20060804, 22:39  #122 
Nov 2003
2·1,811 Posts 
I see no reason why not. Has anybody worked on them? I have no idea, maybe Thomas or Curtis can tell you more. BTW, I see that the file contains more than 5000 Ks, how did you select exactly these 11 out of 5000?
And I just tried sieving k=15335906269828439. In the n=110k range no n survived sieving to 85M. In the n=10200k range only 12 did! 
20060805, 06:26  #123  
Jun 2003
631_{16} Posts 
Quote:
Why I am working on these extremely low weight k's? Looking at most of large megabit primes found in the top 5000 DB, they are either mersenne numbers or other numbers that can be tested really fast, like k<32 for proth and riesel. Then there are k's that have low weight. Consider for example all the huge SOB primes. These SOB k have such low weight that they should not have found a prime in the n range they were searched for. Yet projects like rieselsieve, PSP and SOB continue to beat the odds and find new megabit primes. So I think, that if we choose a bunch of k's and work of them, irrespective of weight, one of them would eventually beat the odds and spit out a prime. To test this hypothesis, I am reserving the lowest 11k's that I know of, to test them to a large n value. The following k's had 0 values left under 1M. I think these are riesel number and not low wieght numbers, but I do not know how to prove it. Is there a way to decide on their identity? 1531543060309739 24495411634339871 27697189380823769 31153994867516291 61624064322011353 61670219307871063 79259968463949613 Thanks Last fiddled with by Citrix on 20060805 at 06:27 

20060805, 16:28  #124 
Nov 2003
E26_{16} Posts 
I checked k=1531543060309739 using the output of ksieve with p<2000 and found the covering set to be [3, 5, 7, 13, 17, 19, 73, 193, 257, 1153] and modulus=288. Here is the relevant part of the output:
Code:
3  1531543060309739*2^11 +2... 5  1531543060309739*2^21 +4... 7  1531543060309739*2^01 +3... 13  1531543060309739*2^41 +12... 17  1531543060309739*2^01 +8... 19  1531543060309739*2^21 +18... 73  1531543060309739*2^51 +9... 193  1531543060309739*2^441 +96... 257  1531543060309739*2^41 +16... 1153  1531543060309739*2^1881 +288... 
20060810, 08:36  #125  
Jun 2003
5·317 Posts 
Quote:
I think my hypothesis was wrong, the k's should have some substantial wieght else, no prime will be found. Thanks. 

20060811, 04:06  #126 
Sep 2005
Raleigh, North Carolina
151_{16} Posts 
Reserving k=41343149

20060813, 10:33  #127  
Sep 2005
Raleigh, North Carolina
337 Posts 
Quote:


20060823, 17:11  #128 
Jun 2004
106_{10} Posts 
k=10453199 tested until n=440000, no primes. Releasing

20060824, 02:35  #129 
Sep 2005
Raleigh, North Carolina
337 Posts 
Status Update on k=256453:
Primes at: n=607 n=41359 n=233779 Tested to 810k Continuing to 1M 
20060902, 01:07  #130  
"Curtis"
Feb 2005
Riverside, CA
11715_{8} Posts 
Quote:
Second, the phrase "eventually beat the odds" makes no sense. If you search long enough, the odds say you WILL find a prime. You can hope to get lucky, which is really what the lowweight search is about; but saying weight has no relevance, or needs to be above a certain cutoff (which you concluded after striking out to 1M on 11 kvalues, which was what, 250 tests?), is folly. I think you're confusing the depth of a search with the time taken TO search. Your original idea to test the very lowestweight k's was fine, but to give up after a week and 11 candidates proved nothing. If you hope to find a 200k digit prime, it's going to take 36 Ghzmonths on average, no matter how to try to do the search. Hope this helps. curtis 

20060916, 01:45  #131 
Sep 2006
3^{2} Posts 
I would like to reserve the following k (I have indicated limits I have already tested them to and primes found):
k=131069 (to 290K), no additional primes beyond n=16 and 112 found by Joss k=9705763 (to 635K), prime at n=49335 I have also done testing on some other low weight k's not listed (if yall are interested): k=792729463 (to 330K), prime at n=4271, 24671 k=29330981023 (600K), no primes yet I am not really interested in these latter two k's, so if you add them to the list, they can be considered available for reservation. Andrew Last fiddled with by humanoverlord on 20060916 at 01:46 
20060916, 02:42  #132 
Nov 2003
2×1,811 Posts 
Andrew
Welcome to RPS!
I just updated our low weight stats page with your results, it's normally updated by Mike but I was just "in the office" updating our k<300 page so I did it this time. BTW, maybe you have already noticed, we are currently processing 36 low weight Ks in our 3rd Drive, we are now at n=1,570,000. If you have some spare cpu cycles you are welcome to join. All candidates are sieved to 4.2T. If you have any questions, please don't hesitate to ask. Happy hunting! Last fiddled with by Kosmaj on 20060916 at 02:43 
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