A Sierpinski/Riesel-like problem

[sweety439]

1,17
2,2
3,1
4,1
5,0
6,2
7,1
8,1
9,5
10,5
11,1
12,8
13,2
14,29
15,3
16,1
17,1
18,1
19,1
20,2
21,0
22,1
23,1
24,5

With CK=25

k = 5, 21 remain at n=2000

[sweety439]

1,167
2,4
3,2
4,1
5,6
6,1
7,209
8,2
9,1
10,3
11,34
12,6
13,7
14,4
15,1
16,15
17,4
18,2
19,1
20,4
21,1
22,1
23,8
24,4
25,1
26,990
27,38
28,3
29,632
30,4
31,1
32,12
33,3
34,3
35,2
36,1
37,1
38,2
39,17
40,41
41,2
42,1
43,502611
44,152
45,3
46,5
47,122
48,4
49,7
50,2
51,1
52,1
53,2
54,329
55,1
56,2
57,4
58,127
59,96
60,2
61,7

With CK=62

k=43 prime given by CRUS

Conjecture proven

[sweety439]

1,223
2,2
3,4
4,3
5,1
6,1
7,6
8,2
9,1
10,2
11,2
12,2
13,581
14,1
15,42
16,1
17,175
18,2
19,4
20,1
21,27
22,2
23,534
24,1
25,1
26,37
27,40
28,5
29,1
30,2
31,6
32,3
33,1
34,1
35,2
36,1
37,155
38,10
39,8
40,1
41,3
42,11
43,2
44,3

With CK=45

Conjecture proven

[sweety439]

1,16703
2,1
3,6
4,(partial algebra factors)
5,1
6,1
7,32
8,1
9,(partial algebra factors)
10,1
11,15
12,1
13,1
14,8
15,2
16,21
17,2
18,2
19,10
20,2
21,1
22,7
23,1
24,8
25,5
26,1
27,1
28,85
29,2
30,1
31,1
32,2
33,2
34,6
35,2

With CK=36

k=1 prime given by generalized repunit prime search

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*184^q - 1) * (m*184^q + 1)
odd n:
factor of 5

This includes k = 4, 9

Conjecture proven

[sweety439]

1,0
2,2
3,1
4,1
5,4
6,1
7,1
8,8
9,(partial algebra factors)
10,6783
11,4
12,8
13,1
14,4
15,2
16,3

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*185^q - 1) * (m*185^q + 1)
odd n:
factor of 2

This includes k = 9

k=10 prime given by CRUS

k = 1 remain at n=66337, see post https://mersenneforum.org/showpost.p...&postcount=225

[sweety439]

1,7
2,2
3,1
4,1
5,1
6,1
7,1
8,1
9,5
10,4
11,1
12,112717
13,1
14,4
15,1
16,(partial algebra factors)
17,2
18,1
19,1
20,1
21,2
22,1
23,3
24,1
25,1
26,1
27,1
28,4
29,1
30,2
31,1
32,388
33,2
34,1
35,13
36,0
37,3
38,1
39,1
40,3
41,2
42,7
43,44
44,14
45,1
46,4
47,1
48,4
49,5
50,2
51,32
52,11
53,1
54,2
55,2
56,1
57,1
58,9
59,1
60,1
61,1
62,2
63,1
64,1
65,2
66,5

With CK=67

k=12 prime given by CRUS

All k where k = m^2 and m = = 4 or 13 mod 17:
for even n let k = m^2 and let n = 2*q; factors to:
(m*186^q - 1) * (m*186^q + 1)
odd n:
factor of 17

This includes k = 16

k = 36 remain at n=2000

[sweety439]

Update the status pdf files.

Also newest files for Riesel problems and Sierpinski problems

[sweety439]

Originally Posted by sweety439

Newest status for b<=128 and k<=128:

Riesel

Sierpinski

For the status for b<=128 and k<=128, see Sierpinski and Riesel

[sweety439]

Riesel bases have extended to 200

https://docs.google.com/document/d/e...FgpcOr1XfA/pub

Also Sierp bases file is now building ....

https://docs.google.com/document/d/e...b9OKKSpYh0/pub

[sweety439]

Originally Posted by sweety439

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

(201*141^5279-1)/20 is probable prime.

R141 is proven.

(consecutive proven Riesel bases: R139 to R144)

[sweety439]

Originally Posted by sweety439

Update the status pdf files.

Also newest files for Riesel problems and Sierpinski problems

Files updated to include the newest status for R63, S63, S81, S97, S106 (the old files only include S81 and S97)