progress of second pass tests

[RicovanderPol]

1: progress in second pass tests

everybody now knows already that we are doing second pass test, because we were to far behind (??). May be it would be an good idea then to show were we are in doing second pass tests. At the project status page You can see that the boundary for first pass test has arrived approximatly the 10 milion. why don't we show such a boundry for second pass tests? it would then be possible to monitor the progress made.

2: because we are now doing second pass tests, all people sieving are able to sieve more. which is in the end benificiary to all the people who factor. but because we are arriving at n's above 10 milion, there should maybe spend more time at managing the equilibirium between those who sieve and those who factor. if to many people factor, then the sieving will not clear out enough factors. who can explain to me where the equilibrium lies?


3: why have some k-numbers more pending tests then other k's? is it only due to sieving??

good luck hunters, we have an excellent pray!!

[vjs]

Well couple clarifications...

Sieve I think you have that 100%.

I think you have factoring and prp confused.

Prp is where we test particular k/n pairs for primality (i.e. firstpass n=10m and secondpass n~3M) ... what most of the people do.

Factoring is like sieving where we are checking for factors just before a number is prp'ed. Doesn't find primes but it will find factors for non-prime numbers. One in every 60 or so factoring tests results in a factor and that k/n pair doesn't have to be tested. Also the time it take to factor 60 tests is about the same time it takes to prp test one k/n pair so it's about a wash in time... P-1 factoring vs PRP.

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Now on your points and questions,

Yes, there is actually a page that shows where each prp level is at...

http://www.seventeenorbust.com/secret <-- It's not so secret anymore....

dropped-tests 288 7169117 9997858 89 +4603613
error-fix 416 5163711 7807623 0 +45739
first-pass 0 n/a n/a 112 +∞
garbage 1212 5166543 7594947 0 +67112
global 0 n/a n/a 0 n/a
largest-prime 12976 13467910 13999982 0 n/a
missing-test 0 n/a n/a 0 n/a
(not queued) n/a n/a n/a 4 n/a
residue-recovery 0 n/a n/a 0 n/a
second-pass 48092 2910281 4999946 1446 +72235

If you look at secondpass it's easy to see that that level is currently at n=2910281, and there are 48092 tests between now and n=4999946.

First pass is at 0, this basically means no new tests are being handed out, this que will eventually fill with n>10M. However there have been 112 test handed back today, this means that 112 test n<10M were completed.

Dropped test, these are the tests that people have abandon or taken longer than 90 days to complete. They are currently being handed out now b/c they are handed out before secondpass tests are.

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O.K. on sieving, sieving will for a very long time be more efficient than P-1 or prp. Tis is becuase sieving finds factors for tests in less time that in take to test them. We just can't predict with k/n will be factored. SO it may take a long time before that factor is useful. But at one point it will become useful.

A rough estimation for when sieving will nolonger be benifital. When the time it takes to find one factor is longer than time it take to test a k/n with n=15M twice. (And this is probably an underestimate by quite a bit)

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Factoring will never clear out enough factors to make sieve ineffective. The advantage is that sieve checks the whole range n<50M, where P-1 only check a small window that we need now. They go hand in hand. The trick is to not let P-1 get to far ahead, Too far ahead IMHO would be n=11m. In addition if P-1 were to reach n=11m sieve would still find factors between 10M<n<11m b/c sieve will find factors that P-1 won't.

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Some k's just have more test in a given n-range. It has to due with the denisty of the k. It's just the way it is... Sieving reduces this number by an equal percentage.

If you find 10 factors for 2 k's, k1 and k2, and there is four times as k2 than k1, Chances are you would have found two factors for k1 and 8 factors for k2.

Hope this answers some of your questions, but I'm sure it's just created others.


(Sorry I wrote this very quickly and didn't edit)