Sierpinski base 604
 

Primes found:

[code]
3*604^2+1
4*604^1+1
6*604^4+1
7*604^1+1
9*604^1+1
10*604^3+1
12*604^17370+1
13*604^1+1
15*604^19+1
16*604^124+1
18*604^3+1
19*604^49+1
[/code]

Conjecture proven.

R800, R888 and R900 completed to n=100K.
There is only one prime: 4*800^33837-1
Results attached, bases released.

Sierp 516
 

Sierp 516 the last k (122*516-n-1) tested n=25K-50K. Nothing found

Results attached - Base released

Results
 

Sierpinski base 542 primes found:

[code]

3*542^1+1
4*542^15982+1
5*542^1+1
6*542^1+1
7*542^8+1
8*542^1+1
9*542^51+1
10*542^12+1
11*542^4909+1
12*542^20+1
14*542^1+1
15*542^109+1
16*542^364+1
17*542^3+1
18*542^69+1
19*542^18950+1
20*542^5+1
21*542^1+1
22*542^98+1
23*542^89+1
24*542^1+1
25*542^116+1
26*542^3+1
27*542^334+1
28*542^34+1
29*542^859+1
30*542^156+1
31*542^4+1
[/code]

k =2 and 13 remain at n=25000. Released.

Sierpinki base 574 primes found:

[code]
3*574^1+1
4*574^1+1
6*574^2+1
7*574^1+1
9*574^1+1
10*574^1+1
12*574^3+1
13*574^6+1
15*574^110+1
18*574^1+1
19*574^3+1
21*574^2+1
22*574^3+1
[/code]

k=16 remains at n=25000. Released.

Riesel base 620 primes found:

[code]

2*620^2-1
3*620^2-1
4*620^1773-1
5*620^4-1
6*620^1-1
7*620^1-1
8*620^10-1
9*620^9-1
10*620^1-1
11*620^1434-1
12*620^6-1
13*620^1-1
14*620^2-1
15*620^562-1
16*620^11-1
17*620^2-1
18*620^1-1
19*620^1-1
21*620^39-1
[/code]

k=20 remains at n=25000. Released.

Sierpinski base 620 primes found:

[code]

2*620^13+1
3*620^1+1
4*620^18+1
5*620^41+1
6*620^4+1
7*620^6+1
8*620^5+1
9*620^1+1
10*620^138+1
11*620^53+1
14*620^1+1
15*620^3+1
16*620^54+1
17*620^91+1
18*620^1+1
19*620^12+1
20*620^1+1
21*620^3+1
[/code]

k=12 and 13 remain at n=25000. Released.

Results
 

Sierpinski base 636 primes found:

[code]

2*636^2+1
3*636^141+1
5*636^1+1
6*636^3+1
7*636^11+1
8*636^8+1
10*636^1+1
11*636^1+1
12*636^3+1
13*636^1+1
15*636^9850+1
16*636^1+1
17*636^2+1
18*636^5+1
20*636^1+1
21*636^8+1
22*636^2+1
23*636^1+1
25*636^1+1
26*636^4+1
[/code]

Proven.

Sierpinski base 643 primes found:

[code]
4*643^5+1
10*643^42+1
12*643^1+1
16*643^1+1
18*643^3+1
[/code]

k=6 remains at n=25000. Released.

Sierpinski base 665 primes found:

[code]

2*665^45+1
4*665^1334+1
6*665^2+1
8*665^5+1
10*665^6+1
12*665^2+1
14*665^1+1
16*665^4+1
18*665^1+1
20*665^61+1
22*665^28+1
24*665^2+1
26*665^1+1
28*665^6+1
30*665^2+1
32*665^33+1
34*665^4+1
36*665^5749+1
[/code]

Proven.

Riesel base 668 primes found:

[code]

2*668^486-1
3*668^1-1
4*668^1-1
5*668^330-1
6*668^1-1
7*668^67-1
8*668^4-1
9*668^1-1
10*668^1-1
12*668^59-1
13*668^41-1
[/code]

k=11 remains at n=25000. Released.

