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Old 2020-12-21, 22:21   #1134
sweety439
 
Nov 2016

22·3·5·47 Posts
Default Riesel base 137

Code:
1,11
2,2
3,27
4,1
5,12
6,1
7,1
8,2
9,(partial algebra factors)
10,5
11,0
12,2
13,0
14,4
15,0
16,231
With CK=17

All k where k = m^2 and m = = 3 or 5 mod 8:
for even n let k = m^2 and let n = 2*q; factors to:
(m*137^q - 1) * (m*137^q + 1)
odd n:
factor of 2

This includes k = 9

k = 11, 13, 15 remain at n=2000

Last fiddled with by sweety439 on 2021-02-25 at 22:38
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Old 2020-12-21, 22:24   #1135
sweety439
 
Nov 2016

22·3·5·47 Posts
Default Riesel base 138

Code:
1,2
138,1
275,1
412,2
549,4
686,1
823,1
960,1
1097,6
1234,28
1371,1
1508,2
1645,1
1782,2
With CK=1806

Only list k == 1 mod 137 since other k are already in CRUS

no remain k with k == 1 mod 137, totally list of the remain k is {408, 688, 831, 1074, 1743}, all remain at n=300K, see CRUS

Last fiddled with by sweety439 on 2021-02-27 at 06:57
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Old 2020-12-21, 22:25   #1136
sweety439
 
Nov 2016

22×3×5×47 Posts
Default Riesel base 139

Code:
1,163
2,1
3,114
4,(partial algebra factors)
5,1
With CK=6

All k where k = m^2 and m = = 2 or 3 mod 5:
for even n let k = m^2 and let n = 2*q; factors to:
(m*139^q - 1) * (m*139^q + 1)
odd n:
factor of 5

This includes k = 4

Conjecture proven
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Old 2020-12-21, 22:26   #1137
sweety439
 
Nov 2016

1011000001002 Posts
Default Riesel base 140

Code:
1,79
2,2
3,1
4,5
5,30
6,1
7,7
8,2
9,1
10,1
11,108
12,2
13,7
14,16
15,1
16,1
17,8
18,6
19,1
20,2
21,1
22,1
23,2
24,1
25,1
26,4
27,1
28,1
29,18
30,2
31,1
32,16
33,12
34,1
35,6
36,1
37,1
38,448
39,2
40,9
41,8
42,1
43,3
44,2
45,1
With CK=46

Conjecture proven
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Old 2020-12-21, 23:59   #1138
sweety439
 
Nov 2016

22·3·5·47 Posts
Default

A (Sierpinski/Riesel) base b has 2-cover if and only if b+1 is not prime or prime power
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Old 2020-12-22, 00:00   #1139
sweety439
 
Nov 2016

282010 Posts
Default

The formula for Sierpinski conjectures in CRUS is k*b^n+1
The formula for Riesel conjectures in CRUS is k*b^n-1
The formula for Sierpinski conjectures in this project is (k*b^n+1)/gcd(k+1,b-1)
The formula for Riesel conjectures in this project is (k*b^n-1)/gcd(k-1,b-1)
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Old 2020-12-22, 00:03   #1140
sweety439
 
Nov 2016

22·3·5·47 Posts
Default

The reason for (k=27 is excluded from S8 in this project) (k=4 is excluded from S16 in this project) (k=1 is excluded from R4 in this project) (k=1 is excluded from R8 in this project) (k=1 is excluded from R16 in this project) (k=1 is excluded from R36 in this project) (k=1 is excluded from R100 in this project) (k=1 is excluded from R128 in this project) is the same as (k=1 is excluded from R14 in CRUS) (k=1 is excluded from R18 in CRUS) (k=1 is excluded from R20 in CRUS) (k=1 is excluded from R24 in CRUS) (k=1 is excluded from R30 in CRUS) (k=1 is excluded from R32 in CRUS) (k=1 is excluded from R38 in CRUS) (k=1 is excluded from R42 in CRUS)
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Old 2020-12-22, 00:05   #1141
sweety439
 
Nov 2016

22·3·5·47 Posts
Default Riesel base 141

searched to n=2000, see the text file for the status, 0 if no (probable) prime found for this k

CK=285

Only k = 201 remain at n=2000
Attached Files
File Type: txt R141 status.txt (1.9 KB, 18 views)

Last fiddled with by sweety439 on 2020-12-22 at 00:19
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Old 2020-12-22, 00:13   #1142
sweety439
 
Nov 2016

22×3×5×47 Posts
Default Riesel base 142

Code:
1,1231
2,1
3,26
4,3
5,1
6,3
7,1
8,7
9,1
10,2
11,14
With CK=12

Conjecture proven
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Old 2020-12-22, 00:14   #1143
sweety439
 
Nov 2016

22·3·5·47 Posts
Default Riesel base 143

Code:
1,3
2,2
3,16
4,1
With CK=5

Conjecture proven
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Old 2020-12-22, 00:17   #1144
sweety439
 
Nov 2016

22×3×5×47 Posts
Default Riesel base 144

Code:
1,(full algebra factors)
2,24
3,1
4,(full algebra factors)
5,1
6,1
7,5
8,1
9,(full algebra factors)
10,1
11,1
12,1
13,1
14,4
15,10
16,(full algebra factors)
17,1
18,1
19,4
20,1
21,1
22,1
23,134
24,2
25,(full algebra factors)
26,5
27,2
28,2
29,4
30,519
31,1
32,3
33,1
34,8
35,1
36,(full algebra factors)
37,3
38,1
39,964
40,1
41,1
42,1
43,2
44,6
45,3
46,97
47,2
48,1
49,(full algebra factors)
50,2
51,3
52,1
53,1
54,8
55,1
56,1
57,20
58,35
With CK=59

All k = m^2 for all n; factors to:
(m*12^n - 1) * (m*12^n + 1)

This includes k = 1, 4, 9, 16, 25, 36, 49

Conjecture proven
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