Bases 33-100 reservations/statuses/primes

[Siemelink]

Originally Posted by gd_barnes

Per Robert Gerbicz's improved Riesel list, the conjecture for Riesel base 48 is k=3226 with a covering set of {5, 7, 461}. I have now confirmed it.

Gary

Oopsie. My own program also gives 3226. I remember I made this riesel by hand and overlooked the smaller possibility. I created my own program because programming is fun and eliminate mistakes like this.

Willem.

[gd_barnes]

Reserving Riesel base 36. I'll take it up to either n=5K or 10K depending on resource availability.

This is an interesting base because it should be somewhat primeful and is a perfect square, which means that some k's may be eliminated by previous base 6 primes.


Gary

[Siemelink]

Originally Posted by gd_barnes

Reserving Riesel base 36. I'll take it up to either n=5K or 10K depending on resource availability.

This is an interesting base because it should be somewhat primeful and is a perfect square, which means that some k's may be eliminated by previous base 6 primes.

Gary

Hi Gary,

I am also running Riesel 36, I've gotten it to 22500 by now. I think I have said sometime that I was working on it, but I can't find the post just now.
Anyway, as this base is complicated I'd be happy to figure as double check.

I don't have this base quite ready, so I'll post some of it:
Conjecture 116364
Odd 37
6m+2 97
6m+4 43
6m+6 13

[Siemelink]

Originally Posted by Siemelink

I don't have this base quite ready, so I'll post some of it:
Conjecture 116364
Odd 37
6m+2 97
6m+4 43
6m+6 13

And here are the remaining k.

Cheers, Willem.

[gd_barnes]

Originally Posted by Siemelink

Hi Gary,

I am also running Riesel 36, I've gotten it to 22500 by now. I think I have said sometime that I was working on it, but I can't find the post just now.
Anyway, as this base is complicated I'd be happy to figure as double check.

I don't have this base quite ready, so I'll post some of it:
Conjecture 116364
Odd 37
6m+2 97
6m+4 43
6m+6 13

Argh! I'm nearing n=5K and was sieving to n=25K. No, I don't ever remember you stating it or I would have shown it reserved on the web page. I'll stop my effort at n=5K. Of course k==(1 mod 5) and (1 mod 7) as well as k's that are perfect squares are removed.

It's a very nice base for being so large with such a large conjecture. I'm estimating ~60-70 k's will remain at n=100K, although it's a huge effort just to get it that high.

The reason that I was running it is that I have all the base 6 primes and that helped eliminate quite a few k's after I ran it solely on PFGW up to n=2500. But if you've already searched to n=22.5K, that's n=45K base 6, so you've found all but likely the largest 2-3 base 6 primes that apply to base 36...and those are shown on the web page.

Can you please send the primes to me on Riesel base 35 now? I've run it up to n=2K for my usual double-check so if you want to send them all from n=2K to wherever you stopped, then that will be fine. I can't balance it otherwise.


Thanks,
Gary

[gd_barnes]

Per an Email and 2 PM's here are 138 primes on Riesel base 35 from Karsten for n=5000-6315:

227548 5007
246796 5007
237026 5026
207388 5035
266522 5044
150560 5054
178946 5060
222458 5060
224968 5061
71858 5068
212746 5069
192416 5070
169846 5075
237196 5075
260926 5085
154166 5094
49184 5100
267614 5116
145588 5117
36086 5120
127228 5121
139430 5122
108124 5129
271048 5131
108466 5143
192284 5144
174560 5152
259324 5169
115748 5182
193802 5192
40364 5198
244702 5205
139136 5210
224942 5214
212150 5232
250916 5238
24274 5243
37456 5247
43610 5264
182840 5270
195176 5274
14974 5277
148646 5278
97582 5301
119960 5302
87948 5303
115324 5311
163582 5313
194582 5326
199396 5331
209464 5341
286294 5341
165668 5368
40096 5371
210322 5373
213482 5382
192818 5394
278260 5397
51314 5402
72016 5413
106616 5420
11508 5421
171614 5426
11570 5430
30202 5445
198350 5476
62078 5484
285658 5511
159958 5519
9194 5540
99698 5564
257884 5601
139562 5602
79498 5607
39692 5622
91778 5640
277520 5664
37898 5676
65534 5680
3628 5683
92768 5690
275070 5712
170572 5727
97098 5734
253340 5734
11672 5736
116660 5752
192890 5758
128948 5776
245150 5794
152462 5798
256688 5804
13936 5819
254998 5819
96142 5823
226164 5823
137062 5825
210976 5837
95600 5864
79004 5894
223232 5898
71578 5899
30196 5933
257062 5945
193774 5947
200710 5957
250060 5963
230948 5964
215972 5966
157576 5969
130472 5986
100348 5987
109810 5995
270332 6000
139814 6002
285308 6006
52282 6009
51972 6010
280268 6016
265658 6032
157420 6033
100294 6035
147878 6044
64808 6066
144920 6076
263630 6102
138518 6108
121222 6125
261524 6150
242362 6173
286394 6176
42992 6256
22920 6259
273698 6264
25924 6279
184408 6291
191776 6301
62252 6306

He also tested much higher and found that 94*35^37683-1 is prime.

