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Old 2020-05-26, 11:12   #749
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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Quote:
Originally Posted by sweety439 View Post
R112 has totally 37 k's remain:

9, 31, 68, 72, 79, 142, 187, 310, 340, 349, 421, 424, 451, 498, 529, 619, 636, 646, 703, 749, 758, 790, 853, 898, 940, 948, 981, 1008, 1018, 1024, 1051, 1093, 1204, 1254, 1268, 1349, 1353
Code:
k     n
9     5717
31
68    1710
72    2566
79
142   2153
187
310
340
349   1545
421
424
451
498   6038
529
619   5441
636   1291
646   2706
703
749   2732
758
790   1886
853   1382
898   1067
940
948
981   2858
1008
1018
1024  5681
1051
1093  1495
1204
1254  1887
1268
1349  1345
1353
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Old 2020-05-26, 11:14   #750
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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Quote:
Originally Posted by sweety439 View Post
...
896 = 112*8, thus k=896 and k=8 are from the same family.

Code:
k     n
8     4526
92    2300
122   2878
183   1253
209
269
428   2473
467
547
553   1833
668   1014
677   5723
813   4616
926   1357
941
943   1924
947   1004
953   6802
983   1398
1013  3501
1131  2768
1171  1712
1217  3872
1286  1775
1292
1346  3609
1412
1445  2419
1463
1470  3096
1499
1517
1573  1297
1581  2043
1604
1613
1664
1696
1712  4836
1780
1791  1820
1807  3619
1920  5333
1937
2082  5308
2189  1433
2237  2908
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Old 2020-05-26, 11:15   #751
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
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Quote:
Originally Posted by sweety439 View Post
...
1008 = 112*9, thus k=1008 and k=9 are from the same family.

Code:
k     n
9     5717
31
68    1710
72    2566
79
142   2153
187
310
340
349   1545
421
424
451
498   6038
529
619   5441
636   1291
646   2706
703
749   2732
758
790   1886
853   1382
898   1067
940
948
981   2858
1018
1024  5681
1051
1093  1495
1204
1254  1887
1268
1349  1345
1353
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Old 2020-05-26, 11:21   #752
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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The (probable) prime (621*3^20820+1)/2 = (23*3^20823+1)/2 is not listed in any Sierpinski problem literature because 23 was eliminated by (23*3^3+1)/2, but 621 was still unresolved.
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Old 2020-05-26, 11:25   #753
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"99(4^34019)99 palind"
Nov 2016
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Quote:
Originally Posted by sweety439 View Post
896 = 112*8, thus k=896 and k=8 are from the same family.

Code:
k     n
8     4526
92    2300
122   2878
183   1253
209
269
428   2473
467
547
553   1833
668   1014
677   5723
813   4616
926   1357
941
943   1924
947   1004
953   6802
983   1398
1013  3501
1131  2768
1171  1712
1217  3872
1286  1775
1292
1346  3609
1412
1445  2419
1463
1470  3096
1499
1517
1573  1297
1581  2043
1604
1613
1664
1696
1712  4836
1780
1791  1820
1807  3619
1920  5333
1937
2082  5308
2189  1433
2237  2908
Primes given by CRUS:

Code:
k     n
547   8124
1780  62794
Also, by CRUS, k=1696 was already tested to n=1M with no prime found.
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Old 2020-05-26, 11:27   #754
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
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Quote:
Originally Posted by sweety439 View Post
1008 = 112*9, thus k=1008 and k=9 are from the same family.