Sierpinski base 683 primes found:

[code]
2*683^1+1
4*683^2+1
6*683^1+1
8*683^91+1
12*683^5+1
14*683^25+1
16*683^84+1
[/code]

k=18 remains at n=25000. Released.

Riesel base 695 primes found:

[code]
2*695^10-1
4*695^149-1
6*695^384-1
8*695^4-1
10*695^1-1
12*695^7-1
14*695^9970-1
16*695^1-1
18*695^2-1
20*695^8-1
22*695^1-1
24*695^2-1
[/code]

k=26 remains at n=25000. Released

Results
 

Sierpinski base 702 primes found:

[code]

2*702^3+1
3*702^2+1
4*702^9+1
5*702^1+1
6*702^1228+1
7*702^87+1
8*702^4+1
9*702^2+1
10*702^8+1
11*702^1+1
12*702^12+1
13*702^1+1
14*702^1+1
15*702^1+1
16*702^4+1
17*702^8+1
18*702^1+1
19*702^1+1
20*702^2+1
21*702^21+1
22*702^8+1
23*702^2+1
24*702^2+1
25*702^1+1
26*702^1+1
27*702^2+1
28*702^2+1
29*702^1+1
30*702^1+1
31*702^33+1
32*702^68+1
33*702^1+1
34*702^1+1
35*702^1+1
36*702^3+1
37*702^63+1
38*702^2+1
40*702^1+1
41*702^4+1
42*702^62+1
43*702^1+1
44*702^2+1
45*702^2+1
46*702^8+1
47*702^1422+1
48*702^2+1
49*702^15+1
50*702^13+1
51*702^1+1
52*702^3+1
53*702^25+1
54*702^307+1
55*702^1+1
56*702^1+1
57*702^72+1
58*702^2+1
59*702^17+1
60*702^2+1
61*702^408+1
62*702^1087+1
63*702^4+1
64*702^5+1
65*702^1+1
66*702^5+1
67*702^8+1
68*702^1+1
69*702^5+1
70*702^13+1
71*702^1+1
72*702^388+1
73*702^5+1
74*702^1+1
[/code]

k=39 remains at n=25000. Released

Sierpinski base 743 primes found:

[code]
2*743^1+1
4*743^246+1
8*743^71+1
12*743^2+1
14*743^10449+1
16*743^4+1
18*743^6+1
22*743^12+1
24*743^42+1
26*743^1+1
28*743^2+1
30*743^1+1
[/code]

k=10 remains at n=25000. Released.

Sierpinski base 747 primes found:

[code]
2*747^4+1
4*747^2+1
6*747^1+1
8*747^2+1
10*747^13+1
12*747^118+1
14*747^1+1
16*747^1+1
18*747^4+1
20*747^2+1
22*747^3560+1
24*747^1+1
26*747^1+1
28*747^2+1
30*747^2+1
[/code]

Proven.

Riesel base 782 primes found:

[code]
2*782^4-1
3*782^3-1
4*782^3-1
5*782^2-1
6*782^1-1
7*782^1685-1
8*782^8-1
9*782^3-1
10*782^3-1
11*782^2-1
13*782^11-1
15*782^7-1
16*782^1-1
17*782^4-1
18*782^510-1
19*782^3-1
20*782^16-1
21*782^1-1
22*782^1-1
24*782^3-1
25*782^3-1
26*782^2-1
27*782^4-1
[/code]

k=14 remains at n=25000. Released.

Results
 

Riesel base 815 primes found:

[code]
2*815^2-1
4*815^1-1
6*815^1-1
10*815^3-1
14*815^470-1
[/code]

k=8 remains at n=25000. Released.

Riesel base 836 primes found:

[code]
2*836^330-1
3*836^2-1
4*836^1-1
5*836^56-1
7*836^1-1
9*836^1-1
10*836^21-1
12*836^11-1
13*836^1-1
14*836^2-1
15*836^1-1
17*836^10-1
18*836^214-1
19*836^3-1
20*836^38-1
22*836^5-1
23*836^350-1
24*836^1-1
25*836^1-1
27*836^1-1
28*836^213-1
29*836^2-1
30*836^8-1
[/code]

k=8 remains at n=25000. Released.

