Bases 6-32 reservations/statuses/primes

[gd_barnes]

Originally Posted by Siemelink

Hi everyone,

Here are my current results on the base 19 riesel conjecture. With pfgw I discoverd 4920 k's that have no prime under n < 2000.
I've sieved with srsieve, tested with LLR and found 3030 PRPs for different k. All prps under 17,000 have been confirmed prime with pfgw. My minimum n is 17,000, as it creeps higher I'll confirm the PRPs.

Having fun, Willem.

A tremendous effort Willem!! Nicely done! To be specific for everyone's reference, there are 4920 - 3030 = 1890 k's remaining at n=17K for Riesel base 19.

Willem, can you send me an Email with a file that has all of the primes for n<2000 also? I'll need it for future historical reference.

My Email address is:
gbarnes017 at gmail dot com

Like I did for Sierp base 19, I'll create a separate web page that shows all of the k's remaining, probably on Wednesday.

One more thing...I'll be done in a couple of days searching Riesel base 19 to n=10K. I'll then unreserve it. If you want to take it higher after your done with your effort, it's all yours. There will likely be about 1600 k's remaining since the conjecture is lower than yours.


Thanks,
Gary

[Siemelink]

Originally Posted by gd_barnes

A tremendous effort Willem!! Nicely done! To be specific for everyone's reference, there are 4920 - 3030 = 1890 k's remaining at n=17K for Riesel base 19.

Willem, can you send me an Email with a file that has all of the primes for n<2000 also? I'll need it for future historical reference.

Thanks,
Gary

Sorry, I didn't keep this. I am confident that I didn't skip any k. I've run the whole range twice with:

ABC2 $b*19^$a-1 // {number_primes,$b,1}
a: from 1 to 2000
b: from 2 to 1119866 step 6

and

ABC2 $b*19^$a-1 // {number_primes,$b,1}
a: from 1 to 2000
b: from 6 to 1119866 step 6

My command was: pfgw <formula_in_a_file> -f100 -l
To get the remaining k I used: grep 2000-1 pfgw.out

Willem.

[gd_barnes]

Originally Posted by Siemelink

Sorry, I didn't keep this. I am confident that I didn't skip any k. I've run the whole range twice with:

ABC2 $b*19^$a-1 // {number_primes,$b,1}
a: from 1 to 2000
b: from 2 to 1119866 step 6

and

ABC2 $b*19^$a-1 // {number_primes,$b,1}
a: from 1 to 2000
b: from 6 to 1119866 step 6

My command was: pfgw <formula_in_a_file> -f100 -l
To get the remaining k I used: grep 2000-1 pfgw.out

Willem.

OK, I'll run those scripts for a while on a core or two to get the primes. It shouldn't take too long.


Gary

[gd_barnes]

Sierp base 16 k=2908, 6663, and 10183 are now at n=125K; no primes.

Since they are so low weight, I'm going to go ahead and take them on up to n=200K. (n=800K base 2)


Gary

[rogue]

I will take all Riesel and Sierpinski k for base 28.

[Siemelink]

I will take Riesel Base 25 to n=25,000. I've done the inital run with pfgw, I have exactly 1000 k's left.

Willem.

[KEP]

Any of your clever users, who has an idea as to what this means: "Running N+1 test using discriminant 5, base 56532+sqrt(5)", I should add that this happens above k=2100 maybe higher, when performing following command line: "input.txt -f100 -l2.5K.txt -tp" while working on Riesels Base3. So anyone knows what it means, and if unnescescary, how it can be avoided? since it creates a title wave of data...

Regards

KEP

Ps. Also does anyone knows for how long it will run this kind of test and howcome it just all the sudden at different k and n values switch to this kind of test in stead of just doing a regular test like it starts out to do?

[rogue]

5076*28^29557-1 is prime (found with phrot, verified by PFGW).

This was a heavy k. It wiped out slightly more than half of the remaining tests for the 4 k that haven't been tested to 50K.

[gd_barnes]

Originally Posted by Siemelink

Hi everyone,

Here are my current results on the base 19 riesel conjecture. With pfgw I discoverd 4920 k's that have no prime under n < 2000.
I've sieved with srsieve, tested with LLR and found 3030 PRPs for different k. All prps under 17,000 have been confirmed prime with pfgw. My minimum n is 17,000, as it creeps higher I'll confirm the PRPs.

Having fun, Willem.

Willem,

On the web pages when listing primes and considering k's remaining, we don't consider k's remaining that are a multiple of the base and where the k-value divided by a power of the base (i.e. k/b^q) leaves a k that is also remaining or where the smallest prime found is the same. These would result in duplicate primes being shown or k's being tested. Therefore, I have removed the following 88 k's from Riesel base 19:

2736, 6156, 6954, 33516, 33744, 43776, 51984, 61256, 62966, 66006, 74594, 75164, 98496, 103854, 115596, 116964, 120726, 127604, 132126, 152114, 156104, 191064, 197676, 221616, 226176, 255246, 255854, 256614, 279186, 316464, 325964, 331056, 339644, 361836, 372704, 374034, 399114, 402116, 421496, 424764, 440876, 461586, 461624, 463904, 498636, 523944, 532646, 536256, 547466, 578664, 588506, 589266, 636804, 641136, 648546, 653106, 670434, 675146, 700416, 744876, 758936, 766916, 767904, 807804, 810236, 815366, 831744, 832086, 876584, 895926, 901854, 936396, 944414, 946086, 946466, 952394, 970976, 983706, 987696, 999666, 1009584, 1014144, 1014524, 1020186, 1052144, 1062746, 1092006, 1103444

If you are testing them, you may also wish to remove them.

The following 14 k's are multiples of the base but still remain because k/b^q contains a prime that is too small (i.e. n=1) to be valid for these larger k's.

53694, 124754, 192014, 234194, 255474, 265164, 419444, 486324, 595004, 640224, 650864, 666824, 928454, 946124

This leaves 1802 k's remaining (instead of 1890) for Riesel base 19 at n=17K. They are now all shown on the Riesel base 19 reservations page.

I have not looked at or considered the algebraic factors that you have apparently found just yet. Very nice find! Most likely, more k's will be removed after I take a look at it.


Gary

[rogue]

All base 28 k (both Sierpinski and Riesel) are tested to n = 50,000. I am continuing these.

[KEP]

I will start up sieving k=404 for Base 12 with n=100K to n=500K. ETA is not availeable yet, since I'm just about to start the sieving :)

KEP!