And yet more results
 

Riesel base 615 primes found:

[code]
2*615^1-1
4*615^1-1
6*615^2-1
8*615^1-1
10*615^2-1
14*615^1-1
16*615^1-1
18*615^1-1
20*615^2-1
24*615^1-1
26*615^3-1
28*615^2-1
30*615^2-1
32*615^4-1
[/code]

k=12 and 22 remain at n=25000. Released.

Sierpinski base 688 primes found:

[code]
3*688^14+1
4*688^1+1
6*688^1+1
7*688^1+1
9*688^2+1
10*688^2+1
12*688^2433+1
13*688^19+1
15*688^1+1
16*688^3+1
18*688^3+1
19*688^106+1
21*688^1+1
22*688^1+1
24*688^405+1
25*688^1999+1
27*688^4+1
28*688^2+1
30*688^1+1
31*688^3+1
33*688^3+1
34*688^2+1
36*688^5+1
37*688^1+1
39*688^1+1
40*688^754+1
42*688^60+1
43*688^6+1
45*688^2+1
46*688^1+1
48*688^10+1
49*688^1+1
51*688^1+1
52*688^21+1
55*688^2+1
57*688^1+1
58*688^26+1
60*688^1+1
61*688^1+1
63*688^11+1
64*688^1949+1
66*688^60+1
69*688^5+1
70*688^3+1
72*688^1+1
73*688^38+1
75*688^3+1
76*688^1+1
78*688^2+1
79*688^14+1
81*688^15+1
82*688^1+1
84*688^1+1
85*688^1+1
87*688^8+1
88*688^158+1
90*688^95+1
91*688^49+1
93*688^2+1
94*688^5+1
96*688^232+1
97*688^2+1
99*688^1+1
100*688^7+1
102*688^1+1
[/code]

k=54, 67, and 103 remain at n=25000. Released.

Riesel base 866 primes found:

[code]
2*866^78-1
3*866^2-1
4*866^1-1
5*866^14-1
7*866^7227-1
9*866^1-1
10*866^2193-1
12*866^1-1
13*866^1-1
14*866^18-1
15*866^2-1
17*866^6-1
18*866^55-1
19*866^1-1
20*866^12734-1
22*866^1-1
23*866^244-1
24*866^77-1
25*866^1-1
27*866^29-1
28*866^1-1
29*866^4-1
30*866^16-1
32*866^8-1
33*866^2-1
34*866^1-1
[/code]

k=8 remains at n=25000. Released.

Sierspinski base 983 primes found:

[code]
2*983^5+1
4*983^2+1
6*983^20+1
10*983^6+1
12*983^141+1
14*983^1+1
16*983^22248+1
18*983^6+1
20*983^1+1
22*983^442+1
24*983^1+1
26*983^673+1
28*983^2+1
30*983^17+1
32*983^69+1
34*983^2+1
36*983^11+1
38*983^7+1
[/code]

k=8 remains at n=25000. Released.

Sierp 758
 

Sierp 758 the last k (8*758^n+1) tested n=25K-50K. Nothing found

Results attached - Base released

Sierp 781
 

Sierp 781 the last k (370*781^n+1) tested n=25K-50K. Nothing found

Results attached - Base released

Reserving R527, R548, R549, R557 and R563 to n=100K sieving and testing

OK, guys I'm back in town now and will have much more time to update things.

Of course that means that the work will slow down. It only gets super heavy when I'm gone. :smile:

Riesel base 666 results. 1 prime was previously reported, 1k remainng.

Reserving R628.

Riesel 1025
 

Riesel 1025 tested from n=45.9K to n=50K.
No reservation, just getting n to a nice round number.
Nothing found. Results attached. Base released

More house cleaning. Reserving S461 from n=75.7K to n=100K.

S518 is complete to n=25K; 4 primes found for n=5K-25K; 7 k's remaining; base released.

Results
 

Riesel base 737 primes found:

[code]
2*737^352-1
4*737^153-1
6*737^1-1
8*737^2-1
10*737^1-1
12*737^32-1
18*737^15-1
20*737^2-1
28*737^20591-1
30*737^1-1
32*737^128-1
34*737^1-1
36*737^17-1
38*737^8-1
[/code]

k=14, 16, 22, and 26 remain at n=25000. Released


Sierpinski base 737 primes found:

[code]
2*737^3+1
6*737^1+1
8*737^1+1
10*737^2+1
12*737^7+1
14*737^13+1
16*737^7132+1
18*737^1+1
20*737^1+1
24*737^11+1
26*737^1+1
28*737^10+1
30*737^1+1
32*737^11+1
34*737^2+1
36*737^5+1
[/code]

k=4 and 38 remain at n=25000. Released


Riesel base 773 primes found:

