[quote=gd_barnes;211852]How is k=8 proven composite by partial algebraic factors?

8*863^4492-1 is prime!

Short analysis:
n==(1 mod 2); factor of 3
n==(0 mod 3); algebraic factors because a^3*b^3-1 has a factor of a*b-1

This leaves n==(2 or 4 mod 6) that need to be searched.

The best example for a small n is n=16, which has a 15-digit smallest factor, i.e.:
290,080,942,920,023 *
2,610,619,153,408,518,748,349,564,802,570,449

Now the base is proven. :-)


Gary[/quote]

Oops, sorry, I've missed it.

Riesel base 521, k=28.
Primes:
2*521^8-1
4*521^1-1
8*521^2-1
10*521^1-1
12*521^2-1
18*521^1-1
20*521^10-1
22*521^3-1
24*521^1-1

Trivially factors: k=6,14,16,26

Base proven.

[quote=unconnected;212048]Riesel base 666, k=898
Remaining k's:
74*666^n-1
139*666^n-1

k=144 and k=289 proven composite by partial algebraic factors (even n - diff. of squares, odd n - factor of 29).
Trivially factors - 316 k's.

Primes attached.[/quote]

That's very good for such a high base! :-)

Just to confirm: Your search limit was n=25K. Is that correct?

For the somewhat larger conjectured unproven bases such as this, it's best if a results file is provided for n>2500.

Riesel Base 789
 

Riesel Base 789
Conjectured k = 236
Covering Set = 5, 79
Trivial Factors k == 1 mod 2(2) and k == 1 mod 197(197)

Found Primes: 108k's - File attached

Remaining k's: 5k's - Tested to n=25K
74*789^n-1
116*789^n-1
120*789^n-1
126*789^n-1
146*789^n-1

k=4, 64, 144 proven composite by partial algebraic factors

Trivial Factor Eliminations: 1k
198

Base Released

[quote=gd_barnes;211589]Cool! No, afaik, stopping when a prime is found for a base would not be needed in PRPnet for our needs. It just came in handy for me on a pure PFGW search on many bases with 1k remaining. It would be handy if PFGW itself could stop on a k/base combo.[/quote]
I am not certain but i would guess that using the the serp/riesel feature would stop a k just on the base the prime was found not other bases as well. Really i would guess it is a stop on a k/base pair when a prime is found

[quote=henryzz;212277]I am not certain but i would guess that using the the serp/riesel feature would stop a k just on the base the prime was found not other bases as well. Really i would guess it is a stop on a k/base pair when a prime is found[/quote]

Why are you guessing? Are you referring to PFGW or PRPnet? Mark already answered for PRPnet.

[quote=gd_barnes;212337]Why are you guessing? Are you referring to PFGW or PRPnet? Mark already answered for PRPnet.[/quote]
Misread sorry

Riesel bases 917, 911, 930, and 656
 

I posted none over the weekend, so I will post four today.

Primes found:

2*917^210-1
4*917^3-1
6*917^1-1
8*917^16-1
10*917^7-1
12*917^1-1
14*917^184-1

With a conjectured k of 16, this conjecture is proven.

2*911^14-1
4*911^1-1
10*911^1-1
12*911^2-1
18*911^2-1

The other k have trivial factors. With a conjectured k of 20, this conjecture is proven.

[code]
2*930^2-1
3*930^1-1
4*930^1-1
5*930^1-1
6*930^2-1
7*930^2-1
8*930^101-1
9*930^1-1
10*930^13-1
11*930^2-1
12*930^1-1
13*930^354-1
14*930^2-1
15*930^11-1
16*930^1-1
17*930^1-1
18*930^4-1
19*930^1-1
[/code]

With a conjectured k of 20, this conjecture is proven.

[code]
2*656^10-1
3*656^2-1
4*656^11-1
5*656^90-1
7*656^1-1
8*656^4-1
9*656^1-1
10*656^11-1
12*656^12-1
13*656^1-1
14*656^2-1
15*656^1-1
17*656^198-1
18*656^1-1
19*656^3-1
20*656^878-1
22*656^1-1
23*656^18-1
24*656^2-1
25*656^3-1
27*656^37-1
28*656^1-1
29*656^140-1
30*656^9-1
32*656^2-1
33*656^1-1
34*656^1-1
35*656^6-1
37*656^11-1
38*656^2-1
39*656^1-1
40*656^393-1
42*656^1-1
43*656^19-1
44*656^4-1
45*656^2-1
47*656^54-1
48*656^6-1
49*656^1-1
50*656^734-1
52*656^15-1
53*656^8-1
54*656^1-1
55*656^61-1
57*656^5-1
58*656^1-1
59*656^8-1
60*656^1-1
62*656^2-1
63*656^2-1
64*656^1-1
65*656^124-1
67*656^1-1
68*656^2-1
69*656^1-1
70*656^37-1
72*656^48-1
73*656^5-1
[/code]
The other k have trivial factors. With a conjectured k of 74, this conjecture is proven.

Riesel base 683, k=20
Primes:
2*683^540-1
4*683^1-1
6*683^2-1
8*683^8-1
10*683^1-1
16*683^3-1
18*683^36-1
14*683^1124-1

Trivially factors: k=12
Base proven.

Reserving Riesel 611 and 628 to n=25K

S1001 is done to 40K, 2 [I]k[/I] remain. Emailed. Base released.