20091102, 22:49  #23 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
Also no primes to n=10k. Unreserving Riesel 811.
Last fiddled with by TimSorbet on 20091102 at 22:50 
20091109, 23:20  #24 
Mar 2006
Germany
2999_{10} Posts 
Riesel Base 989
tested just for fun the remaining k=2 from n=25000 and found this:
Primality testing 2*989^268681 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 23, base 8+sqrt(23) Calling BrillhartLehmerSelfridge with factored part 54.54% 2*989^268681 is prime! (873.8538s+0.0080s) so this is my first proven base (very small one but a beginning ) 
20091110, 00:23  #25  
"Gary"
May 2007
Overland Park, KS
3·7·563 Posts 
Quote:
One thing of interest about this base: Although there are many bases with a conjecture of k=4 that are proven with only a prime for k=2, this is the 1st such base proven with a prime at n>250. The current bases proven by finding only a prime for k=2 at n>100 are: Riesel base 989, n=26868 Riesel base 779, n=220 Riesel base 629, n=186 Riesel base 449, n=174 Riesel base 29, n=136 All bases where b==(29 mod 30) will have a conjecture of k=4 on both sides and will only need to be tested for k=2 because odd k's will have a trivial factor of 2. Afaik, all of the Riesel bases <= 1024 have been done but most of the higher Sierp bases have not been. If anyone wants to take on the task of doing some of them, most can be done almost instantly and will have a prime at n<10. If you decide to do this, please let me know ahead of time. Most will likely test very quickly but multiple bases take quite a while to add to the pages even for a small conjecture. I'll want to know which bases so I can start adding them to the pages before getting all of the info. Edit: There is only one such Riesel base <= 1024 remaining to be proven. The highest one: base 1019, which has currently been tested to n=25K. So there you go Karsten...another possible one to prove. Doing so would prove all Riesel bases <= 1024 where b==(29 mod 30). :) Gary Last fiddled with by gd_barnes on 20091110 at 22:24 Reason: add base to list of k=2 primes 

20091111, 06:14  #26 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89×113 Posts 
I'll take Sierp. base 961 to 50K, for starters.

20091112, 00:55  #27 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89×113 Posts 
Sierp. base 961 around 15K; 3 primes, 9 to go.
Last fiddled with by Batalov on 20091112 at 01:01 
20091112, 04:26  #28 
"Gary"
May 2007
Overland Park, KS
3·7·563 Posts 

20091112, 19:22  #29 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89×113 Posts 
I'll take Riesel base 811.

20091113, 03:18  #30 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·113 Posts 
Riesel base 811 is proven:
8*811^317831 is 3PRP! (189.6443s+0.0104s) 258*811^280101 is 3PRP! (179.3691s+0.0093s) Running N+1 test using discriminant 3, base 1+sqrt(3) Special modular reduction using FFT length 32K on 8*811^317831 Calling BrillhartLehmerSelfridge with factored part 100.00% 8*811^317831 is prime! (2419.9390s+0.0107s) Running N+1 test using discriminant 3, base 3+sqrt(3) Special modular reduction using zeropadded FFT length 48K on 258*811^280101 ...running... will let you know if it's not prime. 
20091113, 22:04  #31 
"Gary"
May 2007
Overland Park, KS
11823_{10} Posts 
Great work Serge. Another one bites the dust!
Those b==(1 mod 30) bases sure are prime. 
20091113, 22:13  #32 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·113 Posts 
I am running a lot of odd high bases, just to get a feeling.
I will carefully catalog what's there, and the ranges and result files, but for now, some cleared k's to include into the webpage: 508*31^7188+1 is 3PRP! (1.4761s+0.0008s) <== that's Sierp base 961 586*31^15728+1 is 3PRP! (6.6518s+0.0013s) 636*31^8674+1 is 3PRP! (2.3250s+0.0008s) 120*601^46631 is 3PRP! (4.1509s+0.0024s) 378*811^6792+1 is 3PRP! (7.5817s+0.0011s) Last fiddled with by gd_barnes on 20100118 at 13:17 Reason: remove bases <= 500 
20091114, 11:30  #33  
"Gary"
May 2007
Overland Park, KS
11823_{10} Posts 
Quote:
This is only the 3rd base proven with TWO primes of n>25K and the very 1st Riesel base! The other two are Sierp bases 11 and 23, the latter of which is the only one with two primes of n>100K. What's so remarkable is that the base is 35X larger than any previous base with this attribute! There is only one k remaining on 9 bases that would end up having 3 or more primes of n>25K if we can get them proven. They are Riesel bases 22, 23, 27, 49, and 72 and Sierp bases 9, 10, 17, and 33. If proven, Riesel base 22 would have 5 primes of n>25K and Sierp base 17 would have 4. All the rest above would have 3. Sierp base 17 would be the 1st one with 3 primes of n>100K! Gary Last fiddled with by gd_barnes on 20091114 at 11:30 

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