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-   -   Bases 2 & 4 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=9830)

 gd_barnes 2008-01-15 21:39

For the Sierp odd-n conjecture, here's an update of both lists with the primes that I found and the Sierp base 4 primes with even k's removed from my list. There was only 1 Sierp base 4 prime not on my list. I ended up testing up to n=118K on all k's before stopping.

I was a little confused as to why you have three k's on your list that have a prime at n=1.

This balancing should make things much easier.

Your list with my primes and test limits:
[code]
tested to
k 2k (n-1 base 2) prime
9267 18534 1967862
32247 64494 1770506
37953 75906 118K
38463 76926 58753
39297 78594 118K
50433 100866 118K
53133 106266 118K
56643 113286 1 (??) 56643*2^1+1 is prime!
60357 120714 118K
60963 121926 73409
61137 122274 118K
62307 124614 44559
70467 140934 118K
75183 150366 35481
78153 156306 1 (??) 78153*2^1+1 is prime!
78483 156966 1 (??) 78483*2^1+1 is prime!
78753 157506 63761
80463 160926 118K
84363 168726 118K
85287 170574 118K
91437 182874 118K
93477 186954 63251
93663 187326 82317
[/code]

My list with Sierp base 4 primes and test limits and removal of even k's:
[code]
k prime test limit comments
2943 108041
9267 1.97M Sierp base 4
17937 53927
24693 357417 Sierp base 4
26613 89749
32247 1.77M Sierp base 4
35787 36639
37953 118K
38463 58753
39297 118K
46623 79553
50433 118K
53133 118K
60357 118K
60963 73409
61137 118K
62307 44559
70467 118K
75183 35481
78753 63761
80463 118K
84363 118K
85287 118K
91437 118K
93477 63251
93663 82317
[/code]

The bottom line as now shown on both lists is that we have 13 k's remaining, 11 of which have been tested to n=118K and the other 2 of which have been tested very high with Sierp base 4. This balances with the 14 odd k's that I said I had remaining previously minus the one removed from Sierp base 4.

Gary

 Jean Penné 2008-01-16 08:13

[QUOTE=gd_barnes;122911]For the Sierp odd-n conjecture, here's an update of both lists with the primes that I found and the Sierp base 4 primes with even k's removed from my list. There was only 1 Sierp base 4 prime not on my list. I ended up testing up to n=118K on all k's before stopping.

I was a little confused as to why you have three k's on your list that have a prime at n=1.

This balancing should make things much easier.

Your list with my primes and test limits:
[code]
tested to
k 2k (n-1 base 2) prime
9267 18534 1967862
32247 64494 1770506
37953 75906 118K
38463 76926 58753
39297 78594 118K
50433 100866 118K
53133 106266 118K
56643 113286 1 (??) 56643*2^1+1 is prime!
60357 120714 118K
60963 121926 73409
61137 122274 118K
62307 124614 44559
70467 140934 118K
75183 150366 35481
78153 156306 1 (??) 78153*2^1+1 is prime!
78483 156966 1 (??) 78483*2^1+1 is prime!
78753 157506 63761
80463 160926 118K
84363 168726 118K
85287 170574 118K
91437 182874 118K
93477 186954 63251
93663 187326 82317
[/code]

My list with Sierp base 4 primes and test limits and removal of even k's:
[code]
k prime test limit comments
2943 108041
9267 1.97M Sierp base 4
17937 53927
24693 357417 Sierp base 4
26613 89749
32247 1.77M Sierp base 4
35787 36639
37953 118K
38463 58753
39297 118K
46623 79553
50433 118K
53133 118K
60357 118K
60963 73409
61137 118K
62307 44559
70467 118K
75183 35481
78753 63761
80463 118K
84363 118K
85287 118K
91437 118K
93477 63251
93663 82317
[/code]

The bottom line as now shown on both lists is that we have 13 k's remaining, 11 of which have been tested to n=118K and the other 2 of which have been tested very high with Sierp base 4. This balances with the 14 odd k's that I said I had remaining previously minus the one removed from Sierp base 4.

Gary[/QUOTE]

Good work, Gary!

I agree for the three k's that must be eliminated because they yield a prime for n = 1 which is, indeed, an odd exponent!!

