Riesel Base 999 k = 1776
k=1776 even n's trivial - odd n's difference of squares

Riesel Base 639 (One of my reservations)

k=1136 even n's trivial - odd n's are difference of squares

I have removed this from my testing

[QUOTE=MyDogBuster;207953]Riesel Base 741
Remaining k's: Tested to n=25K
64*741^n-1
[/QUOTE]

what about this:

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why?

[quote]what about this:

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why? [/quote]First of all, my covering set was wrong. s/b 7, 37 not 5, 37

Other than that, I don't have a clue. I am NOT a math person. I'm sure k=64 is probably algebraic, but don't ask me why.

[QUOTE=rogue;208087]2*857^2-1
4*857^195-1
8*857^22-1

With a conjecture of k=10, k=6 remains. I'll continue on it[/QUOTE]

6*857^23082-1 is prime

Conjecture proven

[QUOTE=kar_bon;208116]what about this:

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why?[/QUOTE]

I don't understand the question. All n where n%10=7 are divisible by 11, thus there would be no n where n%10=7 in the output file after sieving. You can remove all n where n is even since 64=8^2.

Sierpinski Base 1007
 

2*1007^7+1
4*1007^6+1
6*1007^1+1

The conjectured k = 8. This conjecture is proven.

Sierpinski Base 986
 

2*986^1+1
3*986^3+1
5*986^1+1
7*986^6+1

1 is a GFN (which has not been tested).
4 has trivial factors.

k=6 remains. I'll continue testing it.

[QUOTE=rogue;208144]2*986^1+1
3*986^3+1
5*986^1+1
7*986^6+1

1 is a GFN (which has not been tested).
4 has trivial factors.

k=6 remains. I'll continue testing it.[/QUOTE]

6*986^21633+1 is prime. This conjecture is proven.

Reserving R1011 as new (conj. k=208).

Likewise, reserving R/S1001 and S1011.