20081017, 01:24  #45  
May 2007
Kansas; USA
2^{6}×3×53 Posts 
Quote:
Not possible, even if you assume a doubling of computer speeds every 2 years, which is highly unlikely! You are forgetting that base 1000 for 1000^50000000 is a much larger test than 2^50000000. Even so, taking all k's on Riesel base 2 up to n=50M will be a serious challenge in most of our lifetimes. Yep, I'll find time to update the web pages. It might be a couple of months before I get all this info. in there but it will get there. There's one thing that I want to bring up here: Neither I nor anyone else here can claim ownership of these conjectures. This project has only been intended to organize such efforts towards the conjectures not being worked on by others, not own them. We will not be offended if anyone wants to break off and create a separate project for a specific base or two. The base 5 project has made HUGE progress on its own in a few short years on an extremely tough base and personally, I'm glad that they have done it so that we don't need to. The same applies to Sierp base 4. KEP, you really enjoy base 3 so if you want to create a separate project for it, go right ahead. I'll be glad to assist with that. One guarantee: It's a lot more work to administer these things than you'll ever imagine in the beginning. All of that said, if another effort is 'dropping the ball' such as has happened with RieselSieve, you can bet we will step in and pick up the slack if the effort goes dormant for too long and there has been little communication about when it will start up again. But if the effort subsequently 'comes back', we'll gladly let them pick it back up again and communicate any progress made. Gary 

20081017, 01:34  #46  
May 2007
Kansas; USA
2^{6}×3×53 Posts 
Quote:
Very interesting odds Karsten! It's even more difficult than what I had attempted to compute in another thread, which had the Riesel base 2 conjecture with a better than 5050 chance of being solved by n=16T (n=16*10^12). That is, I had computed that there should be < 0.5 of a k remaining at that point. I've now realized that there's one large error that I made in my computations. I assumed the primes would continue to come at the same exponential reducing rate. That is an incorrect assumption because the k's remaining will have respectively less average weight than the k's where primes have been already found. Therefore I'm sure that Gallot's estimate is far more accurate. Edit: In KEP's defense here, he did not state that the conjectures needed to be proven to realize his dream; only that they need be tested to n=50M. That seems to be a reasonable goal for Riesel base 2 in most of our lifetimes but not for 2046 bases, i.e. 2 bases each for 2 thru 1024! :) Gary Last fiddled with by gd_barnes on 20081017 at 01:43 

20081017, 04:49  #47  
Jun 2003
Oxford, UK
3·5^{4} Posts 
Quote:
Robert  could you disclose to what cover these are tested. Your program requires every cover to be tested. For example it is possible (but unlikely) for a 5cover to be smallest. 

20081017, 07:16  #48 
Jun 2003
Oxford, UK
3·5^{4} Posts 
Robert G's list produces lower values than Siemelink's as follows:
Code:
66 101954772 71 1132052528 120 166616308 127 93902377422 156 2113322677 175 278467080 195 582483712 238 5415261 240 2952972 280 513613045571841 303 85368 323 93896 325 112882226 345 1295243216 358 27606383 435 31732727570 453 4658266 511 40789000085994 525 8364188 541 15546458 570 12511182 591 30820 661 2518794379382 685 518792 728 212722 777 23485096 796 27199220 799 1885767686976 801 40381102 826 131420459393 855 7419914968008 876 51768432 906 171998037 910 5005381602981 946 2156122023 960 61681833328 963 22349616 966 699327630 981 112303013130 1020 94655888 Last fiddled with by gd_barnes on 20100516 at 08:14 Reason: put conjectures in code 
20081017, 09:57  #49 
Mar 2006
Germany
3×947 Posts 
Riesel base 35 status
LLRtested for all k's upto n=6050
sieved to 3.9B=3.9*10^9 124 primes found so far (from 1559) 5.4M candidates left 
20081017, 10:52  #50  
May 2007
Kansas; USA
27C0_{16} Posts 
Quote:
In order to update the web page, I'll need to get a list of the primes. Otherwise, the highest primes list will be out of sync with the nrange tested. I'll create a page of the k's remaining at n=5K from Willem's earlier posted list a little later today. 

20081017, 15:04  #51  
"Robert Gerbicz"
Oct 2005
Hungary
3·461 Posts 
Quote:
As I remember I tested for exponent=144 but for low limit for primes (limit=10000), after it was switched to test exponent=8,24,36,48 for large limit. But today I think it was really unnecessary, here it is a quick stat for the Sierpinski side b=21024: Code:
number of period=2 is 525 number of period=3 is 53 number of period=4 is 224 number of period=6 is 107 number of period=8 is 18 number of period=9 is 2 number of period=12 is 75 number of period=16 is 1 number of period=18 is 2 number of period=24 is 11 number of period=36 is 2 number of period=48 is 1 number of period=72 is 1 number of period=144 is 1 max prime in coverset=731881 at b=855 Code:
number of period=2 is 528 number of period=3 is 53 number of period=4 is 230 number of period=6 is 105 number of period=8 is 23 number of period=10 is 2 number of period=12 is 63 number of period=16 is 1 number of period=18 is 1 number of period=24 is 9 number of period=36 is 5 number of period=48 is 1 number of period=144 is 1 max prime in coverset=921601 at b=959 I would be glad if some of you could find a better k value. Last fiddled with by R. Gerbicz on 20081017 at 15:07 

20081017, 23:01  #52  
May 2007
Kansas; USA
2^{6}×3×53 Posts 
Quote:
Willem, Can you send me all your primes on Riesel base 35? Thanks, Gary 

20081018, 02:03  #53  
May 2007
Kansas; USA
2^{6}·3·53 Posts 
Quote:
Karsten, Per your Email showing primes found up to n=6060, I have now listed all k's remaining and highest primes found for Riesel base 35. Willem, Your list of k's remaining for this base had a slight error in it. You had both k=94 and 115150 remaining. Since 115150=94*35^2, it can be eliminated. The list of primes that you found will help me do a little more verification. Karsten, You can eliminate k=115150 from your testing. The web pages reflect the removal. Once you do that, you might check your file to verify that there are 1434 k's remaining at n=6060. Gary 

20081018, 12:35  #54 
Jun 2003
Oxford, UK
11101010011_{2} Posts 
I ran both Sierpinski and Riesel to 1024 with 12cover and using all primes less than 10 million and no better values were found. I plan to look at 7 or 8 very high kcandidates to see if they can be bettered

20081019, 08:38  #55  
May 2007
Kansas; USA
2^{6}×3×53 Posts 
Quote:
Per Robert Gerbicz's improved Riesel list, the conjecture for Riesel base 48 is k=3226 with a covering set of {5, 7, 461}. I have now confirmed it. This reduces the k's remaining at n=10K from 74 to 55 and changed the top 10 primes. The web pages will be updated accordingly. I checked his list vs. what we show up to Riesel base 50 and that was the only incorrect conjecture that I found. Gary Last fiddled with by gd_barnes on 20081019 at 08:43 

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