Sierpinski base 846 primes found:

[code]
2*846^1+1
3*846^1+1
5*846^1+1
6*846^1+1
7*846^1+1
8*846^2+1
10*846^1+1
11*846^88+1
13*846^3+1
15*846^408+1
16*846^1+1
17*846^5+1
18*846^13+1
20*846^1+1
21*846^13+1
22*846^8+1
23*846^6+1
26*846^1+1
27*846^3371+1
28*846^1+1
30*846^2+1
31*846^1+1
32*846^1+1
33*846^1+1
35*846^1+1
36*846^2+1
37*846^3+1
40*846^2+1
41*846^1+1
42*846^1+1
[/code]

Proven.

Sierpinski base 879 primes found:

[code]
2*879^1+1
4*879^1+1
6*879^2+1
8*879^4+1
12*879^2+1
14*879^167+1
16*879^2+1
18*879^1+1
20*879^1+1
22*879^6+1
24*879^1183+1
26*879^24+1
28*879^4+1
30*879^1+1
32*879^4617+1
[/code]

k=10 remains at n=25000. Released.

Results
 

Sierspinki base 893 primes found:

[code]
2*893^1+1
4*893^10+1
6*893^7+1
10*893^12+1
12*893^8+1
14*893^1+1
16*893^20+1
18*893^2+1
22*893^2+1
24*893^1+1
26*893^519+1
28*893^2+1
30*893^7+1
[/code]

k=8 and 20 remain at n=25000. Released.

Sierpinski base 898 primes found:

[code]
3*898^6+1
4*898^1+1
6*898^29+1
7*898^1+1
9*898^15+1
10*898^2+1
13*898^35+1
15*898^3+1
16*898^1+1
18*898^2+1
19*898^165+1
21*898^1+1
24*898^30+1
27*898^1+1
[/code]

k=28 remains at n=25000. Released.

Sierpinski base 919 primes found:

[code]
4*919^1+1
6*919^5092+1
10*919^8+1
18*919^386+1
22*919^1+1
[/code]

k=12 remains at n=25000. Released.

Sierpinski base 924 primes found:

[code]
2*924^4+1
3*924^3+1
4*924^1+1
5*924^1+1
6*924^10+1
7*924^1+1
8*924^1+1
9*924^1+1
10*924^1+1
11*924^2+1
13*924^9+1
14*924^8031+1
15*924^2+1
16*924^386+1
17*924^2+1
18*924^1+1
19*924^19+1
20*924^1+1
21*924^10+1
22*924^4+1
23*924^43+1
24*924^49+1
26*924^14+1
27*924^5+1
28*924^1+1
29*924^15+1
30*924^4+1
31*924^4+1
32*924^1+1
33*924^1+1
34*924^7+1
35*924^1+1
[/code]

Proven.

Sierpinski base 930 primes found:

[code]
2*930^1+1
3*930^1+1
4*930^2+1
5*930^1+1
6*930^1+1
7*930^217+1
9*930^24+1
10*930^2+1
11*930^7+1
12*930^1+1
13*930^207+1
14*930^7+1
15*930^12+1
16*930^3+1
17*930^2+1
18*930^1+1
19*930^3+1
[/code]

k=8 remains at n=25000. Released.

Sierpinski base 993 primes found:

[code]
2*993^1+1
4*993^39+1
10*993^1+1
12*993^2+1
14*993^1+1
16*993^1+1
18*993^3+1
20*993^1+1
22*993^8+1
24*993^1+1
26*993^1+1
28*993^104+1
32*993^13+1
[/code]

k=6, 8, and 34 remain at n=25000. Released.

If I've kept track of my reservations correctly, I only have S887, S948, and S998 remaining for these small conjectures.

Nice work rogue! I'm in awe at the work that you're putting in. You're putting my efforts with R603 (currently at ~19K) and S928 (at 12.8K) to shame!

[QUOTE]If I've kept track of my reservations correctly, I only have S887, S948, and S998 remaining for these small conjectures. [/QUOTE]

That's what I show also. I did get an extra one in S702. I didn't see a reservation for it but it may be there. I'll process it.

S647 is complete to n=25K; 2 primes found for n=5K-25K; 4 k's remaining; largest prime 58*647^22212+1; base released.