Stats

[S485122]

Originally Posted by Anonymous

BTW, how would I go about factoring a number with ECM? The only programs that I've found that do ECM are Prime95, and GMP-ECM (I can't figure out how to get Prime95 to ECM anything that's not a Mersenne number; and as for GMP-ECM, which I downloaded a precompiled copy of, it didn't include much in the way of hints on how to use it).

You could try the new style of ECM workunits in Prime95 :

ECM2=k,b,n,c,B1,B2,curves_to_do[,specific_sigma,B2_start]
(New style) Tests numbers of the form k*b^n+c.

Jacob

[ltd]

I see that some of the information on the sieve submission page is a little bit unclear. So i will try to make things a little bit clearer.

The entry "known factors" counts only factors which have an exact match in the transfer table. (k, n and factor must be identical) So if you report several different factors for one k/n pair they will be counted as different factors.

But the main database (which is also used to calculate the stats information) only holds the FIRST reported factor for a k/n pair. So even when the submission page counts a new factor it is still possible that you get no points for it.

For the low factors beeing reported as new there is again a simple answer. The sieve submission looks only at a factor table generated by the submission form itself. I did not reimport all the old factors created before the sieve submission page started. So there are several posibilities to report factors but get no points for them.

You will get points for factors for k/n pairs which are already llr double checked and even if you report a factor for a k where short before a prime was found.

Hope that helps,

Lars

P.S.

I have still to import two of the low factors i know.

[ltd]

One more thing before you ask.

There is a number of manual llr reusults that needs import. They are not lost i only had not enough time to do the work.

Lars

P.S. missing ECM/msieve factors finaly imported

[mdettweiler]

Originally Posted by ltd

I see that some of the information on the sieve submission page is a little bit unclear. So i will try to make things a little bit clearer.

The entry "known factors" counts only factors which have an exact match in the transfer table. (k, n and factor must be identical) So if you report several different factors for one k/n pair they will be counted as different factors.

But the main database (which is also used to calculate the stats information) only holds the FIRST reported factor for a k/n pair. So even when the submission page counts a new factor it is still possible that you get no points for it.

For the low factors beeing reported as new there is again a simple answer. The sieve submission looks only at a factor table generated by the submission form itself. I did not reimport all the old factors created before the sieve submission page started. So there are several posibilities to report factors but get no points for them.

You will get points for factors for k/n pairs which are already llr double checked and even if you report a factor for a k where short before a prime was found.

Hope that helps,

Lars

P.S.

I have still to import two of the low factors i know.

Ah, that makes more sense now. Thanks!

[mdettweiler]

Originally Posted by S485122

You could try the new style of ECM workunits in Prime95 :

ECM2=k,b,n,c,B1,B2,curves_to_do[,specific_sigma,B2_start]
(New style) Tests numbers of the form k*b^n+c.

Jacob

Hmm, that sounds what I'm looking for...however, I can understand what I'm supposed to punch in for k, b, n, and c, but what should I enter for B1, B2 and curves_to_do?

[mdettweiler]

I've noticed that on the Riesel stats page, the "days since last prime" and "PRP tests since last prime" counters haven't been reset, even though this post and this post show that there were two primes found on the Riesel side of the project in quick succession. (I imagine the "number of open k" wasn't updated either, but I can't say for sure since I wasn't watching that particular stat closely.)

Is this an error? Or did both 'primes' turn out to be PRP but not actually prime?

[masser]

Some of the features on the stats page are updated manually by ltd, I believe. I am sure that when he gets a chance to update them, he will.

[mdettweiler]

Originally Posted by masser

Some of the features on the stats page are updated manually by ltd, I believe. I am sure that when he gets a chance to update them, he will.

Ah, I see now. Thanks!

Edit: Duh, I should have just looked earlier in the thread.

Originally Posted by axn1

Team changes, primes found, etc are manually updated by Lars -- so depends on his availability.

[Joe O]

Originally Posted by Anonymous

Hmm, that sounds what I'm looking for...however, I can understand what I'm supposed to punch in for k, b, n, and c, but what should I enter for B1, B2 and curves_to_do?

