mersenneforum.org - Bases 6-32 reservations/statuses/primes

mersenneforum.org (https://www.mersenneforum.org/index.php)

- Conjectures 'R Us (https://www.mersenneforum.org/forumdisplay.php?f=81)

- - Bases 6-32 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=9740)

Sierp b17:
one more k down, one remaining; n ~188K

Sierp b18:
one k remaining, no prime; n ~221K

We had gotten off on a large tangent discussing the amount of CPU time needed and k's remaining for Sierp base 19 and other efforts that was barely related to reservations/statuses. Actually, it was ME that was mostly off on the tagent. lol

I have moved the discussion to a new separate thread [URL="http://www.mersenneforum.org/showthread.php?t=10447"]here[/URL].

That said, if any reservations are reduced or otherwise changed as a result of the discussion, please still post them in this thread.

Thanks,
Gary

[quote=gd_barnes;136978]Willem,

For historical reference, I have to get all of the primes found, both small and large, at some point from you. Do you happen to have all of them available for Riesel base 7 to k=1M?

Thanks,
Gary[/quote]

Here are all the base 7 primes that I have at the moment. I don't have the primes with n<2000 at the moment. I wrote a script that drops them all in a file, I'll generate them again.

Willem.

[code]
622346 2042
857604 2071
479886 2091
481106 2097
273744 2117
865632 2126
853722 2137
683118 2154
183528 2155
736688 2164
999392 2168
501810 2177
895782 2190
697178 2198
489812 2202
519072 2222
843008 2243
780588 2298
994062 2314
255048 2322
751476 2337
472784 2356
579356 2365
635928 2366
482696 2401
716216 2409
524778 2444
932046 2447
866198 2478
997902 2525
419618 2554
384852 2556
515756 2595
510246 2654
282398 2698
844956 2701
17244 2703
512756 2713
967206 2714
456296 2823
450098 2842
619686 2909
117032 2949
367214 2969
293456 2986
468836 3051
662708 3102
268614 3129
491556 3163
559652 3201
662252 3249
556464 3303
892992 3321
721362 3402
578808 3410
413186 3449
698394 3632
48252 3758
319182 3964
600582 4049
835950 4107
94950 4125
149822 4221
668022 4448
652524 4507
418862 4516
552938 4588
92018 4618
550646 4638
127668 5674
945878 5702
529968 5908
953412 6168
451988 6738
140744 7257
969302 7481
121848 7576
802932 7821
438882 7838
878928 8046
728528 8504
961448 9247
848684 10152
217304 10181
516108 10307
501372 10900
177224 10907
213932 11277
764814 12181
405018 12275
620408 12578
325382 13834
140144 14097
731634 14132
597732 14604
437754 15967
940146 17631
258582 18801
78648 19918
478826 21805
434556 26167
571388 26879
874026 30253
706712 32437
401994 32471
[/code]

[QUOTE=gd_barnes;136983]Willem,

I'm analyzing and balancing k's remaining on Riesel base 25 now. You apparently eliminated 20 k's between n=10K and 15K but I don't see any primes listed for them in any of your attachments here.

Thanks,
Gary[/QUOTE]

Here are all the primes that I have for base 25.

Willem.

[QUOTE=Siemelink;137055]Here are all the primes that I have for base 25.

Willem.[/QUOTE]

And here are the remaining k's

Willem.

[quote=Siemelink;137053]Here are all the base 7 primes that I have at the moment. I don't have the primes with n<2000 at the moment. I wrote a script that drops them all in a file, I'll generate them again.

Willem.

[code]
622346 2042
857604 2071
479886 2091
481106 2097
273744 2117
865632 2126
853722 2137
683118 2154
183528 2155
736688 2164
999392 2168
501810 2177
895782 2190
697178 2198
489812 2202
519072 2222
843008 2243
780588 2298
994062 2314
255048 2322
751476 2337
472784 2356
579356 2365
635928 2366
482696 2401
716216 2409
524778 2444
932046 2447
866198 2478
997902 2525
419618 2554
384852 2556
515756 2595
510246 2654
282398 2698
844956 2701
17244 2703
512756 2713
967206 2714
456296 2823
450098 2842
619686 2909
117032 2949
367214 2969
293456 2986
468836 3051
662708 3102
268614 3129
491556 3163
559652 3201
662252 3249
556464 3303
892992 3321
721362 3402
578808 3410
413186 3449
698394 3632
48252 3758
319182 3964
600582 4049
835950 4107
94950 4125
149822 4221
668022 4448
652524 4507
418862 4516
552938 4588
92018 4618
550646 4638
127668 5674
945878 5702
529968 5908
953412 6168
451988 6738
140744 7257
969302 7481
121848 7576
802932 7821
438882 7838
878928 8046
728528 8504
961448 9247
848684 10152
217304 10181
516108 10307
501372 10900
177224 10907
213932 11277
764814 12181
405018 12275
620408 12578
325382 13834
140144 14097
731634 14132
597732 14604
437754 15967
940146 17631
258582 18801
78648 19918
478826 21805
434556 26167
571388 26879
874026 30253
706712 32437
401994 32471
[/code][/quote]

After matching everything up, we balance with a couple of exceptions on Riesel base 7:

515756*7^2595-1 is NOT prime! It has a factor of 19.