Here are the gathered results for +1, n even :

1) Remaining :

[CODE] k tested up to (n base 2)

23451 1950964
60849 1907154
[/CODE]

Indeed, all are from Sierpinski base 4 project.

2) Primes :

[CODE]2379*2^8114+1 is prime! Time: 85.883 ms.
8139*2^25954+1 is prime! by Citrix 01/02/05, 06:08AM
9609*2^5422+1 is prime! Time: 68.815 ms.
10281*2^7444+1 is prime! Time: 186.376 ms.
11709*2^6882+1 is prime! Time: 176.373 ms.
12711*2^5092+1 is prime! Time: 67.712 ms.
14661*2^91368+1 is prime! by Jean Penné 27/01/05, 10:03PM
15441*2^20584+1 is prime! by Footmaster 27/01/05, 03:17PM
17169*2^6450+1 is prime! Time: 168.967 ms.
21069*2^23006+1 is prime! by Footmaster 27/01/05, 03:51PM
21699*2^72874+1 is prime! by Footmaster 27/01/05, 06:43PM
23799*2^105890+1 is prime! by Ken_g6 29/01/05, 05:45PM
23901*2^11292+1 is prime! Time: 801.239 ms.
30579*2^48594+1 is prime! by Mark 28/01/05, 12:02AM
33771*2^178200+1 is prime! byJean Penné 29/01/05, 08:10PM
33879*2^378022+1 is prime! by Footmaster 20/06/05, 12:21PM
35889*2^7770+1 is prime! Time: 372.790 ms.
39231*2^13716+1 is prime! Time: 924.592 ms.
39759*2^4594+1 is prime! Time: 61.723 ms.
40269*2^8458+1 is prime! Time: 389.306 ms.
41289*2^13514+1 is prime! Time: 917.695 ms.
41709*2^80594+1 is prime! by geoff 29/01/05, 05:38AM
42717*2^905792+1 is prime! by Jean Penné 14/10/05, 08:18PM
44469*2^13134+1 is prime! Time: 841.834 ms.
51171*2^93736+1 is prime! by masser 31/01/05, 04:18PM
52419*2^4578+1 is prime! Time: 61.466 ms.
52701*2^6976+1 is prime! Time: 177.811 ms.
52839*2^32558+1 is prime! by masser 27/01/05, 11:19PM
53979*2^7590+1 is prime! Time: 367.499 ms.
55611*2^40212+1 is prime! by Citrix 29/01/05, 05:46PM
56019*2^8094+1 is prime! Time: 379.657 ms.
56139*2^4858+1 is prime! Time: 64.132 ms.
58791*2^79420+1 is prime! by Mystwalker 27/01/05, 11:21PM
60891*2^40144+1 is prime! by Jean Penné 29/01/05, 09:30AM
61371*2^12576+1 is prime! Time: 821.165 ms.
62391*2^5472+1 is prime! Time: 124.840 ms.
63411*2^72064+1 is prime! by Footmaster 31/01/05, 06:05PM
[/CODE]

Regards,
Jean

 jasong 2008-01-16 11:23

If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K.

If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base.

 gd_barnes 2008-01-16 17:44

+1 odd-n conjecture web page update document

1 Attachment(s)
Karsten,

Attached is a notepad document that is an update of the web page that you sent me via PM that has many primes filled in and some corrections for the +1 odd-n conjecture. 6 of the k's had primes at n=1; 3 of which already had a higher prime and 3 of which had no prime found.

This balances with the 13 k's remaining at n=118K shown earlier in this thread.

Gary

 gd_barnes 2008-01-16 18:10

[quote=jasong;122939]If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K.

If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base.[/quote]

You got it. I haven't done any sieving on base 4 past my original testing limit of n=100K. Jean or Karsten, do you have a sieve file for Riesel base 4 k=16734?

Jasong, I'm not sure I quite follow you here about 2X length of LLR'd value of lower base. I can only speculate that you might like to save sieving/LLRing time if Riesel k=16734/2=8367 base 2 has known testing above n=200K (n=100K base 4) to avoid double-testing.

When setting up the pages, I checked all k's on bases that are powers of 2 for primes in the prime archives at the top-5000 site and at [URL="http://www.rieselprime.org"]www.rieselprime.org[/URL] (converted from base 2) before putting anything up for testing. As shown on the latter site, k=8367 has only been tested to n=10K base 2 (n=5K base 4) and has no primes that are odd-n so you're OK there.

