Minimum size of next prime

[kfx]

When will this number go up?, can somebody please explain how this n"works"?

[hc_grove]

It will go up as soon as the test of 21181*2^2115523+1 finishes.

The number of digits in k*2^n is approximately log(k)+n*log(2) or in our cases 0.3*n+5 (or 4 for the smaller k's).

Judging from the graphs of the remaining tests, the second smallest number being tested at the moment is 24737*2^2325702+1 which is a number with a little over 700000 digits.

As others pointed out when Louie announced the addition of this number to the stats page, it's held back by the slowest machines, and it would be a lot more interesting to known the number of digits in the largest number tested, which is well beyond 950000 at the moment.

Edit: The largest completed test is 22699*2^3293614+1, a number with 991481 digits. (And some spelling fixed too)

.Henrik

[OberonBob]

yeah, what's with that 21181*2^2115523+1? It has been stuck there for at least a month. Man, it really annoys me, almost everyday I check, and it's still there. It must be like a <200 MHz computer checking that n. In the long run, of course it doesn't really matter. but.......

[Lagardo]

Of course it might be stuck there because it reported a prime and all hands are busy rechecking and doublechecking and trying to get in contact with the owner of the machine and such.

It's possibe ...

[OberonBob]

don't get us all excited.

[Nuri]

Infact, a n=2.1m test should have roughly 40 blocks. That means, with the current settings of 10 days per block (only), a user with an intention to hold the benchmark (or someone devoting his resources to sieving or anything else) can easily hold a test of that size for up to 400 days (by crunching and submitting 1 block every 10 days).

BTW, it'd be really great if it was because of a prime, but I guess that's not the case.

[smh]

Yes, exponents can get 'stuck' for a long time. As long as you do 1 block in 10 days the test will stay assigned to you. Theoratically it can take a couple of years before that exponent is completed.

I have some mixed feelings with this. It doesn't really matter how long it takes to test a number, as long as it gets tested. Every cpu that is helping is one. OTOH, What if we miss a prime? I still think an expiration time of 10 days is quite long. Even on a slow computer a single block can be done in a couple of hours.

Is it somehow possible to make a list available of which eponents are assigned, to whom, when and when the last communication was? A page a la the GIMPS status page?

[jjjjL]

i guess the max size under test is cool too since that will grow all the time. the min size is a little static.

the reason i don't do just the max size is because it's basically a number that says "this is a number larger than any prime we're likely to find today"

anyway, i added the max size to the stats page. almost at 1 million

-Louie

[Nuri]

Thanks Louie,

That's one of the stats features I'd love to see on the stats page. Thinking that it was just 210,000 four months ago when I first decided to join the project, it's great that we're almost at 1 million digits now. And of course, it'd be cool to watch it go up and up as days go by.

On the deadline issue, I also have mixed feelings like smh. It's hard to decide. Two alternatives come to my mind.

1- May be, in addition to the 10 day per block deadline, a second deadline for completing tests should be introduced.

Sometimes people go for one week holidays etc. (which adds up to 2+5+2=9 days away from home), so 10 days is fair for block deadlines. But, not returning a n=3million test within, say, 3 (or 6, I dunno) months is not normal.

2-Or, perhaps, Louie can manually re-release the tests that are holding the benchmarks.

This way, minimum size of next prime for the project will not be staying there for weeks (which I felt like years have passed so far for the famous 636840 digits figure). Of course, the first user holding the benchmark should still be credited for his work, and would be allowed to finish his test (which will turn out to be a free double check). It'd be an interesting case if that specific number turns out to be a prime, and I guess, then both users should have their names on the primes pages.

Just a couple of thoughts.

Anyway, happy crunching everyone.

[Mystwalker]

Originally posted by Lagardo
Of course it might be stuck there because it reported a prime and all hands are busy rechecking and doublechecking and trying to get in contact with the owner of the machine and such.

It's possibe ...

At least Louie didn't decline it.

[Moo_the_cow]

I don't know what is going on with that low n number,
but if you want, I'll do a prp test on it and post the residue
here. It'll only take 3-4 days......

Also, I just realized that
quote:
_________________________________________________
It will go up as soon as the test of 21181*2^2115523+1 finishes.
__________________________________________________

Actually, it's the test of 21181*2^2115524 that needs to
be finished. 21181*2^2115523 divides by 3 or some other
low p.

[priwo]

I think I would like nuris idea of a second deadline for finishing a complete test within 3 month - if this is possible.

[smh]

Originally posted by Nuri
Sometimes people go for one week holidays etc. (which adds up to 2+5+2=9 days away from home), so 10 days is fair for block deadlines. But, not returning a n=3million test within, say, 3 (or 6, I dunno) months is not normal.

During summer holidays many people take a 2 - 4 week vacation so should the block expiration be set to 1 month? I liked the old 5 day expiration time. Maybe give the client an option to extend a reservation during a vacation (lets say, max 1 month, once a test).

Or give the client an option to release a test, or not ask for a new test after the current one finishes.

[smh]

Originally posted by jjjjL
i guess the max size under test is cool too since that will grow all the time. the min size is a little static.

the reason i don't do just the max size is because it's basically a number that says "this is a number larger than any prime we're likely to find today"

anyway, i added the max size to the stats page. almost at 1 million

-Louie

Maybe you should call it a bit different, like 'Largest test assigned' or something like that

[eatmadustch]

it's gone up now
it's now 700111 digits!

[OberonBob]

:shocked:

[jefmwols]

Here's the output I got when testing this number.

21181*2^2115523 + 1 factor : 3

[Thommy3]

n Upper Bound: The largest value of n for which it is known that no primes exist for multipliers less than n. In other words, all multipliers less than or equal to n have been tested either by Seventeen or Bust or by other members of the Sierpinski search community.

