A Sierpinski/Riesel-like problem - Page 35

sweety439 · 2017-08-14, 17:14

These k's for these Sierpinski bases cannot be eliminated with current technology, since they are GFN's or half GFN's without known (probable) primes. (include the k's > CK, but not include the k's without from testing, i.e. k's that are multiples of base (b) and where (k+1)/gcd(k+1,b-1) is not prime)

Code:

base   k
2      65536
3      3433683820292512484657849089281
4      65536
5      625
6      1296
7      2401
8      256, 65536
9      3433683820292512484657849089281
10     100
11     14641
12     12
13     815730721
14     196
15     225
16     65536
17     83521
18     18
19     361
20     160000
21     2046526777500669368329342638102622164679041
22     22
23     279841
24     331776
25     625
26     676
27     1853020188851841, 3433683820292512484657849089281
28     614656
29     250246473680347348787521
30     185302018885184100000000000000000000000000000000
31     1
32     4, 16, 256, 65536
33     1406408618241
34     1336336
35     661233485303375668149836762254674220999159684294975425898101273336493477472686208784580230712890625
36     1296
37     37
38     1
39     2313441
40     1600
41     63759030914653054346432641
42     42
43     11688200277601
44     197352587024076973231046656
45     2025
46     46^512
47     23811286661761
48     5308416
49     2401
50     1
51     19252683449641888890260123354856276823237618025475304982087581524852141411154717334003958315833698636313043201
52     52
53     62259690411361
54     27327525884414205519790497974303154461449992065060438016
55     1
56     9834496
57     10556001
58     58
59     3481
60     60
61     13845841
62     1
63     1
64     256, 65536
65     10309258098174834118790766041464760922826826572418212890625
66     4356
67     1
68     1
69     513798374428641
70     70
71     71^16384
72     72
73     650377879817809571042122834561
74     808551180810136214718004658176
75     1004524257206332858195774182519244277500547468662261962890625
76     1238846438084943599707227160576
77     1
78     78
79     6241
80     40960000
81     3433683820292512484657849089281
82     45212176
83     1
84     7056
85     3039563674866725366216700431136500455038221930406808846390168104209843587706907906166586830210007974528707563877105712890625
86     1
87     10772290133751755506346104768641
88     59969536
89     1
90     65610000
91     1
92     1
93     93
94     37157429083410091685945089785856
95     9025
96     2708192040014184559945134363758220403329915059847434832829218816
97     1
98     1
99     1
100    100
101    10201
102    102^64
103    112550881
104    1
105    121550625
106    126247696
107    1
108    108
109    1
110    12100
111    531089433205482293807404177813761
112    375817263084708503965641077546115954135779496817219617550715846656
113    113^128
114    662148260948741787228316709317924977225312314678010411233675575296
115    174900625
116    13456
117    117
118    37588592026706176
119    200533921
120    120^128
121    14641
122    1
123    1
124    15376
125    25, 625
126    15876
127    1
128    16, 256, 65536
256    65536
512    2, 4, 16, 32, 256, 65536
1024   4, 16, 256, 65536

sweety439 · 2017-08-14, 18:11

Quote:

Originally Posted by sweety439

These k's for these Sierpinski bases cannot be eliminated with current technology, since they are GFN's or half GFN's without known (probable) primes. (include the k's > CK, but not include the k's without from testing, i.e. k's that are multiples of base (b) and where (k+1)/gcd(k+1,b-1) is not prime)

If we do not include the k's > CK, then they are:

Code:

base   k
2      65536
6      1296
10     100
12     12
15     225
18     18
22     22
31     1
32     4
36     1296
37     37
38     1
40     1600
42     42
50     1
52     52
55     1
58     58
60     60
62     1
63     1
66     4356
67     1
68     1
70     70
72     72
77     1
78     78
83     1
86     1
89     1
91     1
92     1
93     93
97     1
98     1
99     1
104    1
107    1
108    108
109    1
117    117
122    1
123    1
124    15376
126    15876
127    1
128    16
512    2, 4, 16
1024   4, 16

sweety439 · 2017-08-15, 10:06

Quote:

Originally Posted by sweety439

These are the text files for R70 and R88, tested to n=1000.

Found some primes in CRUS (i.e. gcd(k-1,b-1) = 1) for R88.

17*88^1362-1
68*88^2477-1
89*88^1704-1
179*88^4545-1
212*88^5511-1
380*88^8712-1
444*88^19708-1
464*88^20648-1
477*88^5816-1
522*88^1108-1
536*88^1731-1

sweety439 · 2017-08-15, 17:06

Found some primes in CRUS (i.e. gcd(k-1,b-1) = 1) for R70.

278*70^1320-1
434*70^3820-1
489*70^2096-1
729*70^28625-1

sweety439 · 2017-08-16, 17:16

Update newest text files for Sierpinski/Riesel conjectures bases <= 128 (except R3, R6, SR40, SR52, SR66, S70, SR78, SR82, SR96, R106, SR120, SR124, SR126, S127) and bases 256, 512 and 1024.

sweety439 · 2017-08-16, 17:40

Quote:

Originally Posted by sweety439

The first few bases remain at n=1024 for these k's are:

Sierpinski k=1:

31, 38, 50, 55, 62, 63, 67, 68, 77, 83, 86, 89, 91, 92, 97, 98, 99, 104, 107, 109, 122, 123, 127, 135, 137, 143, 144, 147, 149, ...

