that. Gary 
Reserving k=120023475
A monsterweight for its size, I am reserving k=120023475 for inclusion in my huge sieve of highweight k's from n=200K to 400K. I think this is the smallest k to have a Nash weight > 7000 shown on the summary site.
I'll fill the gap below prior testing and then separately test up to n=200K first. Gary 
Reserving k=16995, 26565, and 49335
I'm going to reserve these smaller k's to begin a 'side effort' separate from my largek veryheavyweight search. It'll be nice to search some k's that don't take so long. I'll fill the large gaps in k=26565 and 49335 and then test them all from where they were left off at.
Gary 
List of all reservations
Since I now have 16 k's reserved, I want to put all of them in one place and my planned upcoming efforts on them.
I am done sieving the range of n = 200K to 400K and am now LLRING all of my 12 large heavyweight k's as follows: 19437 102765 3545685 111546435 115029915 120023475 290499495 686701125 775784295 968911515 1019340795 3428677395 1. 2 cores will be working on the range of n = 333335 to 400K to get a top5000 prime quickly. 2. 1 core now and a 2 core later will be working on the range of n = 200K to 333334 to fill in the gap. I also have reserved the following k's and after getting them tested and verified up to n = 200K, I will be doing the same with them as the above in a separate effort. 16995 26565 49335 I also have reserved k=2145. I get sieve files from Curtis periodically on that one and test them shortly afterword. It has now been tested up to n=280K. Gary 
reserving 28397655
currently sieving 
Good luck levitate!

I would like to reserve 3,333,333 and 3,015,015.
I just found this forum and I would like to search these two k values if they have not been searched and are not currently being tested. Thanks, Adam 
They are both available AES. Good luck and feel free to PM me if
you need any help. 
Ending k = 3,333,333 at n = 400,000

Hey all, I'd like to reserve k = 105105 for 33,219,261 <= n <= 33,554,432. A high weight k with lots of candidates, this should last ... a while.

[QUOTE=lavalamp;120024]Hey all, I'd like to reserve k = 105105 for 33,219,261 <= n <= 33,554,432. A high weight k with lots of candidates, this should last ... a while.[/QUOTE]
It sure will, considering the high n value you have. If you're looking for a 10 million digit prime, you'd be better off testing k=3, 5, or 7, as they have a lower FFT size and take about half as much time to test than k=105105 in your 33,219,261 <= n <= 33,554,432 range. Also, I don't think there's a need to post reservations of k's that have an n value higher than 10M, since RPS won't be getting there for decades (unless all of the GIMPS crunchers switch to RPS today). 
Ah, I didn't know that. You really weren't kidding about half as much time either. I ran a few tests and the iteration time for k = 105105 was 100.7 ms, for k = 3 (all other things equal) it was 48.7 ms.
In that case I think I'll work on k = 27, since it's the most dense of the very small ks and the iteration time is only 48.9ms. Plus this project will run as an extension of [url=http://12121.vocabulate.com/]12121[/url]/[url=http://12121.vocabulate.com/27k/]2721[/url] as I am working with Justin. 
Ending [URL="http://www.adamsutton.net/index.php?view=article&catid=35%3ArpsCategory&id=48%3A3015015&option=com_content&Itemid=55"]k = 3,015,015 at n = 470,000[/URL]

228461805*2 from n= 30000 to n= 55000
Found 2 primes. Ending it. 
[QUOTE=kuratkull;124746]228461805*2 from n= 30000 to n= 55000
Found 2 primes. Ending it.[/QUOTE] i show the range n=300k to 550k in the summary. ok!!?? 
Reserving k=1003 from n=10K. :smile:

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[quote=Anonymous;128587]Reserving k=1003 from n=10K. :smile:[/quote]
Status for k=1003: now at n=100K. lresults for 10K100K are attached. Continuing with this k. :smile: One prime was found in the range 10K100K: 1003*2^459871 is prime! 
From the Top5000:
[CODE] rank description digits who year comment       901 1003*2^5841031 175836 L51 2004 1354 1003*2^4826551 145297 L51 2004 19266 1003*2^1441631 43401 g327 2003 [/CODE] 
[quote=Kosmaj;128612]From the Top5000:
[code] rank description digits who year comment       901 1003*2^5841031 175836 L51 2004 1354 1003*2^4826551 145297 L51 2004 19266 1003*2^1441631 43401 g327 2003 [/code][/quote] Yes, I noticed those when I was first checking out the kbut I decided to start at n=10K anyway to fill any gaps that may be left around. After all, what's the point of all this searching for primes if you're going to do it willynilly and leave gaps? :smile: 
1 Attachment(s)
k=1003 is now tested, completely and contiguously, to n=500K. Two primes were confirmed in my range of n=10K500K, at n=144163 and n=482655; one new prime was found, at n=45987. (All these primes have been reported in the respective postprimeshere threads.)
I am releasing k=1003, though I may come back to it in the future; however, if anyone else wants to search this k, then by no means let that stop you from reserving it, as that only holds things up and is contrary to the best interests of the prime searching community. :smile: Residuals for n=100K500K are attached. (BTW, in case anyone thinks the times listed for n=390K500K look funny, that's because the results for that range were converted from the results files from an internal LLRnet server that I ran that range on. LLRnet records the total time the client had the test "checked out", rather than the actual time it took to perform the test. So, don't worry, the funny timings aren't a sign of instability. :smile:) 
hi i'll take k=1121 from n=10k, thanks

Welcome to RPS, Buzzo. Good luck with the search!
If you want help/advice setting up a sieve, PM me. If you are experimenting with the software/methods and want a short project, I recommend searching 10k400k or lower. You are not very likely to find a top5000 prime this way, but the project should take just a few CPUweeks on a modern machine. Testing 10k100k will take just a day or so; sieve a day or less, then test 10100k. Curtis 
[QUOTE=VBCurtis;133068]Welcome to RPS, Buzzo. Good luck with the search!
If you want help/advice setting up a sieve, PM me. If you are experimenting with the software/methods and want a short project, I recommend searching 10k400k or lower. You are not very likely to find a top5000 prime this way, but the project should take just a few CPUweeks on a modern machine. Testing 10k100k will take just a day or so; sieve a day or less, then test 10100k. Curtis[/QUOTE] okay, thanks for the advicei've decided to do 10k300k. i figured out how to get srsieve/sr1sieve going on my own, but thanks for the offer to help anyway! 
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