20091220, 11:10  #67 
"Gary"
May 2007
Overland Park, KS
10111000100001_{2} Posts 
I'm done with Riesel and Sierp bases 512 and 1024. These got a little tricky, especially on the Sierp side. There was both algebraic factors and unusual GFNs as well as testing from RPS and ProthSearch that helped eliminate some k's that I didn't. I only tested them to n=2500 but with testing from other projects, all of the remaining k's are at n>=145K. 2 are proven, one has 1 k remaining, and another has 2 k's remaining.
Particulars: Riesel base 512 with a conjecture of k=14 is proven. Although cubed k's would have full algebraic factors, k=1 & 8 were already eliminated with a trivial factor of 7. This was the easy one. Riesel base 1024 with a conjecture of k=81 has k=29 & 74 remaining. All squared k's have full algebraic factors, which eliminates k=9 & 36. After testing to n=2500, I had k=29, 39, & 74 remaining. For odd k's, base 2 Riesel primes convert to base 1024 Riesel primes if n==(0 mod 10). 39*2^407001 is prime, which converts to 39*1024^40701 so it is eliminated. For k=29, it has been tested to n=2M base 2 with no n==(0 mod 10) primes so it remains at n=200K base 1024. For k's==(2 mod 4), base 2 Riesel primes convert if n==(1 mod 10) where n>1. For k=74, it has been tested to n=1.45M base 2 with no n==(1 mod 10) n>1 primes so it remains at n=145K base 1024. Sierp base 512 with a conjecture of k=18 has k=5 remaining and was the most unusual. Since 512=2^9, k=1, 2, 4, 8, & 16 are all GFN's. All cubed k's have full algebraic factors and in this case, it eliminates two of the GFN's, k=1 & 8, so we can't say that "k=1 and 8 are GFn's with no known prime" since it is mathematically impossible for them to have a prime. k=2, 4, & 16 have no known prime so are the only GFN's shown as such. As for k=5 remaining, the base 2 ProthSearch project has searched it to n=5.33M with no n==(0 mod 9) prime, which is the requirement for a base 512 prime. Hence k=5 remains at n=592.2K base 512. (I also updated the search limit for Sierp base 128 k=40.) Sierp base 1024 with a conjecture of k=81 is proven and was a little unusual on its GFN elimination. Since 1024=2^10, k=1, 2, 4, 8, 16, 32, & 64 are all GFN's. k=2, 8 & 32 were eliminated by a trivial factor of 3. All k's that are perfect 5th powers have full algebraic factors, which eliminates k=1. k=64 has a prime at n=1; the only GFN on either of these bases with a known prime. This leaves only k=4 & 16 as GFN's with no known prime. Bottom line: Riesel base 1024 has the following remaining: 29 (200K) 74 (145K) Sierp base 512 has the following remaining: 5 (592.2K) I had hoped to open up some more powerof2 bases testing but this didn't do it. What is remaining is being searched by RPS and ProthSearch. Like Sierp base 128, these aren't worth messing with. The pages will shortly be updated for these bases. Gary 
20091220, 13:34  #68 
"Mark"
Apr 2003
Between here and the
2·59^{2} Posts 
Sierpinski base 605
Completed to n=20000 and released. k=70 remains. Here are the primes.
Code:
2*605^5+1 4*605^2+1 6*605^1+1 8*605^23+1 10*605^12394+1 12*605^5+1 14*605^3+1 16*605^2+1 18*605^1+1 20*605^1+1 22*605^4+1 24*605^3+1 26*605^1+1 28*605^2+1 30*605^34+1 32*605^13+1 34*605^2+1 36*605^5+1 38*605^3+1 40*605^86+1 42*605^1+1 44*605^11+1 46*605^2068+1 48*605^29+1 50*605^11+1 52*605^6+1 54*605^5+1 56*605^3+1 58*605^6+1 60*605^3+1 62*605^1+1 64*605^10+1 66*605^13+1 68*605^1+1 72*605^10+1 74*605^1+1 76*605^4+1 78*605^16+1 80*605^3+1 82*605^2+1 84*605^1+1 86*605^5+1 88*605^2+1 90*605^2+1 92*605^1+1 94*605^4+1 96*605^12+1 98*605^3+1 
20091220, 13:52  #69  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4279_{10} Posts 
Quote:
Besides, I can't edit the other post myself, as it's way past the 1 hour mark, and I'm not a mod here. Last fiddled with by TimSorbet on 20091220 at 13:53 

