20200101, 22:36  #3488 
May 2007
Kansas; USA
27BE_{16} Posts 
Reserving R737 to n=300K for Ian and me.

20200102, 16:38  #3489 
Sep 2011
Germany
2,423 Posts 
R624 tested to n=2.5k + sieved to 1G (2.510k)
19002 remain Results emailed  Base released 
20200102, 16:40  #3490 
Sep 2011
Germany
2,423 Posts 
Reserving R652 as new base using the newbase script up to 2.5k and sieving to 10k (1G) with srsieve2

20200102, 19:25  #3491 
May 2008
Wilmington, DE
5×569 Posts 
S763
Reserving S763 to n=10K

20200103, 09:35  #3492  
May 2007
Kansas; USA
2·5,087 Posts 
Quote:
This leaves 18977 k's remaining for R624 at n=2500. Files are attached for each type of algebraic factors. See the main Riesel page for their breakdown. I removed the applicable k's from the sieve file. Last fiddled with by gd_barnes on 20200103 at 09:49 

20200103, 14:39  #3493  
"Mark"
Apr 2003
Between here and the
3×1,949 Posts 
Quote:


20200103, 18:36  #3494 
Jan 2017
2×13 Posts 
624=16*39
624=4^2*39 Any k that is a square times the leftover nonsquare part of the base (39) has algebraic factors for odd n. These sometimes combine with a trivial factor (in this case 5) to eliminate the k. For example, Riesel base 96 has algebraic factors for k=6*n^2 because 96=4^2*6, or R288 has algebraic factors for 2*n^2 because of 288=12^2*2. There are even cases where the base itself can be used as the nonsquare part, ex R79 where 79*n^2 has algebraic factors on odd n. This can also happen for cubes, 5th powers, etc. but is much less likely to yield a full k elimination. Ex. R432 has algebraic factors for n=1 (mod 3) on k's where k=4*n^3, but it doesn't yield any eliminated k because 432=2*6^3, and to complete the cube in the base 2^2=4 is still needed. 
20200103, 20:34  #3495 
May 2007
Kansas; USA
2×5,087 Posts 
That type 2 algebraic factors that NHood described...I don't recommend that srsieve2 try to catch them...unless you want to go to a long dark place to try to code for and extensively test them. It becomes complex to attempt to nail them down correctly for all bases. The complexity of the different variations of them that NHood describes is mainly why I don't recommend it.
It's unusual for any base to have more than about 5 full k's that can be eliminated that fit that type. Obviously R624 was an exception. Last fiddled with by gd_barnes on 20200103 at 20:38 
20200104, 02:35  #3496  
"Mark"
Apr 2003
Between here and the
3×1,949 Posts 
Quote:


20200104, 02:56  #3497  
May 2007
Kansas; USA
2·5,087 Posts 
Quote:
For testing purposes, use base R624. If you can make it find 35 of these "type2" algebraic factors where the k's are completely removed then the code should be correct. The k's are documented in the "type2" named file attached to that last post. Last fiddled with by gd_barnes on 20200104 at 03:04 

20200104, 09:16  #3498 
Sep 2011
Germany
977_{16} Posts 
Reserving R1008 as new base using the newbase script up to 2.5k and sieving to 10k (1G) with srsieve2

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