Bases 6-32 reservations/statuses/primes

[tcadigan]

I'll take the files:

sieve-sierp-base16-10183.txt
sieve-sierp-base16-10947.txt

[gd_barnes]

Originally Posted by tcadigan

I'll take the files:

sieve-sierp-base16-10183.txt
sieve-sierp-base16-10947.txt

You got 'em. I'll show them as reserved to n=100K. Note that they have been searched to n=30K even though the sieved files start at n=25K so you can delete the n's below 30K.


Gary

[gd_barnes]

Riesel base 16:

k=1478 and 3620 are complete to n=100K which include double-checks to n=65K and 75K respectively. No primes. I'm unreserving them.

Curtis's k=443 has completed a double-check to n=65K.


Gary

[tcadigan]

Originally Posted by gd_barnes

You got 'em. I'll show them as reserved to n=100K. Note that they have been searched to n=30K even though the sieved files start at n=25K so you can delete the n's below 30K.


Gary

10947*2^142748+1 is prime! Time: 30.257 sec.

aka 10947*16^35687+1

results file attached.

taking sieve-sierp-base16-12243.txt
continuing with other reservation

[gd_barnes]

Originally Posted by geoff

Testing is at n=8K, there are 95 candidate k left.

Geoff,

I am done with analysis on most bases for k's that are multiples of the base (MOB). We are now going to include all k's that are MOB that yield a different prime for n>=1 then k / b but we will be excluding GFN's from all consideration. For Sierp base 6, the following situations exist:

k=1296, 7776, and 46656 are GFn's without a prime and are eliminated from consideration.

k=90546 is the only k remaining at n=10K that I found that does not have a prime but whose prime will be different than k / b = 90546 / 6 = 15091. That is 15091*6^1+1 is prime.

I am assuming your total of 95 k's remaining excluded k's that are multiples of the base. So on the web pages that will be updated shortly, you'll see 96 k's remaining at n=8K.

If you could, please add k=90546 to your testing starting at n=10K. Alternatively, I can just put it on the reservation page for people to pick up at a later time.


Thanks,
Gary

[gd_barnes]

Originally Posted by michaf

Another one down for riesel 31:

30792*31^28604-1 is prime

That leaves another 14 k’s to test.

Michaf,

Keep those primes coming!

I just wanted to give you a heads up here. Beginning on Monday, the project will be including k's that are a multiple of the base (MOB) but where the k yields a different prime for n>=1 than k / b -but- it will be excluding Generalized Fermat #'s (GFn's) from all consideration.

I am doing analysis on all bases for these issues but there are a few more difficult ones that I wasn't able to do yet. Base 31 is one of them. The web pages are being updated right now.

If you would like to do some analysis on base 31 for this issue, let me know. I have found the impact to be minimal for most bases. As an example, for Sierp base 6 with a conjecture of k=174308, there were 3 GFn's without a prime that were eliminated and only ONE k remaining without a prime at n=10K that was a MOB and will yield a different prime than k / b.

I can take care of this but if you'd like to try it, that works for me. If there are any questions, let me know.


Thanks,
Gary

[gd_barnes]

Originally Posted by michaf

One for Riesel 31:



Several for Sierpinski 24:

Michaf,

I've done analysis on Sierp base 24 for k's that are multiples of the base. The only one that needs a prime is k=17496. I tested it up to n=6.5K and changed the # of k's remaining from 172 to 173.

Can you test it starting from n=6.5K? If not, I can put it up for reservation.


Thanks,
Gary

[michaf]

If you meant all the 0 mod 31's that I left out:
It was a massive amountof 2 numbers:
28458 --> 918
69998 --> 2258

918*31^17504-1 is prime, so 2848*31^17503-1 is prime too.

What baffles me, is that I have no record of a prime for 2258
I also have not found it in 1mod2, 1mod3 or 1mod5.

duh...just noticed that 2258*31^1-1 is prime :>
which was the problem in the first place.

So this amounts to one problematic number, I will incorporate it in my search,

Originally Posted by gd_barnes

Michaf,

Keep those primes coming!

I just wanted to give you a heads up here. Beginning on Monday, the project will be including k's that are a multiple of the base (MOB) but where the k yields a different prime for n>=1 than k / b -but- it will be excluding Generalized Fermat #'s (GFn's) from all consideration.

I am doing analysis on all bases for these issues but there are a few more difficult ones that I wasn't able to do yet. Base 31 is one of them. The web pages are being updated right now.

If you would like to do some analysis on base 31 for this issue, let me know. I have found the impact to be minimal for most bases. As an example, for Sierp base 6 with a conjecture of k=174308, there were 3 GFn's without a prime that were eliminated and only ONE k remaining without a prime at n=10K that was a MOB and will yield a different prime than k / b.

I can take care of this but if you'd like to try it, that works for me. If there are any questions, let me know.


Thanks,
Gary

[gd_barnes]

Originally Posted by michaf

If you meant all the 0 mod 31's that I left out:
It was a massive amountof 2 numbers:
28458 --> 918
69998 --> 2258

918*31^17504-1 is prime, so 2848*31^17503-1 is prime too.

What baffles me, is that I have no record of a prime for 2258
I also have not found it in 1mod2, 1mod3 or 1mod5.

duh...just noticed that 2258*31^1-1 is prime :>
which was the problem in the first place.

So this amounts to one problematic number, I will incorporate it in my search,

Great! Yes, the n=1 primes are the potential problems for k * b (as well as n=2/n=3/other low primes for k * b^q).

I'll add k=69998 to the pages for Riesel base 31. Since k=2258 was eliminated immediately, I'll show k=69998 reserved by you and tested to n=0K.

Thanks for taking care of that!


Gary

[tcadigan]

12243*2^198772+1 is prime! Time: 53.926 sec.

aka 12243*16^49693+1

results file attached.

[tcadigan]

completed reservation for 10183

no prime

results file attached.

taking:
sieve-sierp-base16-13438.txt
sieve-sierp-base16-14910.txt