Riesel base 3 reservations/statuses/primes

[henryzz]

Reserving 650-660M (to 25k)

[gd_barnes]

Originally Posted by KEP

Hello Michaf

I'm only interested in the non-primed k's, and their coorespondant n-value. If you has only taken your k's to n=1000, just let me know so I can take them to n=25000. However the primes should be send to Gary, since I'm only interested in the primes for n>25000

Regards

KEP

Ps. Does anyone know about algebraric factors for Riesel base 3, since Flatlander apparently had a k (510669604*3^n-1) which had algebraric factors. Is this true or false?

It is false. No k in base 3 should have algebraic factors such that the k could be eliminated that I am aware of. Let me define "having" algebraic factors such that the k could be elimianted without a prime being found:

Having algebraic factors means that a k has such factors that COMBINE with numeric factors to make a FULL covering set and hence eliminate a k-value from consideration.

k=510669604 is a perfect square. Like any other k that is a perfect square, it has algebraic factors for all even n. BUT...it still must be searched for all odd n. There is no covering set for the odd n. Here are the factors for the first few small odd-n:

n   factors
1  1201*1275611
3  23*61*9827569
5  13*71*83*877*1847
7  11*101530402177
9  2402353*4184027

Upon a little further check, I found an odd n with a smallest factor of nearly 8 trillion!:
510669604*3^55-1 = 7,976,141,243,627*11,169,048,639,317,939,512,801

This clearly demonstrates that there is no pattern of any kind of covering set of numeric or algebraic factors on the odd n. It should eventually yield a prime.

Editor note (lol):
510669604*3^1065-1 is prime!


Gary

[gd_barnes]

Originally Posted by michaf

I think the primes <1000 are kinda uninteresting; if needed they can be reproduced quick enough. Also, they take too much space ;)
I'll process upto 25k then, and mail the primes 1k-25k to Gary, and the remaining k's to you.

I just got a bunch of primes from for what appears to be k=500M-510M/n=1K-6.2K and k=500M-502M/n=6.2K-25K. Micha, have you tested k=502M-510M for n=6.2K-25K yet?

Kenneth, since you're doing this, starting with my next update of my web pages, I'm going to just link to your website for k's remaining and reservations. Are you OK with that? We can both manage the remaining mini-drive I. I'll move it over to your sub-forum.

As for k's remaining, you'll need to do what I've been doing...that is make sure no extra k's are left in as a result of multiples of the base whenver anyone sends you a group of k's that are remaining. You've been highly accurate in sending them to me the last 2 times so clearly you understand how to verify it.


Gary

[gd_barnes]

Originally Posted by michaf

First results:

500M-510M:
Left are (tested to 25k)

500145402
500968542
501526364
501628284

Primes will be mailed to Gary in the next few minutes

Micha,

There are 2 problems here:

1. It is extremely highly unlikely that there are only 4 k's remaining in a k=10M range. I will go so far as to say that it's virtually impossible. What range have you tested? This might be reasonable for k=500M-502M. I see that all k's remaining are in that range. Upon testing k<10M to n=60K, we still have 10 k's remaining and at least 2-3 k's were eliminated with primes for n>100K! As you know the k's remaining will generally be higher for the same k-range as the k's get higher since the numbers are higher so the possibility of only 4 k's remaining at n=25K is even smaller for k=500M-510M than for k<10M.

2. There are 2 k's here that shouldn't be remaining. I'll see if you guys can find them.

Edit: I just now looked at your 2nd primes file for n=6.2K-25K. It only contains primes for k=500M-502M. Therefore, I believe what I stated in #1 is correct. You have only listed k's remaining for k=500M-502M.

Are you testing KEP here? lol


Gary

[KEP]

Originally Posted by gd_barnes

I just got a bunch of primes from for what appears to be k=500M-510M/n=1K-6.2K and k=500M-502M/n=6.2K-25K. Micha, have you tested k=502M-510M for n=6.2K-25K yet?

