what happens next?
 

"We have 1556088 untested values left under n=50 Million"


One day when all these untested values are done, what happens?
Does the project end? Or does it restart sieving and PRP'ing for some higher value like n=100 million? (for example)

We haven't thought that far. It will take atleast 10 years to get there, if we had all the computers from GIMPS.

This is the short answer. Though we are hoping we will find all the primes (12 left to be found) soon and the project would end by 50 million.

We are open to suggestions, if you have any.

Citrix

edit: If the project is incomplete at that time and we have enough computing power, I personally would like to continue to a higher value.

10 years?? :cry:
Oh well... plenty of work for the future then.

By the way... what's the relation between these untested values and the candidates in the prp range reservation thread? There are so few candidates comparing to the untested values...

[QUOTE=NeoGen]10 years?? :cry:
Oh well... plenty of work for the future then.

By the way... what's the relation between these untested values and the candidates in the prp range reservation thread? There are so few candidates comparing to the untested values...[/QUOTE]

10 years is an estimate. We could be done by tommorow, if we find all the primes, but the probability of that is low.

All untested numbers need to be PRPed. The numbers in the PRP reservation thread are the numbers most likely to produce a prime and the numbers that are easiest to PRP right now.

Citrix

I am rather new to this prime hunting but I would like to go after 10 million digit prime.
It will take time..... if I am correct any PRP candidate will take 3 month to 1 year depending on today computerpower you have.
Starting sieve some 10 million digit range wery deep would be fine by me.
Maybe it is boring for some one not having any results for looooong time.:sleep:

if you want to be the one who discovers the 10 million digit prime, the best would be to refer to GIMPS. There are some suggestions at Seventeenorbust from time to time to open a "largest Prime" queue, but it never went very far.
The main problem is that these tests are quite likely to be wasted, as we might find a prime for that very k before.
I prefactored some k,n-pairs fairly deep; but I am reluctant to encourage anybody to test these as they wouldn't be assigned by the server, so one wouldn't get any credit, and the residue submission would be manual, giving the admins even more work to do.
If you are really interested, you will easily find the thread at sob.
H.

As always, you can do anything you want at PSP.

If someone wants to do a 10 Million digit PRP test, they are most welcomed to do so (get in touch with ltd). But as hhh pointed out, it is not the best thing to do right now.

Other than that I had an idea. If we take the k with the least number of candidates and concentrated our effort on that k, we might be able to take it to 10M+ digits and find a prime. Though the probability of finding a prime is low, and this will be like a gamble. But if we are lucky we would get the $100K.

Citrix

For k=156511 there are ~54000 numbers left. We could do some p-1, ecm , P+1 and get rid of more numbers. Then do PRP etc.

Citrix

There is an "low n ECM factoring" thread, and has only 16 numbers there. If it helps to eliminate more of those untested values we could jump on them and get them quickly done.
But alas, there isn't a tutorial on that thread. I don't have a clue on how to do it, or what program to use for the job... lol

[QUOTE=NeoGen]There is an "low n ECM factoring" thread, and has only 16 numbers there. If it helps to eliminate more of those untested values we could jump on them and get them quickly done.
But alas, there isn't a tutorial on that thread. I don't have a clue on how to do it, or what program to use for the job... lol[/QUOTE]

It doesn't really help the project, it is just for fun. That is why there is no tutorial.

Citrix

I can see the problem with 10Million digit. I will jump on the train with you whatever decision will be made.
If you have some wery slow PC´s (like I have) that can´t be to any use other than multisieving (NewPGen) then it could be som fun multisieving big numbers whatsoewer the maingoal is.
Just an idea.

Sorry for bumping this old thread again but something crossed my mind.

The estimated time to complete, that was said to be around 10 years, is it counting with double checks already? Or will that add up to 20 years instead?

Really it depends on number of primes, number of users etc. The project might be over in 5 years. It is impossible to give any estimates.

Though if we take the same time as SOB, the project should be over in the next 6-7years. (Assuming we soon have as many users as SOB)

Citrix

My doubts were more about the lenght of work in double checking.
Is it necessary to double check every candidate? Or maybe only retest some values who comeback with strange results?
If so, that will effectively double the "theorical maximum time" the project would take, right? Or is the process of double checking faster?

In principle all residues must be double checked as there are only a few cases where you can really see that a residue is wrong.
But due to the fact that we continue sieving all the time we reduce the number of double checks.
For example for the k values where we have no prime found there are 5782 n values where we have done a first PRP test but after that there was a factor found so no need to do a PRP double check anymore.

This shows again the importance of sieving as at the moment (thanks to Brucifer but also all the other sievers) we have removed ~1% of the open tests by sieving within 15 days!!!:bow: :bow:
These numbers will never see a PRP test.

Lars

Edit:
Forgot to answer the last question: A double check takes the same time as the first PRP check.(But lets hope there are new faster client in the future)

[QUOTE=NeoGen]10 years?? :cry:
Oh well... plenty of work for the future then.
QUOTE]


Neogen, just to explain things better. We are currenty finding 1000 factors daily (Thanks to Brucifier and others). If we could maintain this rate of factors it would take us 5 years to reach 50m. As we sieve larger and larger ranges, it gets difficult to find factors and this rate would drop. So if we could match the rate drop by adding new machines, the project would reach 50M in 5 years. If we could double our effort then 2.5 Years. This is assuming we are not doing PRP.
If we find a prime with PRP it reduces about 6 months of work at a time. Also primes are difficult to predict. So the PRP ascpect is difficult to predict.

But if we can keep getting new users as the project gets more and more difficult and we maintain our rate of factors we should reach 50M in less than 5 years.

I hope that answers your question.

Citrix

I'm getting more of the "big picture" everyday! Thanks guys!

And that time might even be shortened as the users will (hopefully) get faster, more powerful machines during the years. :)

We would get an exponetial boost as soon as SOB joins forces with us. I hope that time comes soon.( ie we are able to catch up with them really fast).

Citrix

By the way... I read in places that the sieving part is only good up until a certain point, and beyond that it is better to just make the primality tests than sieving because the factors found are very few compared to the effort spent in sieving them.

How do we know if we reached that point?

[QUOTE=NeoGen]By the way... I read in places that the sieving part is only good up until a certain point, and beyond that it is better to just make the primality tests than sieving because the factors found are very few compared to the effort spent in sieving them.

How do we know if we reached that point?[/QUOTE]

Lets say it takes 1 week to do a primality test. So if we sieve for 1 week on the same computer and do not find a factor then we have reached this point. In reality we will never reach this point. (Though there is such a theoretical point, I expect it to be around 10^35 (will take decades to sieve upto there))


Citrix

I think it's not that easy to explain, because the effort-increasing factor (pun not intended) is different.

For primalty tests, effort increases with bigger n values.
For sieving, factor density decreases (and thus effort per factor increases ) with higher sieving depth.

Furthermore, primalty tests and sieving affect each other when it comes to usefulness. There is no sense in sieving deep when you don't do a lot of primalty testing, because those early primalty tests are not that hard (and you have to consider easier sieving due to found primes...).
On the other hand, a lot of primalty testing without thorough sieving is inefficient as well, especially when the n values increase. This is because the n value does not affect sieving speed (the size of the n range does).

You have to keep a good balance between primalty testing and sieving to get the most out of it. One could say that you have to sieve deeper the higher n values you test. But as it most efficient to sieve large ranges, the lower bound of the n sieve range can be minimal.