I think this is a very good idea to reserve this base 4 vs. base 16. It is open for both bases. It would be a waste of time for someone to sieve/test k=16734 base 16 and then turn around and do it for base 4. Perhaps that's part of what you're referring to.

In this case, I'll show you as reserving k=16734 on both base 4 and base 16. Otherwise someone could duplicate you base 16.

One caviot...If you find an even-n prime base 4 (n==0mod4 base 2), that will also eliminate the k on base 16 and you could stop testing. But if you find an odd-n prime base 4 (n==2mod4 base 2), I would suggest deleting all odd-n's in your sieve file and continue from there looking for an even-n base 16 prime.

Of course it's your choice to continue on for base 16 but it's a way to kill two birds with one stone. :smile: You could even end up with two different top-5000 primes; one for each base! :grin:

Gary

 gd_barnes 2008-01-19 00:00

I am also proposing that this thread be moved to the "Conjectures 'R Us" project thread.

As discussed with Jean, we will be adding the Riesel and Seirp base 2 even-n and odd-n conjectures as a subproject to our project.

As with the other threads, I'll wait a couple of days before requesting that this be moved.

Gary

 Jean Penné 2008-01-19 14:44

Just for fun and curiosity...

To illustraste the dissymetry between +1, base 2 odd / even exponents, I tested k = 18534/2 = 9267 with even exponents.
In less than 48H, I found that :

9267*2^n+1 is prime for

n = 100, 1556, 1966, 2660, 4342, 4468, 5372, 39538, 65386, 142426

although for odd exponents, I am presently reaching n = 1983943 with no prime!

I will continue even n during some days, just for fun...

Jean

 Jean Penné 2008-01-19 17:22

Gathered results for -1, base 2 even and odd n's

Here are my gathered rsults for k*2^n-1 even and odd exponents.

(I think all these results would be moved in the new projects as soon as possible...)

Even n's, 4 k's remaining to be tested :

[CODE] k tested up to (n base 2)

9519 562416
14361 318510
19401 262578
20049 265144
[/CODE]

Even n's, 19 primes found / known :

[CODE]Normalized As discovered Keller freq.
k n

2181 37890 2181*2^37890-1 is prime! Time : 3.036 sec. f15
6549 5076 6549*2^5076-1 is prime! Time : 35.101 ms. f12
8181 8018 8181*2^8018-1 is prime! Time : 71.021 ms. f12
8961 30950 8961*2^30950-1 is prime! Time : 2.395 sec. f14
11379 32252 11379*2^32252-1 is prime! Time : 2.594 sec. f14
12849 9788 12849*2^9788-1 is prime! Time : 150.938 ms. f13
14859 11228 14859*2^11228-1 is prime! Time : 173.080 ms. f13
15639 66328 15639*2^66328-1 is prime! Time : 11.412 sec. f16
16431 4198 16431*2^4198-1 is prime! Time : 71.150 ms. f12
17889 10628 17889*2^10628-1 is prime! Time : 169.037 ms. f13
21501 7286 21501*2^7286-1 is prime! Time : 68.104 ms. f12
26091 4198 26091*2^4198-1 is prime! Time : 25.548 ms. f12
26511 167154 26511*2^167154-1 is prime! Time : 124.567 sec. f17
26601 46246 26601*2^46246-1 is prime! Time : 5.842 sec. f15
30171 76286 30171*2^76286-1 is prime! Time : 15.664 sec. f16
31431 16942 31431*2^16942-1 is prime! Time : 153.476 ms. f14
31749 5040 31749*2^5040-1 is prime! Time : 35.640 ms. f12
31959 19704 31959*2^19704-1 is prime! Time : 638.666 ms. f14
35259 10540 35259*2^10540-1 is prime! Time : 165.366 ms. f13
[/CODE]

Odd n's, 31 k's remaining to be tested :

[CODE] k 2k tested up to (n-1 base 2)

