[QUOTE=sweety439;449216]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.[/QUOTE]

So find them yourself.

[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? Besides, why there is no website for all S3 to S12 primes and R3 to R12 primes?[/QUOTE]

Because I didn't want to. If you want them search them yourself.

[QUOTE=gd_barnes;449235]So find them yourself.



Because I didn't want to. If you want them search them yourself.[/QUOTE]

These primes are the smallest primes of the form 248*249^n+1, 296*297^n+1 and 497*498^n+1, they are in the CRUS, but not the top 10 primes. What is the smallest exponent?

Besides, see the link [URL]http://harvey563.tripod.com/wills.txt[/URL], R268, k=267 is already tested to n=200K with no prime found (but the CRUS page only writes n=100K), and for non-started bases, R478, k=477 is already tested to n=200K with no prime found, and R1012, k=1011, the smallest prime is 1011*1012^32693-1.

[QUOTE=gd_barnes;449235]
Because I didn't want to. If you want them search them yourself.[QUOTE=sweety439;449235]
I want the smallest exponent...[/QUOTE][/QUOTE]
[in Jar Jar Binks voice] How wude!
:popcorn:

[QUOTE=gd_barnes;448410]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.[/QUOTE]

[QUOTE=sweety439;449285]These primes are the smallest primes of the form 248*249^n+1, 296*297^n+1 and 497*498^n+1, they are in the CRUS, but not the top 10 primes. What is the smallest exponent?
[/QUOTE]

At least one of these has a prime for n<5000, which means that you did not make an effort to find it on your own. As shown above I've already stated that I will not provide primes n<5000 for you.

Based on this, I will no longer provide primes of any size for you. You have shown a lack of willingness to use software for your own research.

I suggest that you find a different forum for your postings. I have deleted quite a few of your posts in these threads. I'm close to the point of deleting everything that you post in this forum in the future regardless of whether it is useful or not.

[QUOTE=gd_barnes;449298]At least one of these has a prime for n<5000, which means that you did not make an effort to find it on your own. As shown above I've already stated that I will not provide primes n<5000 for you.

Based on this, I will no longer provide primes of any size for you. You have shown a lack of willingness to use software for your own research.

I suggest that you find a different forum for your postings. I have deleted quite a few of your posts in these threads. I'm close to the point of deleting everything that you post in this forum in the future regardless of whether it is useful or not.[/QUOTE]

I see the past posts, there is no n<=10000 such that 296*297^n+1 is prime, but 296 is not remain at n=25000 for S297. Thus, the smallest exponent should between 10000 and 25000.

Several weeks ago, I searched (b-1)*b^n+1 for all bases 2<=b<=500 to n=1024, but some bases have no prime with n<=1024. I continued to search and found prime 87*88^3022+1, but found no prime of the form 121*122^n+1. (122 is the first base that I cannot find a prime)

[QUOTE=sweety439;449299]I see the past posts, there is no n<=10000 such that 296*297^n+1 is prime, but 296 is not remain at n=25000 for S297. Thus, the smallest exponent should between 10000 and 25000.[/QUOTE]

But there is a prime n<5000 for 248*249^n+1. I challenge you to find it. Hint: Do not use the factordb. You are wasting someone else's resources.

Is it possible for you to learn software? Can you run such software on your machine? Why is this so difficult for you?

Found a prime 248*249^1851+1.

[QUOTE=sweety439;449306]Found a prime 248*249^1851+1.[/QUOTE]

Good. How did you find it?

[QUOTE=gd_barnes;449307]Good. How did you find it?[/QUOTE]

I used my program, I also used this program to find the primes 87*88^3022+1 and 157*158^1620+1, but cannot find a prime of the form 121*122^n+1.

[QUOTE=sweety439;449353]I used my program, I also used this program to find the primes 87*88^3022+1 and 157*158^1620+1, but cannot find a prime of the form 121*122^n+1.[/QUOTE]

Prime for k 121 Base 122:
[CODE]121*122^6216+1[/CODE]Programms used:
srsieve
PFGW

Time: 12 minutes (including setting up srsieve and PFGW).

Sieving with srsieve until p=1G (srsieve --nmin 2 --nmax 25000 --pmax 1e9 "121*122^n+1")
PRP testing with PFGW (input.npg -f30)

There is another project to search the primes of the form (b-1)*b^n-1 for 3<=b<=2049, see the link [URL]http://harvey563.tripod.com/wills.txt[/URL], R268, k=267 is already tested to n=200K with no prime found (but the CRUS page only writes n=100K), and for non-started bases, R478, k=477 is already tested to n=200K with no prime found, and R1012, k=1011, the smallest prime is 1011*1012^32693-1.

You can also see more primes and test limits in the link above. (Some of the primes and test limits are for the k's > conjectured k, e.g. 112*113^286643-1, but the conjecture of R113 is only 20. The page only searches the primes of the form (b-1)*b^n-1)

Did you change the CRUS page? (for the test limit of R268, k=267)