Conjectures with one k remaining

[rogue]

Originally Posted by Batalov

After sieving, the remaining n's for these are 1 (mod 3), so they don't benefit from algebraic factorization. Shouldn't be 0.

Thanks. Clearly a bug in my code. I need to investigate.

[rogue]

Here is a better list (bug fixed) with differences listed:

    8*86^n+1  1017	 848
   32*87^n+1   342	 342
   8*182^n+1   389	 269
  27*252^n+1  2164	1855
   8*263^n+1   363	 298
  27*328^n+1   870	 758
   8*353^n+1   613	 613
   8*426^n+1  1288	 802
   8*428^n+1   655	 397
   8*497^n+1   943	 738
   8*758^n+1   549	 501
   8*785^n+1   588	 410
   8*828^n+1  1136	 529
   8*930^n+1  1645	1144
   8*953^n+1  1155	 795
    4*72^n-1  1211	 838
   8*321^n-1  1017	 817
   8*328^n-1   915	 774
   9*636^n-1  2840	1758
   8*665^n-1  1582	 972
   9*688^n-1  1252	 641
  32*702^n-1  2339	2216
   8*761^n-1  1527	2285
   8*867^n-1   836	 475

8*761^n-1 must have the wrong value in the list as the Geoff's last version of srsieve and my version give the same value.

[gd_barnes]

We should never have a k remaining on the pages where algebraic factorization would bring the weight to 0. Those should always be shown as eliminated by "partial algebraic factorization". I see that is no longer the case with your corrected code so that is a good thing.

Still...please check your code again. You'll need to enlighten me on how any n's are removed due to algebraic factors on 8*761^n-1. On a sieve with srsieve to P=511 for n=100001-110000, there are 2285 n's remaining, none of which are divisible by 3. (Maybe I'm missing something.) That's one of only 3 that I spot checked.

[rogue]

Originally Posted by gd_barnes

We should never have a k remaining on the pages where algebraic factorization would bring the weight to 0. Those should always be shown as eliminated by "partial algebraic factorization". I see that is no longer the case with your corrected code so that is a good thing.

Still...please check your code again. You'll need to enlighten me on how any n's are removed due to algebraic factors on 8*761^n-1. On a sieve with srsieve to P=511 for n=100001-110000, there are 2285 n's remaining, none of which are divisible by 3. (Maybe I'm missing something.) That's one of only 3 that I spot checked.

The code is fixed. My last post here has the correct numbers, therefore ignore my erroneous post. My point on R761 was that the first post in this thread had the wrong value (probably a copy&paste error). With srsieve 0.6.17 it should have been 2285, not 1527. With srsieve 1.0.1, it is still 2285. In other words, although some n are removed due to algebraic factorizations, those same n have small factors.

Fortunately I haven't been affected with the bases (but was close). I had sieved a couple of k that I had reserved, but hadn't loaded them into my server yet. I just need to resieve them, costing me about 1 week on a single core per k.

[gd_barnes]

Originally Posted by rogue

The code is fixed. My last post here has the correct numbers, therefore ignore my erroneous post. My point on R761 was that the first post in this thread had the wrong value (probably a copy&paste error). With srsieve 0.6.17 it should have been 2285, not 1527. With srsieve 1.0.1, it is still 2285. In other words, although some n are removed due to algebraic factorizations, those same n have small factors.

Fortunately I haven't been affected with the bases (but was close). I had sieved a couple of k that I had reserved, but hadn't loaded them into my server yet. I just need to resieve them, costing me about 1 week on a single core per k.

Ah OK. For some reason, I thought you were implying that the weight should be 1527 for R761. Obviously the first post in this thread erroneously showed that value and that is what you were getting at. It has now been corrected to 2285.

I'm out of town for about 9-10 more days. After inspecting these a little closer after I get back, I'll change the first post to account for the n's removed due to algebraic factors.

[henryzz]

Originally Posted by gd_barnes

Ah OK. For some reason, I thought you were implying that the weight should be 1527 for R761. Obviously the first post in this thread erroneously showed that value and that is what you were getting at. It has now been corrected to 2285.

I'm out of town for about 9-10 more days. After inspecting these a little closer after I get back, I'll change the first post to account for the n's removed due to algebraic factors.

Might be nice to list both. I can imagine people might be interested in searching ks with or without algebraic factors.

[gd_barnes]

Originally Posted by rogue

Here is a better list (bug fixed) with differences listed:

    8*86^n+1  1017     848
   32*87^n+1   342     342
<snip>

8*761^n-1 must have the wrong value in the list as the Geoff's last version of srsieve and my version give the same value.

The list looks good. I have updated the 1st posting to remove n's with algebraic factors from the weights. Thanks Mark!


Gary

[rogue]

With my latest changes to srsieve, some of these get to change once again. I don't think that any of the Sierpinski ones are affected, but some of the Riesel ones are, notably those where k=16 (2^4 and 4^2) and k=64 (2^6, 4^3, and 8^2). I computed these weights. Would someone care to see if I've made a mistake?

64*177^n-1 1016
64*425^n-1 948
16*333^n-1 1389
64*741^n-1 2016

[gd_barnes]

These look good but wouldn't the previous version of srsieve have picked up k=16 correctly since it is only a perfect square? (Or perhaps it was just overlooked in the scheme of things in these lists?) I can see why the previous version would have missed picking up some algebraic factors for k=64 since it is both a square and cube.

I have changed the first post.

[rogue]

Originally Posted by gd_barnes

These look good but wouldn't the previous version of srsieve have picked up k=16 correctly since it is only a perfect square? (Or perhaps it was just overlooked in the scheme of things in these lists?) I can see why the previous version would have missed picking up some algebraic factors for k=64 since it is both a square and cube.

v1.0.1 only looked for the lowest K such that k=K^x. It never considered whether or not x had factors. I believe that one of those conjectures was reserved, so whomever is working on it should use v1.0.2 to eliminate more n. In other words if their current sieve file has n that srsieve v1.0.2 removes via algebraic factorizations, then they should remove those n from their sieve file.

[MyDogBuster]

Added 24*123^n-1 reserved in the PRPNet2 drive to n=250K

Weight is 2758