[B]Riesel base 52 tested to 10k. Unreserving.

[/B]Again, the big primes need removing from the remaining-k file. Sorry.
Also the following k were flagged by srsieve as having a.f.: 900, 16641, 35721, 36864, 46656.

I've not been sleeping well, I'll stick to NPLB for a while, I'm safer there. lol

Found one today on Sierpinski base 33:

1678*33^46632+1 is prime! (445.0087s+0.0710s)

(found PRP with Phrot 0.65, proven with PFGW by N-1 test)

Results for k=1678, n=25K-46623 are attached. :smile:

Riesel Base 37

1008*37^20895-1 is prime! (287.4642s+0.0021s)
590*37^22021-1 is prime! (346.0400s+0.0024s)
5946*37^24822-1 is prime! (387.8000s+0.0025s)
4542*37^28765-1 is prime! (558.5508s+0.0030s)
6288*37^30012-1 is prime! (586.5647s+0.0031s)
2606*37^39006-1 is prime! (963.5454s+0.0045s)
3480*37^39565-1 is prime! (1112.0925s+0.0046s)
3336*37^39794-1 is prime! (1172.1690s+0.0046s)

19 Left

All k's tested to n=40K continuing to n=70K

For Riesel bases I'm not testing ks where (k mod base == 0) AND (k-1 is not prime.)
What is the rule for Sierp?

edit:
Aha!
[quote]1) Assume that all smaller k's have been eliminated
2) when k mod base is not == 0 then you have to test for primes
3) when k mod base == 0 and (k-1) is a prime you have to test for primes
4) when k mod base == 0 and (k-1) is not a prime you do not have to test


BTW, this only works for the Riesel side. [B]The last 2 above would need to be k+1 for the Sierpinski side.[/B][/quote]

[quote=Flatlander;160688]For Riesel bases I'm not testing ks where (k mod base == 0) AND (k-1 is not prime.)
What is the rule for Sierp?

edit:
Aha![/quote]


You will not have algebraic factors on most squared k's like you would on the Riesel side, even if the base is a perfect square. (There are a couple of notable exceptions like k=2500 on Sierp base 16; but they are rare.) That's because x^2+1 cannot be algebraicly factored whereas x^2-1 is (x-1)*(x+1). For cubed and higher power bases, there will be algebraic factors on cubed (or higher power) k's like there are on the Riesel side because x^3+1 can be algebraicly factored in a similar manner to x^3-1.

There will be some GFN's to remove. For GFN's it's simple; just remove POWERS of the base; so for base 6, you would not test k=1, 6, 36, 216, etc. GFN's can only be prime if n is a power of 2; hence are not considered.


Gary

Here is what I have worked on, am currently working on, and plan to work on in the future for Sierp bases <= 100 that are not shown on the pages yet:

Previously:
Base 43 to n=25K. 2 k's remain.
Base 55 to n=25K. 7 k's remain. I need to figure out a way to properly show algebraic factors for a single k on this one. It's different and much trickier than usual.

Currently:
Base 48 and 49 to n=25K. I am currently at n=~20K on both. Base 48 is where I've found some errors in Prof. Caldwell's paper. I'll follow up with him after completing to n=25K.

Plan to work on:
Bases 50, 53, 54, 56, 57, 59, 62, 64, 65, 68, 69, 70, 72 thru 77, 80, 81, 83, 84, 86 thru 90, 92, 94, 98, 99, & 100.

Many are small and will only take a few mins. or hours.

Chris, if you want to work on Sierp bases 42 or 46, those should be good. I expect there will be 35-60 k's remaining on them at n=10K so they aren't too bad. Two others that might only have ~40 k's remaining at n=10K are bases 60 and 61.

For bases with more than ~10-15 k's remaining, Prof. Caldwell's paper only lists the lowest 10-15 of them. I suspect in coming up with the info. on the paper, they did not search all of the k's on bases with high conjectures. That would have taken far too long. Extrapolating from my own testing, the k's that they did search appear to have been searched to n=~30K-40K. Using that info., I can get a reasonable estimate of the # of k's that should be remaining at n=10K or 25K on each base.


Gary

Reserving Sierp base 61.

Sierp base 61 tested to 16k.
20 ks remaining.
Unreserving. (I unreserve when I report unless I say otherwise.)

Testing Sierp base 42 and 46.

Sierp base 42 tested to 15,000.
50 ks remaining.

Sierp base 46 tested to 15,000.
34 ks remaining.

Sierp base 48 is complete to n=25K. 16 k's remain.

Sierp base 49 is complete to n=25K. 7 k's remain.

See details on the web pages.


Gary