20091024, 04:06  #56 
Jun 2003
Oxford, UK
2,039 Posts 
Been working on the Riesel side this week, mainly on E52's. Many new drag racing records, the most noticeable of which is
R 15145054826747 52 19/31 20/32 It is really tough to break all time drag racing records at lower n as maybe a trillion k have been checked to this level. It is prime at n=1,2,3,8,9,10,13,14,15,16,17,20,21,22,26,27,29,30,31,32, so 14 CCs in there. I still have not achieved a better VPS on the Riesel side than 100/5748 nor have I found any new at 110+/10000, so I will persist on the Riesel side, checking at all E levels. If others join the hunt, they should concentrate on the Sierpinski side. A minor record broken, there is a k, approximately 3.1249*10^36, which has 102/10000. This is the largest k to date which is VPS. The smallest k is approx 4.416*10^14, on the Sierpinski side. I also found the first E138 VPS this week, R 25988421035 138 100/9986 100/10000 In all, using Robert Gerbicz's software, I have now discovered 206 new Riesel VPS: 1 is 109/10000, 5 are 107, 8 are 106, and 11 are 105/10000. 67 are E52, 10 E58, 39 E60, 19 E66, 49 E82, 13 E100, 5 E106, 3 E130 and 1 E138. 2 have their hundredth prime between n=5K6K, 14 in the 6000's, 21 in the 7K range, 64 in the 8K and 105 in the 9K. I still find it astonishing that I am the only person on the planet using this crafted software. I do encourage others to join the hunt. 
20091024, 04:21  #57 
Jun 2003
Oxford, UK
2,039 Posts 
If others do take the Sierpinski side, I have checked the following
S 58 to Iteration=0, i=98849 S 60 to Iteration=0, i=24786 S 82 to Iteration=1, i=51248 Robert Gerbicz has checked an unspecified number of S 52. Another interesting thing to find is the first S 268. The in.txt file should be manipulated to check all finds at that level to at least n=10000. So set vpscount to 1, and smith_check to 0 
20091024, 05:26  #58 
Jun 2003
Oxford, UK
2,039 Posts 
Total VPS and their discoverers:
Sierpinski: 195 R Smith/ P Carmody 89 R Smith/ R Gerbicz 8 R Gerbicz 292 Total Riesel: 203 R Smith/ R Gerbicz 114 R Smith/ P Carmody 11 R Chaglassian/ P Carmody 3 R Gerbicz 331 Total 623 Grand Total Last fiddled with by robert44444uk on 20091024 at 05:27 
20091027, 16:29  #59 
Jun 2003
Oxford, UK
2,039 Posts 
Finally broke the century Riesel record, a certain E(60) candidate is 100/5566 and 110/10000.
And another E(66) candidate found 10 minutes later is 100/6660 and 109/10000. Either of these could easily become the most prime k known to date. 
20091109, 11:07  #60 
Jun 2003
Oxford, UK
2,039 Posts 
A week away and the project is purring away nicely, although I am still the only person working on it. This is hard to comprehend given the rewards for small prime hunters and the possibility to discover a nice juicy k that might have 200 primes before n=1,000,000
How can I be the only person in the World doing this? I haven't even got someone, even another geek, to tell me this is a geeky thing I am doing. The week produced no absolute (best of Riesel and Sierpinski) racing records, but plenty of Reisel records. There are now 67 new Reisel racing records to the 113th prime, of which 17 are absolute racing records. And this week also produced one k at 112/10000 and one at 113/10000. Altogether I have found 366 new Riesel VPS, of which 54 are equal to, or better than, 105/10000. Overall, since the software was written, the number of VPS has grown from 320 (195 S and 125 R) to 783 (292 S and 491 R). 
20091109, 12:39  #61  
Mar 2006
Germany
2^{3}×3^{2}×41 Posts 
Quote:
i think there're some reasons why:  there's much less fame for finding 'small' primes than big ones  to test a 30 or 40digit k with a nashweight of 8000 or 9000 will last for years; only to test up to n=100k it's a great effort  another aspect: such big kvalues cannot sieved with srsieve, you have to use newpgen in primorial mode! so sieving will take more time.  the most primes of one k today (as far as i know) is for k=37850187375 from T.Ritschel: 159 primes up to n~620000; the 100th prime is at n=13719. so with your records with 113 primes at n=10000 it's a very big step to find such special k with 200 primes to n=1000000! i think i will continue 'my' k with 130 primes up to n=100k the next weeks. i haven't done much work the last month on the related page here! perhaps you can fill some values there. Last fiddled with by kar_bon on 20091109 at 12:43 

20091109, 16:22  #62  
Jun 2003
Oxford, UK
2,039 Posts 
Quote:
The best at n=10000 I have found has 116, from several years ago. You can use newpgen efficiently without primorial mode using * symbol between primes in E, and it works well but with these numbers only 70% to 75% of n get eliminated. But that is why they are so prime. Most primes is 169 found by me at n=360000. There is a big difference between 169 at 360000 and 159 at 620000. I think getting a super VPS will give a huge advantage and Robert Gerbicz's program gives us the edge. I agree they are quite slow to check above n=160000 But 200 at n=1000000 is doable in my opinion Last fiddled with by robert44444uk on 20091109 at 16:24 

20091109, 17:03  #63 
Jun 2003
14F5_{16} Posts 

20091110, 06:12  #64 
Jun 2003
Oxford, UK
2,039 Posts 
This certainly would be a good objective  I have sieved deeply to n=500000 if anyone is interested. I have forecast that the 200th prime is at about n=2000000
Most primes found (169): 708477982733*M(59)*2^n+1, checked to n=353045, prime for n= 2,3,4,9,16,23,28,41,49,52,58,87,94,98,100,106,130,141,145,149,152,154,161,166,167,175,177,179,181, 183,188,202,216,227,239,272,324,352,371,399,419,434,461,466,478,513,524,565,573,600,618,643,668, 680,703,736,758,807,855,883,908,915,934,945,1044,1049,1054,1200,1224,1250,1463,1810,2234,2317, 2388,2740,2879,3054,3108,3680,3692,3796,3867,3893,3917,3941,4001,4050,4080,4137,5202,5230,5805, 6134,6343,6540,7277,7440,7534,7815,8100,9360,9473,9844,9909,10277,10790,10918,11459,12716, 13641,13824,15863,17072,18041,18601,19470,22777,23750,25140,25558,31512,36659,36833,37522, 37525,38876,39047,39949,40663,43294,44173,46708,49784,50432,51378,51660,55708,58034,58798, 74103,76856,78788,80913,88261,88674,104186,105283,107911,122428,123760,125392,126478,129152, 129850,137749,172113,174521,184521,202474,206409,214727,226714,231290,240057,243709,300332, 340795,352601 But I think there are probably better candidates from the 453 new VPS I have discovered over the last 6 weeks. I am thinking it would be good to develop about 1000 new VPS, and then take these up to n=20000 before slimming down to the best 200 or so. I reckon that there about 10 which would be 165 or better at n=350000, and a reasonable chance of finding a candidate that reaches 175177 primes by n=350000 and 200 by n=1000000. Last fiddled with by robert44444uk on 20091110 at 06:13 
20091110, 11:10  #65  
Feb 2003
2^{7}·3·5 Posts 
Quote:
Quote:


20091110, 14:50  #66 
Mar 2006
Germany
2^{3}·3^{2}·41 Posts 
oh, yes, you're right. i was only referring to the Rieselside of my collection of primes and Payemnumbers!
it's time to make a collection like mine for the '+'side! somebody here to do so? Last fiddled with by kar_bon on 20091110 at 14:51 
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