6927 13854 261944
8367 16734 262044
30003 60006 261942
39687 79374 253076
46923 93846 50174
48927 97854 32872
53973 107946 33286
59655 119310 32880
75363 150726 65610
75873 151746 48586
79437 158874 32788
86613 173226 65582
99363 198726 65742
100377 200754 94060
103947 207894 47788
106377 212754 48224
114249 228498 33078
130383 260766 69970
130467 260934 68508
131727 263454 154104
133977 267954 54508
135567 271134 58004
144117 288234 60384
145257 290514 121452
147687 295374 53488
148323 296646 53126
154317 308634 53408
155877 311754 58384
161583 323166 53702
163503 327006 53678
172167 344334 262032
[/CODE]

Odd n's, 83 primes found / known :

[CODE]Normalized As discovered
k n
903 10227 1806*2^10226-1 is prime! Time : 467.128 ms.
2433 3 4866*2^2-1 = 19463 is prime!
4887 4289 9774*2^4288-1 is prime! Time : 31.737 ms.
5007 6765 10014*2^6764-1 is prime! Time : 132.857 ms.
5163 6183 10326*2^6182-1 is prime! Time : 141.222 ms.
7977 31265 15954*2^31264-1 is prime! Time : 4.011 sec.
9087 4741 18174*2^4740-1 is prime! Time : 90.434 ms.
10113 14535 20226*2^14534-1 is prime! Time : 707.671 ms.
15213 20311 30426*2^20310-1 is prime! Time : 1.643 sec.
19377 18677 38754*2^18676-1 is prime! Time : 781.275 ms.
21813 4283 43626*2^4282-1 is prime! Time : 375.998 ms.
22863 101135 45726*2^101134-1 is prime! Time : 45.990 sec.
25797 1 51594-1 is prime!
27957 21477 55914*2^21476-1 is prime! Time : 1.678 sec.
30357 65361 60714*2^65360-1 is prime! Time : 18.190 sec.
32937 8473 65874*2^8472-1 is prime! Time : 493.300 ms.
33837 4273 67674*2^4272-1 is prime! Time : 165.707 ms.
34533 32899 69066*2^32898-1 is prime! Time : 4.595 sec.
35193 12483 70386*2^12482-1 is prime! Time : 743.684 ms.
37227 1 74454-1 is prime!
44283 4439 88566*2^4438-1 is prime! Time : 465.176 ms.
46107 4277 92214*2^4276-1 is prime! Time : 465.330 ms.
52137 26309 104274*2^26308-1 is prime! Time : 2.757 sec.
55983 9851 111966*2^9850-1 is prime! Time : 714.703 ms.
56493 6891 112986*2^6890-1 is prime! Time : 377.827 ms.
59763 4611 119526*2^4610-1 is prime! Time : 486.253 ms.
60237 1 120474-1 is prime!
60747 1 121494-1 is prime!
61833 4651 123666*2^4650-1 is prime! Time : 313.346 ms.
15663 3 31326*2^2-1 = 125303 is prime!
63153 60295 126306*2^60294-1 is prime! Time : 16.792 sec.
64023 11431 128046*2^11430-1 is prime! Time : 938.154 ms.
66087 1 132174-1 is prime!
67737 4437 135474*2^4436-1 is prime! Time : 380.406 ms.
70743 49387 141486*2^49386-1 is prime! Time : 9.225 sec.
72327 17125 144654*2^17124-1 is prime! Time : 1.523 sec.
72993 23319 145986*2^23318-1 is prime! Time : 2.711 sec.
75093 15371 150186*2^15370-1 is prime! Time : 1.336 sec.
75387 5181 150774*2^5180-1 is prime! Time : 407.256 ms.
78933 11443 157866*2^11442-1 is prime! Time : 1.068 sec.
84807 7389 169614*2^47388-1 is prime! Time : 8.790 sec.
87735 4551 175470*2^4550-1 is prime! Time : 194.893 ms.
88623 13251 177246*2^13250-1 is prime! Time : 1.245 sec.
88743 4619 177486*2^4618-1 is prime! Time : 470.335 ms.
90567 6577 181134*2^6576-1 is prime! Time : 627.684 ms.
91671 8795 183342*2^8794-1 is prime! Time : 641.417 ms.
93507 5449 187014*2^5448-1 is prime! Time : 490.452 ms.
97323 52207 194646*2^52206-1 is prime! Time : 9.747 sec.
100053 28459 200106*2^28458-1 is prime! Time : 4.296 sec.
100353 5147 200706*2^5146-1 is prime! Time : 577.426 ms.
101823 4519 203646*2^4518-1 is prime! Time : 377.304 ms.
102993 48975 205986*2^48974-1 is prime! Time : 9.151 sec.
105123 5555 210246*2^5554-1 is prime! Time : 429.150 ms.
105837 5913 211674*2^5912-1 is prime! Time : 435.785 ms.
27003 3 54006*2^2-1 = 216023 is prime!
115167 8685 230334*2^8684-1 is prime! Time : 355.645 ms.
117303 4451 234606*2^4450-1 is prime! Time : 186.024 ms.
117867 4513 235734*2^4512-1 is prime! Time : 188.221 ms.
120387 5645 240774*2^5644-1 is prime! Time : 230.829 ms.
121557 11817 243114*2^11816-1 is prime! Time : 594.670 ms.
129747 18657 259494*2^18656-1 is prime! Time : 1.299 sec.
132507 4485 265014*2^4484-1 is prime! Time : 187.186 ms.
133023 9087 266046*2^9086-1 is prime! Time : 407.860 ms.
133947 1 267894-1 is prime!
134037 4421 268074*2^4420-1 is prime! Time : 186.659 ms.
142683 22371 285366*2^22370-1 is prime! Time : 1.966 sec.
144393 6567 288786*2^6566-1 is prime! Time : 252.434 ms.
144867 1 289734-1 is prime!
144957 6473 289914*2^6472-1 is prime! Time : 251.359 ms.
145587 1 291174-1 is prime!
148227 5997 296454*2^5996-1 is prime! Time : 235.853 ms.
148803 25019 297606*2^25018-1 is prime! Time : 2.232 sec.
152907 4365 305814*2^4364-1 is prime! Time : 186.700 ms.
154827 9113 309654*2^9112-1 is prime! Time : 408.607 ms.
39093 3 78186*2^2-1 = 312743 is prime!
157383 44059 314766*2^44058-1 is prime! Time : 7.957 sec.
167007 4901 334014*2^4900-1 is prime! Time : 202.140 ms.
167997 18705 335994*2^18704-1 is prime! Time : 1.300 sec.
169527 9329 339054*2^9328-1 is prime! Time : 419.792 ms.
169743 23791 339486*2^23790-1 is prime! Time : 2.079 sec.
170223 4187 340446*2^4186-1 is prime! Time : 184.676 ms.
170733 7307 341466*2^7306-1 is prime! Time : 319.059 ms.
171783 6759 343566*2^6758-1 is prime! Time : 256.343 ms.
[/CODE]

