mersenneforum.org Bases 4-32 reservations/statuses/primes
 Register FAQ Search Today's Posts Mark Forums Read

2008-01-15, 04:18   #155

Sep 2004
UVic

2·5·7 Posts
14910 prime found

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

aka 14910*16^37966+1

results file attached.

continuing existing reservation
Attached Files
 lresults.txt (35.5 KB, 74 views)

 2008-01-15, 07:44 #156 michaf     Jan 2005 479 Posts 69998*31^13618-1 is prime! (with no other primes upto 20k) That eliminates all MOB's for base 31 riesel.
 2008-01-15, 20:29 #157 Siemelink     Jan 2006 Hungary 10C16 Posts Need some more ranges 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.
2008-01-16, 08:23   #158
gd_barnes

May 2007
Kansas; USA

7·1,481 Posts

Quote:
 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

 2008-01-16, 11:23 #159 jasong     "Jason Goatcher" Mar 2005 DB316 Posts If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K. If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base. Last fiddled with by jasong on 2008-01-16 at 11:24
2008-01-16, 11:47   #160
jasong

"Jason Goatcher"
Mar 2005

66638 Posts

Quote:
 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?

2008-01-16, 18:10   #161
gd_barnes

May 2007
Kansas; USA

7×1,481 Posts

Quote:
 Originally Posted by jasong If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K. If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base.
You got it. I haven't done any sieving on base 4 past my original testing limit of n=100K. Jean or Karsten, do you have a sieve file for Riesel base 4 k=16734?

Jasong, I'm not sure I quite follow you here about 2X length of LLR'd value of lower base. I can only speculate that you might like to save sieving/LLRing time if Riesel k=16734/2=8367 base 2 has known testing above n=200K (n=100K base 4) to avoid double-testing.

When setting up the pages, I checked all k's on bases that are powers of 2 for primes in the prime archives at the top-5000 site and at www.rieselprime.org (converted from base 2) before putting anything up for testing. As shown on the latter site, k=8367 has only been tested to n=10K base 2 (n=5K base 4) and has no primes that are odd-n so you're OK there.

I think this is a very good idea to reserve this base 4 vs. base 16. It is open for both bases. It would be a waste of time for someone to sieve/test k=16734 base 16 and then turn around and do it for base 4. Perhaps that's part of what you're referring to.

In this case, I'll show you as reserving k=16734 on both base 4 and base 16. Otherwise someone could duplicate you base 16.

One caviot...If you find an even-n prime base 4 (n==0mod4 base 2), that will also eliminate the k on base 16 and you could stop testing. But if you find an odd-n prime base 4 (n==2mod4 base 2), I would suggest deleting all odd-n's in your sieve file and continue from there looking for an even-n base 16 prime.

Of course it's your choice to continue on for base 16 but it's a way to kill two birds with one stone. You could even end up with two different top-5000 primes; one for each base!

Gary

Last fiddled with by gd_barnes on 2008-01-16 at 18:13

2008-01-16, 19:15   #162
gd_barnes

May 2007
Kansas; USA

7×1,481 Posts

Quote:
 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

 2008-01-16, 21:03 #163 michaf     Jan 2005 479 Posts 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
 2008-01-16, 21:18 #164 michaf     Jan 2005 479 Posts 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...
2008-01-16, 21:24   #165
gd_barnes

May 2007
Kansas; USA

7×1,481 Posts

Quote:
 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
Quote:
 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

 Similar Threads Thread Thread Starter Forum Replies Last Post KEP Conjectures 'R Us 3857 2021-05-09 14:34 gd_barnes Conjectures 'R Us 898 2021-05-08 18:09 gd_barnes Conjectures 'R Us 2281 2021-04-26 18:08 KEP Conjectures 'R Us 1098 2021-04-18 21:07 Siemelink Conjectures 'R Us 1682 2021-04-13 23:50

All times are UTC. The time now is 06:19.

Thu May 13 06:19:24 UTC 2021 up 35 days, 1 hr, 1 user, load averages: 1.60, 1.64, 1.80