Reserve R/S 40

Update sieve files.

Riesel base 145
 

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

CK=1169

(Condition 1):

All k where k = m^2 and m = = 27 or 46 mod 73:
for even n let k = m^2 and let n = 2*q; factors to:
(m*145^q - 1) * (m*145^q + 1)
odd n:
factor of 73

This includes k = 729

(Condition 2):

All k where k = m^2 and m = = 7 or 9 mod 16:
for even n let k = m^2 and let n = 2*q; factors to:
(m*145^q - 1) * (m*145^q + 1)
odd n:
factor of 2

This includes k = 49, 81, 529, 625

Riesel base 146
 

[CODE]
1,7
2,16
3,3
4,5
5,30
6,2
7,1
[/CODE]

With CK=8

Conjecture proven

Riesel base 147
 

[CODE]
1,3
2,1
3,2
4,1
5,1
6,1
7,14
8,2
9,1
10,14
11,0
12,112
13,31
14,3
15,46
16,1
17,1
18,2
19,140
20,1
21,1
22,48
23,4
24,1
25,5
26,1
27,2
28,2
29,1
30,1
31,10
32,1
33,619
34,43
35,4
36,(partial algebra factors)
37,1
38,131
39,12
40,1
41,9
42,1
43,20
44,3
45,1
46,1
47,8
48,96
49,0
50,1
51,0
52,1
53,3
54,1
55,0
56,1
57,13
58,0
59,0
60,1
61,1
62,29
63,0
64,169
65,5
66,3
67,2
68,7
69,13
70,1
71,114
72,2
[/CODE]

With CK=73

searched to n=2000, 0 if no prime found for this k, this base has many k remain at n=2000, and seems to be low-weight base

All k where k = m^2 and m = = 6 or 31 mod 37:
for even n let k = m^2 and let n = 2*q; factors to:
(m*147^q - 1) * (m*147^q + 1)
odd n:
factor of 37

This includes k = 36

Tested R63, completed to n=2000

I will completed all (Riesel or Sierpinski) bases with small CK and only tested to n=1000, to n=2000, this includes bases R63, R127, S63, S81, S97, S106

S63 completed to n=2000

Additional primes not in the list:

1108*63^12351+1
888*63^2698+1
(9*63^2162+1)/2 = (567*63^2161+1)/2

Riesel base 148
 

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

CK=1936

All k where k = m^2 and m = = 44 or 105 mod 149:
for even n let k = m^2 and let n = 2*q; factors to:
(m*148^q - 1) * (m*148^q + 1)
odd n:
factor of 149

The smallest such k is exactly 1936, thus, no k's proven composite by algebraic factors

Riesel base 149
 

[CODE]
1,7
2,4
3,1
[/CODE]

With CK=4

Conjecture proven

[QUOTE=sweety439;566971]Tested R63, completed to n=2000

I will completed all (Riesel or Sierpinski) bases with small CK and only tested to n=1000, to n=2000, this includes bases R63, R127, S63, S81, S97, S106[/QUOTE]

S81 reserving to n=5000

this file is the currently status for n<=2000

Note:

All k=4*q^4 for all n:
let k=4*q^4 and let m=q*3^n; factors to:
(2*m^2 + 2m + 1) * (2*m^2 - 2m + 1)

This includes k = 4, 64, 324

Riesel base 150
 

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

CK=49074

Only list k == 1 mod 149 since other k are already in CRUS

the remain k with k == 1 mod 149 are 30993, 31738

other remain k are {206, 841, 1509, 1962, 3229, 4682, 5245, 5890, 6039, 6353, 6494, 7851, 9061, 9260, 11324, 11477, 11516, 12839, 14373, 16309, 16404, 16424, 16977, 17603, 18859, 19027, 19191, 19226, 20468, 20988, 22238, 22349, 22977, 23396, 23706, 23944, 24614, 24852, 25488, 25704, 25829, 26685, 27032, 28389, 28822, 30050, 31812, 33521, 34429, 34707, 35066, 35344, 36709, 36994, 37137, 39108, 39141, 39712, 39736, 40020, 42012, 42128, 43060, 43789, 44346, 44645, 44832, 46257, 46616, 47717, 48138}, see [URL="http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base150-reserve.htm"]CRUS[/URL]

Riesel base 151
 

[CODE]
1,13
2,5
3,716
4,15
5,3
6,1
7,4
8,4
9,0
10,1
11,4
12,1
13,9
14,1
15,2
16,9
17,1
18,6
19,4
20,1
21,1
22,20
23,8
24,1
25,0
26,1
27,14
28,1
29,25
30,3
31,2
32,1
33,3
34,45
35,6
36,1
[/CODE]

With CK=37

k = 9, 25 remain at n=2000