From the GMP-ECM readme:

The ECM method is a probabilistic method, and can be viewed in some sense
as a generalization of the P-1 and P+1 method, where we only require that
P+t is smooth, with t random of order P^(1/2). The optimal B1 and B2 bounds
have to be chosen according to the (usually unknown) size of P. The following
table gives a set of near-to-optimal B1 and B2 pairs, with the corresponding
expected number of curves to find a factor of given size (column "-power 1"
does not take into account the extra factors found by Brent-Suyama's exten-
sion, whereas column "default poly" takes them into account, with the poly-
nomial used by default: D(n) means Dickson's polynomial of degree n):

       digits D  optimal B1   default B2           expected curves
                                                       N(B1,B2,D)
                                              -power 1         default poly
          20       11e3         1.9e6             74               74 [x^1]
          25        5e4         1.3e7            221              214 [x^2]
          30       25e4         1.3e8            453              430 [D(3)]
          35        1e6         1.0e9            984              904 [D(6)]
          40        3e6         5.7e9           2541             2350 [D(6)]
          45       11e6        3.5e10           4949             4480 [D(12)]
          50       43e6        2.4e11           8266             7553 [D(12)]
          55       11e7        7.8e11          20158            17769 [D(30)]
          60       26e7        3.2e12          47173            42017 [D(30)]
          65       85e7        1.6e13          77666            69408 [D(30)]

          Table 1: optimal B1 and expected number of curves to find a
          factor of D digits with GMP-ECM.

After performing the expected number of curves from Table 1, the
probability that a factor of D digits was missed is exp(-1), i.e.
about 37%. After twice the expected number of curves, it is exp(-2),
i.e. about 14%, and so on.

Example: after performing 8266 curves with B1=43e6 and B2=2.4e11
(or 7553 curves with -dickson 12), the probability to miss a 50-digit
factor is about 37%.

[ltd]

Originally Posted by Anonymous

I've noticed that on the Riesel stats page, the "days since last prime" and "PRP tests since last prime" counters haven't been reset, even though this post and this post show that there were two primes found on the Riesel side of the project in quick succession. (I imagine the "number of open k" wasn't updated either, but I can't say for sure since I wasn't watching that particular stat closely.)

Is this an error? Or did both 'primes' turn out to be PRP but not actually prime?

There were two reasons why you did not see the correct days since last prime.

First for k=90082 i had not updated the data.
Second for k=192908 i had updated the data but i entered the wrong date: 0207-10-06

So this was a very very very old prime.

Lars

[mdettweiler]

Originally Posted by Joe O

From the GMP-ECM readme:

The ECM method is a probabilistic method, and can be viewed in some sense
as a generalization of the P-1 and P+1 method, where we only require that
P+t is smooth, with t random of order P^(1/2). The optimal B1 and B2 bounds
have to be chosen according to the (usually unknown) size of P. The following
table gives a set of near-to-optimal B1 and B2 pairs, with the corresponding
expected number of curves to find a factor of given size (column "-power 1"
does not take into account the extra factors found by Brent-Suyama's exten-
sion, whereas column "default poly" takes them into account, with the poly-
nomial used by default: D(n) means Dickson's polynomial of degree n):
 
       digits D  optimal B1   default B2           expected curves
                                                       N(B1,B2,D)
                                              -power 1         default poly
          20       11e3         1.9e6             74               74 [x^1]
          25        5e4         1.3e7            221              214 [x^2]
          30       25e4         1.3e8            453              430 [D(3)]
          35        1e6         1.0e9            984              904 [D(6)]
          40        3e6         5.7e9           2541             2350 [D(6)]
          45       11e6        3.5e10           4949             4480 [D(12)]
          50       43e6        2.4e11           8266             7553 [D(12)]
          55       11e7        7.8e11          20158            17769 [D(30)]
          60       26e7        3.2e12          47173            42017 [D(30)]
          65       85e7        1.6e13          77666            69408 [D(30)]
 
          Table 1: optimal B1 and expected number of curves to find a
          factor of D digits with GMP-ECM.
 
After performing the expected number of curves from Table 1, the
probability that a factor of D digits was missed is exp(-1), i.e.
about 37%. After twice the expected number of curves, it is exp(-2),
i.e. about 14%, and so on.
 
Example: after performing 8266 curves with B1=43e6 and B2=2.4e11
(or 7553 curves with -dickson 12), the probability to miss a 50-digit
factor is about 37%.

I'm sorry, but it's all Greek to me. I'm wondering, though, are B1 and B2 roughly the same for ECM as they are for P-1? If so, then I'll just use the values that I'm already using for P-1.