# Thread: Which K will be the next to yield a prime?

1. Yeah, because cEMs are wrong. We know we need to fix that.

2. To give you some perspective, in GIMPS doublechecks (or secondpass) has been approximately half in size of first time test for several years now. Since your first pass is at 4M, I think kugano is right in that second-pass should be closer to 4M.

3. Edit for garo,

First pass = 8M

4. What we really need is much higher confidence that first pass tests are correct.

The closer that confidence level is to 100%, the less we should care about double checks. I've made various suggestions, but ultimately I suspect there are much better ideas out there.

All that said, it would be nice to see the DC queue moving forward at the something nearer to the same rate as the first test queue.

5. Well a quick calculation back of the envelope style

Joh14vers6 stated the following times

First pass is 2080 blocks @ 0:01:38/block = 3397 minutes (2.35 days)
Second pass is 9 blocks @ 0:09:38/block = 77.0 minutes (18.6 tests per day)

3397 / 77 = 44.1

So basically from a time perspective one can do 1 normal test or ~44 normal tests.

This translate into an 2.27% error rate...

If our error rate is more than 2.27% we must do more second-pass, if it's less then we are ahead with second-pass.

Of course this only hold true if the following premises are correct...

The error rate for a prime k/n is the same as a non-prime k/n.
(this was stated to be true by kunago recently, he also had a very good explaination of why).

The probablity of any n being prime is the same regardless of n value.
(This was also stated to be true, not sure if this is correct however)
(Update: probablity of k/n prime decreases with increasing n)

The second pass test is always 100% correct
(this is easy because it can be verified against the first pass residue)

The error rate of the client is the same for all n.
(This last one is a tough sell, it's more probable that as the n value increases so does the error rate. If this is the case we simply multiply the time it takes to do a first pass test by some factor related to the error rate... and bring the DC level to higher n accordingly).

Note:
The above analogy 1:44 tests, 2.27% error rate, is very simplistic and doesn't consider factors such as error rates increasing with n, wasted effort, if we ever test all n less than the prime n, prime density, errors on first pass, ability of finding error submitting computers, etc. The majority of these issues however lead to a increase in the resources we should spend on double checks)

Actual estimates are probably closer to "time required for first pass test" should equal "time required to do 20 second pass tests"

6. Mike I agree totally with your suggestions, I'd actually say make a new user or new PC complete 10 double checks in a row first.

Problem being a first time computer may be "cold" and take longer than 30 minutes at 100% CPU before it starts producing errors. Heat builds in the heatsink, case, etc, etc, etc...

I really think the best possibile solution is to do the 100 test injection method kugano did just recently while raising the double check level with respect to first pass. 100 per day is probably too many but ~20 daily would be perfect. They also shouldn't nessarily be dc's just below first pass of course.

What this would do is randomly check both users machines.

Example first pass is currently at 8m, by injecting a recently completed 7.2M test and checking those residues for a match, tests two "probably currently active" machines for errors. Something to consider.

Of course you'd weight the tests, 1 @ 7m, 2 @ 6M, ... 10 @ 2M, etc...

The advantage of this method is if we get an error or non-matching test, we could immediately submit tests from both those computers the next day... find the offender, re-test all of their k/n's, and only assign that user double checks until the computer behaves correctly.

Problem is my method is easier said then done and would take alot on the server side.
Pull random tests, inject, verify Cross check, IP lookup, flag IP, pull IP tests, tripple check injection, verify, deflag one IP, reassign ofender, flag/deflag, ... sounds like a nightmare and alot of overhead, but it could be done.

7. Originally posted by vjs
Well a quick calculation back of the envelope style

Joh14vers6 stated the following times

First pass is 2080 blocks @ 0:01:38/block = 3397 minutes (2.35 days)
Second pass is 9 blocks @ 0:09:38/block = 77.0 minutes (18.6 tests per day)

3397 / 77 = 44.1

So basically from a time perspective one can do 1 normal test or ~44 normal tests.

This translate into an 2.27% error rate...

If our error rate is more than 2.27% we must do more second-pass, if it's less then we are ahead with second-pass.

Of course this only hold true if the following premises are correct...

The time of the first pass test block is calculated, while I did not have that particulair n.

The fasttest block from test with n=7902500 (1975 blocks) is 0:01:42 on this machine.

First pass is 1975 blocks @ 0:01:42/block = 3357.5 minutes (2.33 days)
Second pass is 9 blocks @ 0:09:38/block = 86.7 minutes (16.6 tests per day)
(Actually it was finished in 86.21667 minutes, remember the last block of a test is shorter than a complete block)
3357.5 / 86.7 = 38.7 (If you still take that calculated one than it is 39.2)

This translate into an 2.58% error rate... (calculatedversion 2.55%)

Some corrections.

8. We can doublecheck with normal accounts for quite a while now, but DC did not go up that much at least I expected. If it's because it seems to be slower and because of the lack of credits earned by DC, it would be enough to make a new list in the statistics with 'Tests finished'.
Even with only one computer it would be possible to have good results. And if the runaway client people decide to invest some power there in order to have good positions there, the better it is.
Anyway, the best way to close the credit gap between first pass and DC is to do - DC.

9. Well I actually say that the DC's are still riseing but slowly...

Alot of people have those old P3-500 boxes still trying to finish their old tests, ONce they are done those they will probably switch to second-pass testing.

As for scoring, yes there is less points current;y for second pass but that will change with the new client. Besides what is a 20% difference is scoreing on a older machine when you have a couple P4's as well.

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