Regards,

Jean

 gd_barnes 2008-01-20 06:50

Jean,

Very good! Nice work.

I resumed testing the Sierp odd-n conjecture on 2 cores yesterday starting from n=118K. I'm now up to n=175K. I found primes on 4 more k's, all of which came in one small grouping from n=156K-170K, as follows:

50433*2^156597+1
91437*2^161615+1
61137*2^162967+1
39297*2^169495+1

This leaves 9 k's remaining! :smile:

Testing will pause at n=200K while I sieve a new file for the remaining k's.

I will request that this thread be moved over to the conjectures project shortly.

It will probably be Monday/Tuesday before I can get the project/my site updated to include the info. for this. For the time being, Karsten is keeping good track of things.

Gary

 Jean Penné 2008-01-20 20:29

[QUOTE=gd_barnes;123257]Jean,

Very good! Nice work.

I resumed testing the Sierp odd-n conjecture on 2 cores yesterday starting from n=118K. I'm now up to n=175K. I found primes on 4 more k's, all of which came in one small grouping from n=156K-170K, as follows:

50433*2^156597+1
91437*2^161615+1
61137*2^162967+1
39297*2^169495+1

This leaves 9 k's remaining! :smile:

Testing will pause at n=200K while I sieve a new file for the remaining k's.

I will request that this thread be moved over to the conjectures project shortly.

It will probably be Monday/Tuesday before I can get the project/my site updated to include the info. for this. For the time being, Karsten is keeping good track of things.

Gary[/QUOTE]

Many congrats for this work, Gary, it's very encouraging!

Regards,
Jean

 kar_bon 2008-01-20 23:46

[b]to Gary and Jean:[/b]

i included all data from above in the online-page (you know where).
have a look and than i can make it available for all.

karsten

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