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Old 2008-01-15, 04:18   #155
tcadigan
 
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Default 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
File Type: txt lresults.txt (35.5 KB, 74 views)
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Old 2008-01-15, 07:44   #156
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69998*31^13618-1 is prime!
(with no other primes upto 20k)

That eliminates all MOB's for base 31 riesel.
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Old 2008-01-15, 20:29   #157
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Default 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.
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Old 2008-01-16, 08:23   #158
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Quote:
Originally Posted by Siemelink View Post
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
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Old 2008-01-16, 11:23   #159
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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
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Old 2008-01-16, 11:47   #160
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Quote:
Originally Posted by gd_barnes View Post
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?
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Old 2008-01-16, 18:10   #161
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Quote:
Originally Posted by jasong View Post
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
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Old 2008-01-16, 19:15   #162
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Quote:
Originally Posted by jasong View Post
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
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Old 2008-01-16, 21:03   #163
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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
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Old 2008-01-16, 21:18   #164
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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...
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Old 2008-01-16, 21:24   #165
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Quote:
Originally Posted by gd_barnes View Post
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 View Post
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
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