Kenneth, since you're doing this, starting with my next update of my web pages, I'm going to just link to your website for k's remaining and reservations. Are you OK with that? We can both manage the remaining mini-drive I. I'll move it over to your sub-forum.

As for k's remaining, you'll need to do what I've been doing...that is make sure no extra k's are left in as a result of multiples of the base whenver anyone sends you a group of k's that are remaining. You've been highly accurate in sending them to me the last 2 times so clearly you understand how to verify it.


Gary

I'm OK with that Gary, just link to my webstites. I'm going to update the website later today, once I get some time to do it.

Kenneth.

[michaf]

Originally Posted by gd_barnes

I just got a bunch of primes from for what appears to be k=500M-510M/n=1K-6.2K and k=500M-502M/n=6.2K-25K. Micha, have you tested k=502M-510M for n=6.2K-25K yet?

Gary

He?

I _though_ I did 500 to 510 :)
I _think_ I buggered up someplace...
I _know_ I'll do them again, and be careful now...

[michaf]

Originally Posted by gd_barnes

Micha,

Are you testing KEP here? lol


Gary

I'm testing if he already sobered up yeah :)

I'll redo the range, to be sure :) I must have made a stupid cut & paste mistake someplace.
(besides... I reserved them for _testing_ scripts :) )

[KEP]

Originally Posted by michaf

I'm testing if he already sobered up yeah :)

I'll redo the range, to be sure :) I must have made a stupid cut & paste mistake someplace.
(besides... I reserved them for _testing_ scripts :) )

I've sobered up. I didn't react to your statement, because I thought it was only covering the 500M-502M range, so in other terms I just thought that you posted a partial result

Thanks for redoing the range, because as Gary states, this result is likely to be false and erroneous since more k's should remain. In average 4-5 k's should remain per 1M range, before removal of redundant k's. At least this has been the average per 1M range for k<=250M.

KEP

[Flatlander]

510-520M complete.

4,997,762 primes with n <= 1000.
8 tiny PRPs that proved to be not prime but were found slightly higher (all had n of 2 or 3).
2,167 primes with n > 1000.
63 remaining Ks for Kep to fiddle with.
5,000,000 total.

Remaining Ks to be sent to Kep.
All primes to be sent to Gary. Let's see if we can fill up his hard drive!

[mdettweiler]

Originally Posted by Flatlander

8 tiny PRPs that proved to be not prime but were found slightly higher (all had n of 2 or 3).

Did you post the composite PRP's here?

[gd_barnes]

Originally Posted by Flatlander

510-520M complete.

4,997,762 primes with n <= 1000.
8 tiny PRPs that proved to be not prime but were found slightly higher (all had n of 2 or 3).
2,167 primes with n > 1000.
63 remaining Ks for Kep to fiddle with.
5,000,000 total.

Remaining Ks to be sent to Kep.
All primes to be sent to Gary. Let's see if we can fill up his hard drive!

That may take a while: I have a 360 GB auto-backup drive affectionally referred to as "The book" by the computer store that I got it from 2 months ago.

Good luck filling THAT up! Perhaps if you sent me all primes for n>10 for all k up to 63G! (lol) The drive cost ~$80. If you guys somehow fill it up, you get to buy me another one! he-he-he

The largest space being used for results is (surprisingly) NOT by NPLB nor by base 3 (YET!), it is for my "all" twin prime search, which is currently stalled in the n=50K range for all k<1M. At about 600-700 tests per n-value at a sieve-depth of P=60G, the results for it are eating a large chunk of one of my 2 GB flash drives right now. Once they pass about 1.5 GB, I'll have to dump it to the book.

Edit: I just checked my Email. Chris, you don't need to send me primes for n<1000. Yes, you would fill up the book with THAT! Kenneth, weren't you telling people to just send me primes for n>1000? I think we agreed that we can quickly reconstruct primes n<1000 when it is needed.

I'm only going to save off the primes to my hard drive that were sent for n>1000. I won't delete the Email until later.


Gary