So the smallest test was 21181*2^2115524 + 1 while the Upper bound was: 2115523 for k=21181

...i think

[Lagardo]

Wait a second there -- it's 10 days per BLOCK? I thought it was for the whole test.

My box does a block in 4 minutes. If I scale by GHz only (which isn't quite right, but as an indication) that would mean a 8Mhz PC could do a block in 10 days.

Now I agree that every computer helps, but by the time a 8Mhz is finished testing one number, we'll have expended millenia of P90 time on the higher n for the same k which will be completely wasted if the n that took a year to compute turns out actually to be prime.

In other words: the longer the smallest currently tested n for a given k takes, the higher the preobability that we're wasting computing power on the higher n.

How about some automated system where any user can request a given k/n pair and run it themselves? (Within boundaries, e.g. only if the same pair is checked out by no more than two or three other people or hasn't returned a result yet or such).

While I'm phantasizing about such a system, how about letting users choose which k value to work on? I imagine little races between what would amount to subteams that would form around the various k, "damn, those 21181-guys have gained on us in their upper bound, lets recruit some more people to help keep our 27653 the k with the highest upper boud n". That kind of thing. Sounds like fun to me...

[Mystwalker]

Guess it is fun, yes. But it's not that easy to implement.
One can check chosen k/n pairs by entering the according values into the registry (or the .conf file). Downside: you won't get credited for it, as the server did not give this test to you. You can look into the log file to view the result. Of course, you have to disable block reporting.

The time limit of 10 days were chosen to give ppl a chance who are on vacation for a week. It would be an option to change this setting so that this 10 days limit can't be taken every block - either manually or automatically. Something like "Time limit is 2 days, but every 50 blocks, one can extend one time limit to 10 days." Again, it takes some effort to implement it. But I guess it's easier than hand-picked k/n-pairs...

[wirthi]

Originally posted by Lagardo
Wait a second there -- it's 10 days per BLOCK? I thought it was for the whole test.

To keep the test, you have to "report" it at least every 10 days to the server. Since AFAIK the only way to "report" a test is to send in a block, this limitation could be interpreted as "10 days time per block".

[Marco_N]

Originally posted by wirthi
To keep the test, you have to "report" it at least every 10 days to the server. Since AFAIK the only way to "report" a test is to send in a block, this limitation could be interpreted as "10 days time per block".

That's where the discussion is focussing on. For 50 block test, it may take over 50*10/365.25 ~ 1.3 years to complete. On my machine this takes half a day.

The problem, as stated earlier in this thread, is that valuable processing capability is concurrently being utilized for the same k value. The 'loss' amounts to the amount of processing capability (P90 years) spent on other values of n from the moment a 'prime-n' is being assigned to the moment this 'prime-n' is being reported. To minimize this 'loss', the total time spent on a value for n for a specific k should in my view be kept within reasonable limits.

I therefore would prefer a 1 month limit per n being implemented; this will give people enough time for vacation or business trips.

My $0.02
- Marco

PS I hope that when a prime for a k is reported, during verification no other work for that k is being distributed...

[hc_grove]

Now it dropped to 645820 digits? What happened? :shocked: It doesn't match the upperbounds for any k?

.Henrik

[Joe O]

Take a look at the Current Test Window Min n .

[hc_grove]

Originally posted by Joe O
Take a look at the Current Test Window Min n .

That doesn't explain the drop. The low n's being tested are double checks and should not affect the 'minimum size of next prime', and if they did it should only be around 110000 digits.

.Henrik

[Mystwalker]

There seem to be checks outside of the current test window from time to time. This was well visible when k=27653 was at 3M. The amount of tests currently handed out fluctuated every now and then...

[amcdonald]

I'd also prefer to be able to concentrate crunching to a user-defined K, but there's really no point other than to make it a little more interesting. Right now I'm really satisfied with the project, thanks to mathguy and the TPR website. Now if only we could find those sneaky little numbers... If they are so big it should be easy to find them! I'm gonna look in my psu today, I think they're in either the northbridge or the platter.

[jjjjL]

the incorrect stat was a glitch caused by some database testing i'm doing. it's "fixed" now.

-Louie

[MikeH]

It's nice to see that the minimum size of the next prime has broken another psychological barrier.

At 898895 digits, this would now be the 4th largest prime number. It would seem that 'garbage' is doing a good job.

And not far to go to get to 3rd. All those 'n upper bounds' need to be above 3.022M.

Of course all this assumes that secret and supersecret won't find anything.

[jjjjL]

Yes, garbage is doing it's job.

There is only 1 test for n < 3M. It will be done in about a day.

There are two test for n < 3.022M so unless one of those two is prime, the next prime will be larger than the current 3rd.

I'd say the next barrier would be where the primes become over 1 million digits. There are a total of 19 tests less than that. Assuming a few of those get finished before garbage gets there, the lower limit should raise above 1M by the end of June.

The other intersting bound I noticed is that there are less than 200 secret tests until all numbers n < 500,000 are tested (by SB). So in about a week, we'll have the bound broken too.

-Louie

[Nuri]

I was curious about two things, "are the significantly lagging tests ever being finished", and "do we have data for the error rate for tests larger than those of supersecret".

So, four questions...

How many of the candidates for the 12 tests completed by garbage were later returned by the users that the candidate was originally assigned to?

And how many of those candidates had matching residues?


How many candidates are there for n>1m (or n>2m?) that were tested twice? (i.e. when the test was reassigned by the server because of 10 days inactivity, but the original user still returned the result later on)

And how many of those candidates had matching residues?