Sierpinski k=2:

38, 101, 104, 167, 206, 218, 236, 257, 287, 305, ...

Sierpinski k=3:

83, 123, 191, 261, 293, 303, ...

Sierpinski k=4:

32, 53, 77, 83, 107, 113, 155, 161, 174, 204, 206, 212, 227, 230, ...

Riesel k=1:

51, 91, 135, 142, 152, 174, 184, 185, 200, 230, 244, 259, 269, 281, 284, 311, ...

Riesel k=2:

107, 170, 215, 233, 254, 276, 278, 298, 303, 380, 382, 383, ...

Riesel k=3:

42, 107, 159, 283, 295, 347, 359, ...

Riesel k=4:

47, 72, 115, 163, 167, 178, 212, 218, 223, 232, 240, 270, ...

Some known (probable) primes with bases b<=512 and n>1024 for these k's:

Code:

Sierpinski k=2:

38 (2729)
101 (192275)
104 (1233)
167 (6547)
206 (46205)
236 (161229)
257 (12183)
287 (5467)
305 (16807)
353 (2313)
368 (7045)
395 (2625)
416 (2517)
467 (126775)
497 (1339)

Sierpinski k=3:

358 (9560)
424 (1105)

Sierpinski k=4:

77 (6098)
83 (5870)
107 (32586)
113 (2958)
227 (13346)
242 (4206)
257 (160422)
264 (9647)
293 (1034)
308 (1966)
353 (2086)
355 (10989)
410 (144078)
422 (2634)
440 (56086)
452 (14154)
470 (5218)
482 (30690)
497 (1898)

Riesel k=1:

51 (4229)
91 (4421)
135 (1171)
142 (1231)
152 (270217)
174 (3251)
184 (16703)
230 (5333)
244 (3331)
259 (2011)
284 (2473)
318 (1193)
333 (9743)
360 (2609)
375 (1993)
376 (1223)
391 (9623)
411 (1061)
454 (1217)
469 (5987)
487 (9967)
499 (4691)

Riesel k=2:

107 (21910)
170 (166428)
215 (1072)
233 (8620)
254 (2866)
276 (2484)
278 (43908)
298 (4202)
303 (40174)
380 (3786)
382 (2324)
383 (20956)
434 (1166)

Riesel k=3:

42 (2523)
432 (16002)
446 (4850)

Riesel k=4:

47 (1555)
72 (1119849)
115 (4223)
163 (2285)
167 (1865)
212 (34413)
218 (23049)
240 (1401)
270 (89661)
380 (2039)
422 (21737)
461 (3071)
480 (93609)
491 (1683)
498 (2527)
512 (2215)

sweety439 · 2017-08-18, 02:57

Code:

k,n
1,2
2,1
3,1
4,2

With conjectured k=5, this conjecture is proven.

sweety439 · 2017-08-18, 02:58

Code:

k,n
1,2
2,1
3,4

With conjectured k=4, this conjecture is proven.

sweety439 · 2017-08-18, 03:00

Code:

k,n
1,2
2,5
3,3
4,1
5,6

With conjectured k=6, this conjecture is proven.

sweety439 · 2017-08-18, 03:02

Code:

k,n
2,5
3,183
4,10

With conjectured k=5, k=1 remains.

sweety439 · 2017-08-18, 03:03

Code:

k,n
1,2
2,1
3,1
4,2
5,3
6,1
7,2

With conjectured k=8, this conjecture is proven.

2017-08-15, 17:06	#378
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2×13×113 Posts	Found some primes in CRUS (i.e. gcd(k-1,b-1) = 1) for R70. 27870^1320-1 43470^3820-1 48970^2096-1 72970^28625-1 Last fiddled with by sweety439 on 2017-08-15 at 17:06

2017-08-18, 02:57	#381
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2×13×113 Posts	Sierpinski base 131 Code: k,n 1,2 2,1 3,1 4,2 With conjectured k=5, this conjecture is proven.

2017-08-18, 02:58	#382
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·13·113 Posts	Sierpinski base 134 Code: k,n 1,2 2,1 3,4 With conjectured k=4, this conjecture is proven. Last fiddled with by sweety439 on 2017-08-18 at 02:59

2017-08-18, 03:00	#383
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·13·113 Posts	Sierpinski base 139 Code: k,n 1,2 2,5 3,3 4,1 5,6 With conjectured k=6, this conjecture is proven.

2017-08-18, 03:02	#384
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2×13×113 Posts	Sierpinski base 143 Code: k,n 2,5 3,183 4,10 With conjectured k=5, k=1 remains.

2017-08-18, 03:03	#385
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 B7A₁₆ Posts	Sierpinski base 146 Code: k,n 1,2 2,1 3,1 4,2 5,3 6,1 7,2 With conjectured k=8, this conjecture is proven.

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