There are now 1419 k's remaining at n=6315.


Gary

[kar_bon]

next PRPs:

273182 6332
281584 6335
266722 6343
258072 6349
184976 6350
177514 6369
197486 6390
260638 6407
271946 6412
5396 6416
84568 6441

now at n=6462

[gd_barnes]

Originally Posted by Siemelink

Hi Gary,

I am also running Riesel 36, I've gotten it to 22500 by now. I think I have said sometime that I was working on it, but I can't find the post just now.
Anyway, as this base is complicated I'd be happy to figure as double check.

I don't have this base quite ready, so I'll post some of it:
Conjecture 116364
Odd 37
6m+2 97
6m+4 43
6m+6 13

Originally Posted by Siemelink

And here are the remaining k.

Cheers, Willem.

Go ahead and continue with it. My double-check will stop at n=5K plus some other verifications. I'm currently at n=4600. In doing the verification, I found several problems in your list of primes:

k's with lower primes found than in your list (I proved both mine and yours here):
k-value / my prime n= / your prime n=
14503 / 2340 / 6860
102829 / 2276 / 2414
107285 / 3837 / 4121
115402 / 3416 / 3464

typos or incorrect conversions from base 6 primes:
k-value / my prime n= / your prime n= / comment
19389 / 9119 / 9619 / n=9619 has factor 15017; base 6 prime of n= 18238 / 2 = 9119.
19907 / 8439 / 16878 / n=16878 has factor 37; forgot to divide base 6 prime of n=16878 by 2.
94059 / 2352 / 23052 / n=23052 composite, no small factor; extra "0" in n-value.

Here is the only problem that might affect your current testing:
You have 109772*36^11422-1 as prime. It has a factor of 19. But the k-value right above it is also shown with an n=11422 prime; i.e. 109710*36^11422-1. k=109710 is a converted base 6 prime that I ran a primality proof on.

Bottom line: If you removed k=109772 from your testing, you'll need to add it back in and retest starting at n=11422 (I assume).

Also, can you check your machines to see if they may be missing primes or if you just didn't test certain ranges? The prime for k=14503 was particularly troubling because of the n=4520 difference between mine and your primes. If a prime is completely missed, it could result in a huge amount of additional testing. It's not a really big deal if we don't find the smallest prime (although it is my preference) but it makes me wonder about testing when the smallest is not listed.

The final verification I'm doing is running primality proofs on your entire list to make sure there are no additional composites as a result of typos or other things. It's at n=5K right now with no problems found so far.

Adding k=109772 back in leaves 103 k's remaining at n=22.5K for Riesel base 36. Most excellent for a large base and conjecture.

And finally...your list of k's remaining at n=2000 exactly matched mine. I had almost the exact same spreadsheet/document that you did with less primes found due to lower testing limit, including an exact match on all of the converted Riesel base 6 primes. Very good!

Attached is your list updated with the above corrections.


Gary

[gd_barnes]

Originally Posted by Siemelink

And here are the remaining k.

Cheers, Willem.

Willem,

After making the corrections to your primes noted in the previous post that I made, I ran primality proofs on your entire list. I found one problem:

19315*36^12815-1 is composite

After finishing my testing up to n=5K and finding no prime for the k, I used my own sieved file for n=5K-25K and found a much smaller prime for it:

19315*36^6319-1 is prime

One more small anamoly that isn't really a problem:

I found a smaller prime for k=98420 at n=4722 vs. your n=4965.

Please correct the file that I posted last time to reflect these changes.

One thing you might consider that I do to guarantee finding the smallest prime on each k but also has the added benefit of reducing overall testing time: When testing a base across multiple cores, split the cores up by k-value instead of n-value. For instance, on my testing for this base, I used 2 cores, #1 running k=1 to 58K and #2 running k=58K to 116K. If you split it by n-range, inevitably you end up testing more than you need to.

Also when testing relatively low n-ranges, perhaps n<10K, where many primes are found such as this, I use PFGW even AFTER sieving instead of LLR despite the fact that it is 10-15% slower. The option to make it stop testing a k when it finds a prime means much less manual intervention and mostly offsets the slower testing time. It makes for much cleaner tests. Obviously at the higher n-ranges that take much longer per test where few primes are found, LLR or Prhot are better.

I hope this helps...


Thanks,
Gary

[mdettweiler]

I'll reserve all 31 remaining k's for Riesel base 37--this looks like an easy base to prove, so I think I'll aim to take it to at least n=20K.

Edit: I've moved this post to the "Bases 33-100" thread (it was originally in the Reservations/Statuses thread) since it would probably be more appropriate in the former.

[Siemelink]

Originally Posted by gd_barnes

Go ahead and continue with it. My double-check will stop at n=5K plus some other verifications. I'm currently at n=4600. In doing the verification, I found several problems in your list of primes:

Gary

Yup, that is exactly why I hadn't posted it. I have done some of the doublechecking, but I am no longer clear on what...
The effort is running on a PC with limited access, so no correction possible on the sieve file. I'll wait it out until 25,000 and after that I'll wrap up.

Cheers, Willem.