20200809, 16:44  #364 
"Alexander"
Nov 2008
The Alamo City
2^{3}×47 Posts 
I have completed the (near)Woodall k's, except for k=1993191, to n=350k. I found 2 primes:
pepi37 kindly ran a large chunk of the range, and he found the following 2 primes:
The list of k's tested can be found in the previous post. 
20200815, 00:16  #365 
"Dylan"
Mar 2017
1002_{8} Posts 
k = 50171
k = 50171 is at n = 2.945 M, no primes found, continuing...

20200816, 09:38  #366 
"Alexander"
Nov 2008
The Alamo City
2^{3}×47 Posts 
k = 1549573
k=1549573 has now been tested to n=300k. The known prime at n=260199 (on Prime Pages) was reconfirmed, and no new primes were found. I am releasing this k. The LLR log is attached (it's version 3.8.24, so PRP residues instead of LLR).

20200819, 17:08  #367 
Jul 2018
Martin, Slovakia
137 Posts 
I restarted the search for primes with k = 105105.
So far I have checked up to n = 395 000 and found 4 primes: 105105*2^3287911 105105*2^3339641 105105*2^3588321 105105*2^3870911 Also regarding k=20020913, I have found another prime: 20020913*2^8626921 I will update those k's in Prime Wiki. 
20200819, 18:44  #368 
Jul 2018
Martin, Slovakia
10001001_{2} Posts 

20200908, 05:39  #369 
Aug 2020
2^{3}·3 Posts 
I was testing k = 1281979 for n<= 100000 and interestingly the first 10 n for which this is prime are prime themselves. After that unfortunately there's n = 1005 which obviously isn't. But the ratio of n being prime vs being composite continues to be very high for the remainder of the range.
Is that a known property of some k and is it known why it happens? Is there a connection to Mersenne? Nothing like that on the Proth side, but there the n that yield primes seem to come in pairs of two that are close to each other (510% difference). Though it might just be the brain's inbuild pattern recognition going overboard. So I'll keep testing. If there's something the next n should be in the 3e5 range. ;) Last fiddled with by bur on 20200908 at 05:41 
20200908, 06:41  #370 
Mar 2006
Germany
5436_{8} Posts 
1281979*2^n1 has a Nash weight of 1789, so relatively low.
1281979 1 mod 3 so all primes of that sequence are only odd nvalues. kvalues with 2 mod 3 can only produce primes with even n's, and k's divisible by 3 can produce primes with odd/even nvalues. 1281979*2^n+1 has a low Nash weight of 847, so there should less primes for this sequence. The LiskovetsGallot conjectures study the contribution of odd/even nvalues of such seqs. There exits kvalues which never produce primes for any nvalue like the Riesel problem. PS: If your're done you can list the prime nvalues in this thread and I can include those in the Wiki, both sides (Proth /Riesel) possible. Don't forget to give the search limits then. Last fiddled with by kar_bon on 20200908 at 06:47 Reason: PS 
20200908, 07:44  #371  
Aug 2020
2^{3}×3 Posts 
kar_bon, I never really understood the Nash weight. It is an indicator for how many candidates remain after sieving? So I would think a low weight is good, since few candidates after sieving is favorable? What do I miss?
I don't know what is average number of primes in n < 1e5 range, but I think there were maybe 15 for this k. Is that so little? Proth was giving similar number of primes. Quote:
The main task I want to accomplish is finding a mega prime using Proth20, so I'm currently sieving 3320000 <= n <= 4100000 for Proth side. But I also plan to do the remaining smaller n values for both Riesel/Proth using LLR on CPU. I'll post them here in the future. Last fiddled with by bur on 20200908 at 07:44 

20200908, 09:10  #372 
Mar 2006
Germany
2·1,423 Posts 
The less the Nash weight is the less candidates remain after sieving is correct, but also the less chance to find a prime: low Nash = less cand. = less primes.
You could choose a lower kvalue which produce smaller test timings for same nvalues as 1281979. Check the Wiki for low weight kvalues to see the difference. You could sieve and test some higher ranges to get a feeling of those. Looking other tables in the Wiki and sorting by #primes or Nash could help, too. 
20200908, 16:59  #373  
Aug 2020
2^{3}·3 Posts 
So the number of primes per n decreases stronger than the number of candidates per n?
Here are the n values that produce Riesel primes: Code:
1281979 * 2^n  1 0 <= n <= 20000 3 7 43 79 107 157 269 307 373 397 1005 1013 1765 1987 2269 6623 7083 7365 10199 16219 bold values indicate primes Quote:
I have two computers at work I can use for crunching, both are using CPU for Primegrid projects. I want to keep it that way, because I like the conjecture solving. So the cheapest way to do more crunching would be to buy to midlowend GPUs such as the GTX 1650 and use those for other projects. Then I found out LLR on GPUs is considered a waste of time. But  there's a new software Proth2.0 that apparently tests Proth primes quite efficiently on GPUs. So I decided to find Proth primes. But PG has three Proth prime subprojects and covers a lot of small k's... Around that time I discovered my birth date is a prime number and also large enough not to interfere with PG. Also that it's prime could result in the interesting combination of prime k, prime n and prime b. I know large k hardly change anything in regard to total digits but make computation slower and I also knew the Nash weight is not that high using nash.exe, but I will keep that k. If I find a mega prime with it it will at least be a somewhat rare k ... ;) Last fiddled with by bur on 20200908 at 17:09 

20200908, 18:23  #374 
"Curtis"
Feb 2005
Riverside, CA
10344_{8} Posts 

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