Bases 6-32 reservations/statuses/primes

[henryzz]

i have checked all the prps up to n=8k
at n=4k i had 40ks remaining
at n=5k i had 30ks remaining
at n=6k i had 26ks remaining
at n=7k i had 19ks remaining
at n=8k i have 14ks remaining
for some reason i have less ks remaining at n=8k than kar_bon did at n=15.5k

[kar_bon]

Originally Posted by henryzz

for some reason i have less ks remaining at n=8k than kar_bon did at n=15.5k

will check this perhaps late today.

[henryzz]

i think i had a lucky streak earlier
at n=8k i had 14ks remaining
at n=9k i had 14ks remaining
at n=10k i had 14ks remaining
at n=11k i had 14ks remaining
at n=12k i had 12ks remaining
it has started to even out
i had no primes in 3k between n=8k and n=11k

i am currently at n=12.6k with 11ks remaining
these are the remaining ks:

1069814
1323828
1347432
1529892
1531556
1570340
1588442
1632992
1877488
1878582
1932692

[gd_barnes]

Originally Posted by kar_bon

i'm testing Riesel Base 15 with my new scripts.
for now i tested n<=1M.

the PRP's with n>500 are attached (smaller availlable on request).

there're 15 k's with no primes for n<15.5k:

135202
144400
193524
296686
298342
300870
381714
481292
527774
684682
853776
937474
940130
977666
986914

i'm testing further.
in combination for small n upto about 1000, i have the edit a little the tests with pfgw.
my intention:
with one command/batch test a wide k-range standalone, running till end without any work by hand.
for now the deeper sieve have to manage per hand, all others is ok so far.

Karsten,

I'm getting ready to verify this for inclusion on my web pages. You said there was an attachment with the primes. Did you forget that?


Thanks,
Gary

[gd_barnes]

Originally Posted by henryzz

i think i had a lucky streak earlier
at n=8k i had 14ks remaining
at n=9k i had 14ks remaining
at n=10k i had 14ks remaining
at n=11k i had 14ks remaining
at n=12k i had 12ks remaining
it has started to even out
i had no primes in 3k between n=8k and n=11k

i am currently at n=12.6k with 11ks remaining
these are the remaining ks:

1069814
1323828
1347432
1529892
1531556
1570340
1588442
1632992
1877488
1878582
1932692

I have a core or 2 that I generally dedicate to checking stuff like this. Generally on any new base that is started, I check primes and k's remaining up to n=2K, 3K, or 5K depending on the base. I'll run Riesel base 15 for k=2-2M and n<=5K and see if there are any problems that I see here.

It is very unusual for k=1M-2M to have so many less k's remaining at a lower search depth than k=2-1M. But it's very possible. You never know with primes.


Gary

[henryzz]

Originally Posted by gd_barnes

I have core or 2 that I generally dedicate to checking stuff like this. Generally on any new base that is started, I check primes and k's remaining up to n=2K, 3K, or 5K depending on the base. I'll run Riesel base 15 for k=2-2M and n<=5K and see if there are any problems that I see here.

It is very unusual for k=1M-2M to have so many less k's remaining at a lower search depth than k=2-1M. But it's very possible. You never know with primes.


Gary

that is probably wise especially as i think both of us are using rather new scripts
i am now up to n=14.4k
i have found a prime for 1878582 since my last report so 10ks remaining

[kar_bon]

i've forgot to attach the results.

i also made a mistake:
henryzz is searching 1M<k<2M and not k<1M like me.
i included all primes for n>50, the remaining pairs upto n=100k and the log-file here.
current n is 16181.
14 k's left

i have to check this with my new script again.

[Flatlander]

I would like to work on Riesel base 27 for a while. Has any work been done on the sieve-riesel-base27-100K-1M.txt file?

I have one core sieving and one core running Phrot from the beginning of the file. The sieve file seems to be running a bit faster but I'll be able to judge it better after a few more hours.
I've already tested to n>101k.
Tests are taking about 930 sec.
Sieving is removing candidates about every 700 sec.

[gd_barnes]

Originally Posted by Flatlander

I would like to work on Riesel base 27 for a while. Has any work been done on the sieve-riesel-base27-100K-1M.txt file?

I have one core sieving and one core running Phrot from the beginning of the file. The sieve file seems to be running a bit faster but I'll be able to judge it better after a few more hours.
I've already tested to n>101k.
Tests are taking about 930 sec.
Sieving is removing candidates about every 700 sec.

To the best of my knowledge, no work has been done on it.

Since the sieve file goes all the way up to n=1M, if you personally plan to only test it to, perhaps n=200K or 1/10th of the file, the file is well more than sieved enough for that range. Keep in mind that it is only removing 1/10th of the candidates in the 100K-200K range vs. the 100K-1M range. So for each n=100K-200K removal, it's removing them at about 1 every 7000 secs. It all depends on how far you plan to take it. If you don't find a prime, of course it helps save sieving time for future testers so any extra sieving of the entire file always helps in that regard.

Good luck with it! It's always fun to prove a base. That last one is almost always the hardest.


Gary

[gd_barnes]

Originally Posted by kar_bon

i've forgot to attach the results.

i also made a mistake:
henryzz is searching 1M<k<2M and not k<1M like me.
i included all primes for n>50, the remaining pairs upto n=100k and the log-file here.
current n is 16181.
14 k's left

i have to check this with my new script again.

I have run a check on all k<2M up to n=5K. Karsten, after removing your k's for primes n>5K, I balance exactly with what you have remaining. I'll post all primes and k's remaining for k<1M on the web pages shortly.

One thing that I'll mention: At any time, you could have removed k's that were divisible by 15 where k / 15 still remained. That would have saved you some testing time.

Henry, you'll need to provide me with a list of primes. Preferred would be all primes for n>500 but if you can at least post primes for n>5K, I can balance what you have remaining. Once you do that, I can update the web pages for k=1M-2M.

I show that there are 28 k's remaining at n=5K for k=1M-2M. This count removes k's divisible by 15 if k / 15 is still remaining.

Edit: I can indeed confirm that there are quite a few less k's remaining at the same testing limit for k=1M-2M vs. k<1M. Very unusual!


Gary

[Flatlander]

Originally Posted by gd_barnes

To the best of my knowledge, no work has been done on it.

Since the sieve file goes all the way up to n=1M, if you personally plan to only test it to, perhaps n=200K or 1/10th of the file, the file is well more than sieved enough for that range. Keep in mind that it is only removing 1/10th of the candidates in the 100K-200K range vs. the 100K-1M range. So for each n=100K-200K removal, it's removing them at about 1 every 7000 secs. It all depends on how far you plan to take it. If you don't find a prime, of course it helps save sieving time for future testers so any extra sieving of the entire file always helps in that regard.

Good luck with it! It's always fun to prove a base. That last one is almost always the hardest.


Gary

Well, looking at the top ten primes, I've dusted off my slide rule and calculated that the probability of me finding a prime within weeks/months is exactly:
"Maybe."
But the probability of someone else finding a prime from this file after me is exactly:
"Probably."
That's why I'm sieving even though I'm unlikely to benefit much/at all.
Also, I can't put more than one core on testing because we are looking for the lowest prime.

(Talking of slide rules, I was given one of them to use for my first year at secondary school, then they took them away the next year and told us to buy calculators! Also, at my first school we were taught in imperial units but when I went to secondary school we switched to metric. So I say things like "5 feet and 3 cm".)

btw Searching to n=200k would be 1/9th of the file.