Also, I am interested in the form k*b^n+-1 with both b and k are small, but it does not have an easy prime of this form. (excluding GFNs)

For example:
47*2^583+1
40*5^1036+1
10*17^1356+1
4*23^342+1
8*23^119215+1
32*26^318071+1
12*30^1023+1
36*33^23615+1
2*38^2729+1
5*14^19698-1
32*26^9812-1
25*30^34205-1
37*38^136211-1

I take all k*b^n+-1 for b<=64, k<=64. However, I cannot find a prime of the form 46*35^n+1, but the file shows that 46 is not a remain k for S35.

These are other text files for S5, S6, R4, R5, and R6, up to k=500. (except R4, since if we allow full/partial algebraic factors, then the conjecture of R4 is only 9)

I am another researcher, I do not exclude k's with full or partial algebraic factors, and I do not exclude GFN's. I want to find the smallest Sierpinski/Riesel number (in my definition) to all bases b<=1024, this is the file for b<=256, but with some question marks, are all the terms right? (I know some special cases for GFN's cannot have a prime, even if they have no algebraic factors, e.g. 8*128^n+1, it equals 2^(7*n+3)+1, and if 2^n+1 is prime, then this n must be a power of 2, but 7*n+3 cannot be a power of 2 since a power of 2 must = (1 or 2 or 4) mod 7, and not = 3 (mod 7). Thus, all number of the form 8*128^n+1 with integer n>=1 are composite)

[QUOTE=sweety439;448086]I am another researcher, I do not exclude k's with full or partial algebraic factors, and I do not exclude GFN's. I want to find the smallest Sierpinski/Riesel number (in my definition) to all bases b<=1024, this is the file for b<=256, but with some question marks, are all the terms right? (I know some special cases for GFN's cannot have a prime, even if they have no algebraic factors, e.g. 8*128^n+1, it equals 2^(7*n+3)+1, and if 2^n+1 is prime, then this n must be a power of 2, but 7*n+3 cannot be a power of 2 since a power of 2 must = (1 or 2 or 4) mod 7, and not = 3 (mod 7). Thus, all number of the form 8*128^n+1 with integer n>=1 are composite)[/QUOTE]

You are free to define the reverse conjectures however you see fit. The efforts are welcome and are interesting. But you come to the CRUS project after it has been running for 9 years and now seem to be attempting to re-define the Riesel and Sierp conjectures using your own definition. With that your efforts are not welcome and have now become irritating. I would ask you to take a step back from such an effort. Defining the reserve conjectures is fine. Re-defining the project conjectures is not.

So that you can see where our conjectures came from, I am attaching a complete listing of all of both the Riesel and Sierp conjectures for bases <= 1024. Included are the base, the conjectured k-value, the period, and the complete covering set. Whenever a new base is started, this is the list that we use. I do not recall who created the lists but it was done programatically by one of our more sophisticated programmers. After 9 years we have yet to find an error in the lists.

[QUOTE=sweety439;448075]Also, I am interested in the form k*b^n+-1 with both b and k are small, but it does not have an easy prime of this form. (excluding GFNs)

For example:
47*2^583+1
40*5^1036+1
10*17^1356+1
4*23^342+1
8*23^119215+1
32*26^318071+1
12*30^1023+1
36*33^23615+1
2*38^2729+1
5*14^19698-1
32*26^9812-1
25*30^34205-1
37*38^136211-1

I take all k*b^n+-1 for b<=64, k<=64. However, I cannot find a prime of the form 46*35^n+1, but the file shows that 46 is not a remain k for S35.[/QUOTE]

prime:
46*35^56062+1

[QUOTE=sweety439;448073]<snip>
9*490^n+1 (S490 has 29 k's remaining at n=100K, but not include 9)
9*848^n+1 (S848 has 11 k's remaining at n=100K, but not include 9)
9*908^n+1 (S908 has 9 k's remaining at n=100K, but not include 9)
9*984^n+1 (S984 has 6 k's remaining at n=100K, but not include 9)
9*1030^n+1 (S1030 has 304 k's remaining at n=25K, but not include 9)
18*145^n+1 (S145 has 435 k's remaining at n=25K, but not include 18)
24*45^n+1 (S45 has 36 k's remaining at n=100K, but not include 24)
15*466^n-1 (R466 has 54 k's remaining at n=100K, but not include 15)
15*718^n-1 (R718 has 22 k's remaining at n=100K, but not include 15)
17*88^n-1 (R88 has 30 k's remaining at n=100K, but not include 17)
17*766^n-1 (R766 has 6 k's remaining at n=100K, but not include 17)
17*772^n-1 (R772 has 587 k's remaining at n=25K, but not include 17)
17*852^n-1 (R852 has 130 k's remaining at n=25K, but not include 17)
[/QUOTE]

Primes:
9*490^468+1
9*848^543+1
9*908^1069+1
9*984^315+1
9*1030^941+1
18*145^6555+1
24*45^18522+1
15*466^776-1
15*718^1948-1
17*88^1362-1
17*766^566-1
17*772^1665-1
17*852^240-1


Sweety, I am happy to look up these primes for you but I feel for your part you should be doing searches to at least n=1000 (preferrably n=5000) before making such requests. Using a PFGW script an entire k-value for one side can be searched for all bases <= 1030 to n=1000 in under an hour. It would only take a few hours to search them to n=5000 on a modern machine. For example on my 10-year old extremely slow laptop I am able to search a single k-value on one side to n=5000 in < 1 day. The only real personal effort involved was to determine the bases to be searched by removing bases with trivial and algebraic factors before beginning the search.

My point here is that if you desire such comprehensive lists of primes for the reverse conjectures you should be willing to put in some effort to learn how a PFGW script works and spend more CPU time than just a cursory search to n=200 (or whatever limit that you are searching to).

I searched to 400. For example, I found the prime 17*554^288-1 (the conjecture of R554 is only 4)

However, for forms that the CRUS says there is a known prime, such as 9*984^n+1, I didn't searched so far.

[QUOTE=sweety439;448156]I searched to 400. For example, I found the prime 17*554^288-1 (the conjecture of R554 is only 4)

However, for forms that the CRUS says there is a known prime, such as 9*984^n+1, I didn't searched so far.[/QUOTE]

Obviously you did not search to n=400. In my most recent post in this thread I gave you two primes that were n<400, the lowest of which was n=240.

Please learn how to use PFGW. I will no longer look up primes for you for n<5000. It is a fast search to n=5000 with PFGW or LLR.

I want the smallest exponent n such that (b-1)*b^n+1 is prime for b = 249, 297, and 498.

Besides, due to the website [URL]http://harvey563.tripod.com/wills.txt[/URL], R268, k=267 is already checked to n=200K with no prime found.

I found the website [URL]http://www.noprimeleftbehind.net/gary/primes-kx10n-1.htm[/URL] for the R10 primes. Of course, there is also a website [URL]http://www.rieselprime.de/[/URL] for the S2 and R2 primes, but why you choose R10? not S10? Besides, why there is no website for all S3 to S12 primes and R3 to R12 primes?

[QUOTE=sweety439;449230]I found the website [URL]http://www.noprimeleftbehind.net/gary/primes-kx10n-1.htm[/URL] for the R10 primes. Of course, there is also a website [URL]http://www.rieselprime.de/[/URL] for the S2 and R2 primes, but why you choose R10? not S10? [/QUOTE]

R 10 is very interesting since it produce near-repdigit primes.
S 10 can only produce quasi repdgiti primes.