512756*7^2595-1 IS prime! This is a lower prime than the n=2713 that you found for k=512756.

844956*7^2701-1 is redundant with 17244*7^2703-1. They are the same prime. 844956=17244*7^2. (It makes no difference in the scheme of things but thought I'd point it out here.)

Based on finding the composite for k=515756, I did the following:

1. Checked all of the rest of your list for primality. They indeed are all prime.

2. Continued my run of PFGW up to n=5K to further check your list. Everything else matched up.

3. Tested k=512756 up to n=8K using PFGW. No prime was found.

So it looks like you need to add k=512756 back into your list of k's to test and test it starting from n=8K where I stopped testing it or n=2596 where you likely stopped testing it.

This means that there are now 15 k's remaining at k=1M; 14 of which are at n=35K and 1 of which is at n=8K.

Gary

[quote=Siemelink;137055]Here are all the primes that I have for base 25.

Willem.[/quote]

Willem,

I've done phase 1 of my checking on Riesel base 25. I haven't tried to balance k's remaining yet. PFGW is still running to n=3K as a small overlap of your primes here.

In phase 1, I check all k's for possible removal by looking for algebraic factors, multiples of the base where k/b is still remaining, primes already found by other projects, and primes on the top-5000 site. It is the final 2 items where I have found numerous additional k's that can be eliminated as a result of the Riesel base 5 project:

k's and primes found by the base 5 project that were missed:
176234*25^18302-1
287288*25^54343-1

Primes found by the base 5 project that convert to a different base 25 k-value that can now be eliminated:
250730*25^21424-1
215780*25^22067-1
335960*25^28515-1
102890*25^28981-1
277610*25^36393-1
42470*25^39340-1
156710*25^51275-1
124490*25^67755-1
171770*25^70771-1
114830*25^90953-1
158960*25^98000-1
294410*25^132990-1

On the 2nd list, since we're looking at base 5 to find primes for base 25, if they found a prime for a k-value that is < the conjecture divided by 5, then you can multiply that k-value by 5 and see if it remains for base 25. If so, you can take the base 5 n-value, subtract 1, then divide by 2, and you'll have the converted base 25 n-value.

More specifically, if a prime on base 5 is for a k-value < 346802/5 = 69360, then you may have a prime on base 25 for k*5 at (n-1)/2.

Largest example:
58882*5^265981-1 is prime
convert to:
294410*5^265980-1
and finally convert to:
294410*25^132990-1

Two of these converted primes make the top-10 for base 25 and will be reflected as such.

This eliminates 14 additional k's values for Riesel base 25 and lowers the total k-values remaining from 337 to 323. Of those 323 remaining, 254 are left for us to test and 69 are being testing by the base 5 project.

Further checking ongoing now...

Gary

[quote=Siemelink;137057]And here are the remaining k's

Willem.[/quote]

I've now done a further detailed check against all Riesel base 5 primes and done some misc. searching here-and-there to convince myself of a few things.

Frankly, I'm very concerned with the problems that I've found with your k-values remaining. 11 primes that should have been found by your searching to n=15K were not. They were not in your "Riesel 5" list hence they should have been searched:
[code]
138800*25^2256-1
26000*25^3056-1
84200*25^4678-1
32582*25^7639-1
59126*25^8034-1
38558*25^8148-1
85892*25^8315-1
44654*25^8638-1
35438*25^8724-1
81524*25^9897-1
85424*25^9967-1
[/code]

I ran PFGW to n=5K on the first 3 missing primes above. For the rest of them, fortunately I was able to convert primes previously found by the base 5 project.

Next, the below is something that it would have been difficult for you to know about. The following are 15 k's that were eliminated by the base 5 project but that are not shown in their threads. They are only shown in a link [URL="http://geocities.com/base5_sierpinski_riesel/"]here[/URL].
[code]
41588*25^16559-1
16262*25^18098-1
223070*25^18169-1
278594*25^20264-1
51362*25^20582-1
280292*25^20932-1
150320*25^21023-1
132224*25^23699-1
17978*25^27018-1
250784*25^27159-1
47462*25^27692-1
60932*25^30661-1
156272*25^31444-1
13820*25^37137-1
251756*25^59015-1
[/code]

So above here, we have 11+15=26 primes. From the last post, we have 2+12=14 primes for a grand total of 40 additional primes found. From your previous total of 337 k's remaining, there are now 297 k's remaining.