Code:
k     n
9     5717
31
68    1710
72    2566
79
142   2153
187
310
340
349   1545
421
424
451
498   6038
529
619   5441
636   1291
646   2706
703
749   2732
758
790   1886
853   1382
898   1067
940
948
981   2858
1018
1024  5681
1051
1093  1495
1204
1254  1887
1268
1349  1345
1353
Primes given by CRUS:

Code:
k     n
758   35878
948   173968
1268  50536
1353  7751
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Old 2020-05-26, 11:50   #755
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
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Quote:
Originally Posted by sweety439 View Post
S24 has 27 k's remain at n=1000 with k = 22 mod 23: {1816, 2529, 3679, 4346, 5726, 6899, 7727, 9774, 10326, 10671, 12626, 14006, 14236, 14604, 15409, 18629, 19204, 20676, 20906, 21711, 21849, 22654, 24471, 24701, 25966, 26771, 29071}

R24 has 20 k's remain at n=1000 with k = 1 mod 23: {461, 1841, 2094, 6579, 10926, 12674, 15641, 16124, 17251, 23691, 24151, 24404, 24611, 25646, 26681, 27049, 27670, 29211, 31626, 31994} (k=11064 is included in the conjecture but excluded from testing, since it will have the same prime as k=461)
S24:

Code:
k       n
1816
2529
3679    3813
4346
5726    1118
6899    1023
7727    2596
9774    4379
10326
10671   10732
12626
14006
14236   6422
14604
15409   2003
18629   1463
19204   1031
20676
20906   1028
21711   1544
21849
22654   1319
24471   3550
24701   1272
25966
26771   7860
29071   5548
R24:

Code:
k       n
461
1841    10093
2094
6579
10926   2551
12674
15641
16124
17251   1227
23691   1345
24151   1425
24404
24611   11083
25646
26681   1513
27049
27670   1972
29211
31626   4043
31994

Last fiddled with by sweety439 on 2020-09-02 at 16:40
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Old 2020-05-26, 11:51   #756
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2·13·113 Posts
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Quote:
Originally Posted by sweety439 View Post
S24:

Code:
x       y
1816
2529
3679    3813
4346
5726    1118
6899    1023
7727    2596
9774    4379
10326
10671   10732
12626
14006
14236   6422
14604
15409   2003
18629   1463
19204   1031
20676
20906   1028
21711   1544
21849
22654   1319
24471   3550
24701   1272
25966
26771   7860
29071   5548
R24:

Code:
x       y
461
1841    10093
2094
6579
10926   2551
12674
15641
16124
17251   1227
23691   1345
24151   1425
24404
24611   11083
25646
26681   1513
27049
27670   1972
29211
31626   4043
31994
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Old 2020-05-26, 14:52   #757
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

B7A16 Posts
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Quote:
Originally Posted by sweety439 View Post
...
This should be "k n" instead of "x y"

S24:

Code:
k       n
1816
2529
3679    3813
4346
5726    1118
6899    1023
7727    2596
9774    4379
10326
10671   10732
12626
14006
14236   6422
14604
15409   2003
18629   1463
19204   1031
20676
20906   1028
21711   1544
21849
22654   1319
24471   3550
24701   1272
25966
26771   7860
29071   5548
R24:

Code:
k       n
461
1841    10093
2094
6579
10926   2551
12674
15641
16124
17251   1227
23691   1345
24151   1425
24404
24611   11083
25646
26681   1513
27049
27670   1972
29211
31626   4043
31994

Last fiddled with by sweety439 on 2020-05-26 at 14:53
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Old 2020-05-26, 14:53   #758
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

B7A16 Posts
Default

Quote:
Originally Posted by sweety439 View Post
1008 = 112*9, thus k=1008 and k=9 are from the same family.

Code:
k     n
9     5717
31
68    1710
72    2566
79
142   2153
187
310
340
349   1545
421
424
451
498   6038
529
619   5441
636   1291
646   2706
703
749   2732
758
790   1886
853   1382
898   1067
940
948
981   2858
1018
1024  5681
1051
1093  1495
1204
1254  1887
1268
1349  1345
1353
(187*112^7524-1)/gcd(187-1,112-1) is (probable) prime
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Old 2020-05-26, 15:01   #759
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

B7A16 Posts
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S24 at n=11324
R24 at n=12402
S112 at n=6947
R112 at n=7546
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