20091220, 22:44  #70 
"Gary"
May 2007
Overland Park, KS
7^{2}·241 Posts 
Karsten reported:
50*601^307351 is prime As far as I know, he has not reserved Riesel base 601. 
20091220, 23:41  #71  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{2}·1,117 Posts 
Quote:
BR601a.txt:120*601^46631 is 3PRP! (4.1509s+0.0024s) BR601a.txt:50*601^307351 is 3PRP! (188.4408s+0.0183s) BR601a.txt:624*601^442791 is 3PRP! (564.9792s+0.0151s) EDIT: The file is attached  it was running unattended and then interrupted at 45.36K and I will not continue anytime soon. Overwhelmed by the deluge of new bases, I've stopped short of reporting those that I have reserved, but I'll try to organize and report them all now whereever they are stopped. Last fiddled with by Batalov on 20091221 at 00:09 Reason: sorry for lack of organization 

20091220, 23:44  #72  
"Gary"
May 2007
Overland Park, KS
2E21_{16} Posts 
Quote:
k=300, 482, and 744 still remain and the testing limit on them is n=2500. Gary Last fiddled with by gd_barnes on 20091220 at 23:45 

20091221, 00:20  #73 
Mar 2006
Germany
2,999 Posts 

20091221, 02:23  #74 
"Gary"
May 2007
Overland Park, KS
7^{2}·241 Posts 
OK, I will set the test limit on Riesel base 601 to n=45.36K on the remaining 3 k's. Since Serge states that he will not get back to it, I'll unreserve it.
Thanks for the results Serge. That helps a lot. Gary 
20091221, 05:21  #75 
May 2008
Wilmington, DE
2^{2}×23×31 Posts 
Sierp Base 729
Sierp Base 729
Conjectured k = 74 Covering Set = 5,73 Trivial Factors k == 1 mod 2(2) and 6 mod 7(7) and 12 mod 13(13) Found Primes: 2*729^1+1 4*729^1+1 10*729^2+1 14*729^3+1 16*729^2+1 18*729^53+1 22*729^2+1 24*729^1+1 26*729^2+1 28*729^3+1 30*729^1+1 32*729^6+1 36*729^2+1 40*729^3+1 42*729^24+1 44*729^1+1 46*729^2+1 50*729^1+1 52*729^16+1 54*729^1+1 56*729^28+1 58*729^1+1 60*729^3+1 66*729^6+1 68*729^4+1 70*729^1+1 72*729^1+1 Remaining k's: 8*729^n+1 < Proven composite by full algebraic factors Trivial Factor Eliminations: 8k's Conjecture Proven 
20091221, 12:26  #76 
May 2008
Wilmington, DE
2^{2}×23×31 Posts 
Sierp Bases 869, 899, 914 and 1004
Sierp Bases 869, 899, 914 and 1004 complete n=2.5K25K
2*899^15731+1 is prime  Conjecture Proven Bases Released  Results attached Last fiddled with by MyDogBuster on 20140902 at 09:16 
20091222, 02:41  #77 
May 2008
Wilmington, DE
2^{2}×23×31 Posts 
Almost caught up on my new reservations so:
Reserving Riesel bases 529,676,784,900 to clean up some k's with full algebraic factors Last fiddled with by gd_barnes on 20100118 at 14:39 Reason: remove bases <= 500 
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