[code]
2*773^96-1
4*773^3-1
6*773^1-1
8*773^4-1
10*773^85-1
12*773^424-1
14*773^8-1
16*773^29-1
18*773^1-1
20*773^12-1
22*773^7-1
24*773^172-1
26*773^110-1
28*773^5-1
30*773^1-1
32*773^16-1
34*773^14471-1
36*773^1-1
40*773^5-1
42*773^2-1
[/code]

k=38 remain at n=25000. Released


Sierpinski base 773 primes found:

[code]
4*773^2+1
6*773^1+1
12*773^1+1
14*773^199+1
18*773^98+1
20*773^1+1
22*773^4+1
24*773^1+1
26*773^3+1
28*773^230+1
30*773^6+1
36*773^2119+1
38*773^27+1
40*773^8+1
42*773^1+1
[/code]

k=2, 8, 10, 16, 32, and 34 remain at n=25000. Released. Note that many of these k have a really low weight, so this conjecture will probably be very difficult to prove.


Riesel base 832 primes found:

[code]
2*832^1-1
3*832^19-1
5*832^1-1
6*832^6-1
8*832^127-1
9*832^1-1
11*832^1-1
12*832^2-1
14*832^9-1
15*832^1-1
17*832^1-1
18*832^15-1
20*832^8944-1
21*832^1-1
23*832^2-1
24*832^4-1
26*832^22-1
27*832^2-1
29*832^7-1
30*832^6-1
32*832^2-1
33*832^10-1
36*832^183-1
38*832^2-1
39*832^7-1
41*832^18-1
42*832^13-1
44*832^1-1
45*832^5-1
47*832^1-1
48*832^12-1
[/code]

k=35 remains at n=25000. Released.

More Results
 

Sierpinski base 844 primes found:

[code]
3*844^3+1
4*844^13+1
6*844^14+1
7*844^2+1
9*844^9687+1
10*844^27+1
12*844^3+1
13*844^1+1
15*844^8+1
16*844^4+1
18*844^1+1
19*844^11+1
21*844^2+1
22*844^7+1
24*844^7+1
25*844^1+1
27*844^58+1
28*844^1+1
30*844^1+1
31*844^378+1
33*844^2+1
34*844^1+1
36*844^28+1
37*844^3+1
39*844^1+1
42*844^1+1
43*844^1+1
45*844^304+1
46*844^10+1
48*844^2+1
49*844^1+1
[/code]

Conjecture proven.


Sierpinski base 845 primes found:

[code]
2*845^877+1
4*845^1646+1
6*845^325+1
8*845^1+1
10*845^2+1
12*845^1+1
14*845^1+1
16*845^28+1
18*845^4+1
20*845^1+1
22*845^2+1
24*845^15+1
26*845^11+1
28*845^2+1
30*845^3+1
32*845^17+1
36*845^41+1
38*845^3+1
40*845^2952+1
42*845^1+1
44*845^1+1
[/code]

k=34 remains at n=25000. Released.


Riesel base 846 primes found:

[code]
2*846^4-1
3*846^5-1
4*846^3319-1
5*846^1-1
7*846^7-1
8*846^35-1
9*846^9-1
10*846^12780-1
12*846^1-1
13*846^356-1
15*846^1-1
17*846^2-1
18*846^1-1
19*846^1-1
20*846^8-1
22*846^5-1
23*846^1-1
24*846^2-1
25*846^1-1
28*846^1-1
29*846^1-1
30*846^2-1
32*846^22-1
33*846^1-1
[/code]

Conjecture proven.


Riesel base 951 primes found:

[code]
2*951^1-1
4*951^1-1
8*951^1-1
10*951^21-1
12*951^1-1
14*951^1-1
18*951^1-1
22*951^1-1
24*951^3-1
28*951^1-1
30*951^3-1
32*951^1-1
38*951^1-1
40*951^1-1
42*951^4-1
44*951^1-1
48*951^6-1
[/code]

k=34 remains at n=25000. Released


Sierpinski base 951 primes found:

[code]
2*951^2+1
6*951^3+1
8*951^2+1
10*951^1+1
12*951^32+1
16*951^1+1
20*951^377+1
22*951^4+1
26*951^11+1
28*951^2+1
30*951^46+1
32*951^4+1
36*951^6892+1
38*951^8+1
40*951^3+1
42*951^1525+1
46*951^2+1
48*951^145+1
[/code]

Conjecture proven.


Sierpinski base 953 primes found:

[code]
2*953^1+1
4*953^18+1
10*953^2+1
12*953^1+1
18*953^3+1
22*953^2050+1
24*953^10+1
26*953^7+1
28*953^6+1
30*953^1+1
32*953^1+1
36*953^8+1
38*953^11+1
40*953^232+1
42*953^2+1
44*953^5845+1
46*953^844+1
[/code]

k=8 and 14 remain at n=25000. Released


I don't think I have any other small conjectures reserved. Please let me know if I do.