Bases 6-32 reservations/statuses/primes

[geoff]

Originally Posted by gd_barnes

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.

Actually the 95 k remaining at n=8K includes multiples of 6. I only removed perfect powers of 6 from the original sieve.

Now 60k remain at n=25K. I should be finished to n=30K by the 17th Jan.

[tcadigan]

14910*2^151864+1 is prime! Time: 33.493 sec.

aka 14910*16^37966+1

results file attached.

continuing existing reservation

[michaf]

69998*31^13618-1 is prime!
(with no other primes upto 20k)

That eliminates all MOB's for base 31 riesel.

[Siemelink]

Hidiho,

some of my ranges will finish this week, I'll take some more:
Riesel, for n where it is now to 100000
594*27^n-1
233*28^n-1
1422*28^n-1
2319*28^n-1
4001*28^n-1

Willem.

[gd_barnes]

Originally Posted by Siemelink

Hidiho,

some of my ranges will finish this week, I'll take some more:
Riesel, for n where it is now to 100000
594*27^n-1
233*28^n-1
1422*28^n-1
2319*28^n-1
4001*28^n-1

Willem.

All of them would be from n=25K-100K with the exception of 2319*28^n-1 and 4001*28^n-1, which would be from n=5K-100K.


G

[jasong]

Originally Posted by gd_barnes

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.

That's very interesting. 3 and 7 are troublesome as well. Could there be something special about Mersenne Prime bases? 3 is both a Mersenne Prime and a Fermat Prime, so if there's a connection, it's a double whammy.

5 and 17 are Fermat primes, anything going on with base 17?

[gd_barnes]

Originally Posted by jasong

That's very interesting. 3 and 7 are troublesome as well. Could there be something special about Mersenne Prime bases? 3 is both a Mersenne Prime and a Fermat Prime, so if there's a connection, it's a double whammy.

5 and 17 are Fermat primes, anything going on with base 17?

Robert demonstrated some time ago that bases where b=2^q-1 are the most problematic. I haven't looked beyond base 31 in that regard. Certainly, bases 3, 7, and 15 are the big problem children and base 31 to a lesser extent. (Bases 19 and 25 will most likely prove to be problematic also.)

Michaf has done a nice job on Riesel base 31 with a relatively high conjecture of k=134718 getting it down 14 k's remaining at n=28.9K. But the Sierp side will be a pain with a conjecture of k=6360528.

Sierp base 24 seems to be the most difficult to find primes on for some reason. With a relatively low conjecture of k=30651, it still has 173 k's remaining (> 0.5%) at n=15K. This is by far the highest percentage that I can remember of remaining k's at that level of testing. I haven't analyzed it in depth to determine why this is happening.


Gary

[michaf]

Happy to get riesel31 to a mere 13 primes remaining:

48212*31^30691-1 is prime

That leaves 13 k’s to test

I've now tested upto 31k

[michaf]

and some more fun with sierpinski 24:

21276*24^15196+1 is prime
11874*24^15419+1 is prime
28591*24^15910+1 is prime

That leaves 169 k’s to test

I’ve done upto 16.6k now, so many more to come...

[gd_barnes]

Originally Posted by gd_barnes

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

Originally Posted by michaf

and some more fun with sierpinski 24:

21276*24^15196+1 is prime
11874*24^15419+1 is prime
28591*24^15910+1 is prime

That leaves 169 k’s to test

I’ve done upto 16.6k now, so many more to come...

Micha,

Did you add back MOB k=17496 to Sierp base 24? I had tested it to n=6.5K with no prime and had added one to your remaining k's from before. I had assumed that you had previously removed it per the prior project description. So this would now make 170 k's remaining unless you found a prime for it.


Gary

[jasong]

I'm still hoping for a sieve file.

Also, I've thought about it, and I've decided I'm willing to sieve for any base from 2-31. I'm thinking I might download the various sieve files and see what kinds of numbers I come up with.

Of course, I intend to start with my already reserved number. k=16734 base=4. :)