Now it's just a matter of what do WE need to search that isn't being searched by base 5? There are some problems there also.

The following 6 k-values are being searched by Riesel base 5 that were in your 'regular' list and not your 'Riesel 5' list and hence can be removed from your searching:
35816
154844
164852
239342
245114
325922

The following 15 converted k-values are being searched by Riesel Base 5 that were in your 'regular' list and not your 'Riesel 5' list and hence can also be removed from your searching:
6980
12440
18110
24530
26870
59060
85760
154970
176240
228710
241970
267710
287030
319190
334580

What 'converted' means is that they are a Riesel base 5 k-value multiplied by 5. This occurs anytime a base 5 k-value is k==(1 mod 3) and the k-value is < 346802/5. So if you divide each k-value by 5 in the above list, you see the k-value that is being searched by the base 5 project. (I confirmed they were all there remaining.)

Note that any k-value that is k==(2 mod 3) should either have a prime found by the base 5 project -or- it is a k-value remaining on that project and hence this project. Therefore we need not search any k==(2 mod 3) with this project.

Since k cannot be ==(1 mod 3) on base 25, the bottom line is that we only need search k==(0 mod 3), i.e. k's divisible by 3, with this project.

In the web pages, see that all reserved k's remaining to be searched by us are divisible by 3. Almost all k's that are k==(2 mod 3) are listed as being tested by the base 5 project but it is possible for base 5 to be testing a k==(0 mod 3) although it would be unusual. The same type of thing occurs for bases 4 and 16 vs. base 2.

Balancing:
Taking the prior 268 k's previously remaining for us minus the above 40 primes minus the above 21 k-values that are being searched by the base 5 project leaves us presumably with 207 k -values remaining to search at n=15K. Taking the prior 69 k's previously remaining for the base 5 project plus the above 21 k-values that are also being searched by them leaves with 90 k-values that are being searched by base 5. The web pages show the k-values remaining.

I say 'presumably' because I still need to check your list of primes for n>2K plus mine up to n=2K. Then I'll know for sure. I may end up asking that you rerun your tests starting around n=5K or so if I find too many more problems when doing the comparison.

Willem, I really appreciate your efforts and enthusiasm here on new bases. Unfortunately, I've been a little lax and let some people slide on providing results files on the conjectures. You objected to sending them originally when I asked for them at the beginning of this project. I'm afraid that can't happen anymore. It's taking me too much time to confirm all of this and I don't have a starting point to determine how to resolve the problems. I end up doing many searches myself. It's taken the better part of today for me to find all of this, verify it, and correct k-values remaining for primes that were missed. I'm still searching all of the k-values up to n=2K to get those primes so I still have that verification yet to go. My other searches were isolated to problem k-values.

In the future, I must have the results files anytime anything is submitted here. It only takes a minute to post them here. Then you can delete them off of your computer and I will save them on mine. Perhaps I can let it slide when searching 1-2 k's at higher n-ranges but when starting a new base, I am now making them a requirement. I have no other choice. I don't have the time to find what is causing these kinds of problems. As I've said before, starting new bases in the conjectures is highly problematic. When you throw in primes found by other projects eliminating k-values and potentially algebraic factors, it becomes that much more difficult.

For very large results on large conjectures such as base 7, please divide them up in a manner that you can zip them to me in an Email. My Email address is in post 4 of this thread.

Edit: This was all balanced to k's remaining and primes posted prior to your latest postings. I just now checked those. I see that you found primes for 14 additional k's between n=15K to what appears to be n=~20K. But k=177228 that was remaining at n=10K and NOT remaining at n=15K, I see is now remaining again. Regardless, I've added it back to the pages. Also, I had already removed k=41558 with the prime at n=16559 as per the above. So this nets out to removing 12 k's. There are now 195 k's remaining for us to search and 90 k's for Base 5 to search for a total of 285.

Please let me know two things: (1) Is there a prime for k=177228? (2) Is your search limit now n=20K?

Thanks,
Gary

[QUOTE=gd_barnes;137088] Almost all k's that are k==(2 mod 3) are listed as being tested by the base 5 project but it is possible for base 5 to be testing a k==(0 mod 3) although it would be unusual. The same type of thing occurs for bases 4 and 16 vs. base 2.[/QUOTE]

IIRC, k=151026 is the only sequence being tested by SRB5 that is divisible by 3.

[QUOTE=gd_barnes;137061]So it looks like you need to add k=512756 back into your list of k's to test and test it starting from n=8K where I stopped testing it or n=2596 where you likely stopped testing it.

This means that there are now 15 k's remaining at k=1M; 14 of which are at n=35K and 1 of which is at n=8K.

Gary[/QUOTE]

Hi Gary,

Thank you for the backchecking. In the past I have checked the primes myself as well, I'll be sure to do that again on my various bases.
I have fired up the k that I mistyped and I'll bring it back into the pack.

Willem.