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2010-09-22, 14:44   #903
kar_bon

Mar 2006
Germany

2×1,433 Posts

Quote:
 Originally Posted by Mini-Geek Is there a faster implementation of the method the applet uses? I'd expect an efficient native implementation to run much faster than an applet.
As I know the applet uses the APRT-CLE = Adleman-Pomerance-Rumely Test with Cohen-Lenstra Extension and PRIMO uses the ECPP = Elliptic Curve Prime Proving Test.

2010-09-22, 15:09   #904
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

102538 Posts

Quote:
 Originally Posted by kar_bon As I know the applet uses the APRT-CLE = Adleman-Pomerance-Rumely Test with Cohen-Lenstra Extension and PRIMO uses the ECPP = Elliptic Curve Prime Proving Test.
For this number the applet used the "Rabin probabilistic prime check routine" (the ProbabilisticPrimeTest method in the code), where it does a PRP test for N.bitlength()/2 bases (in this case, 1659 bases).

2010-09-22, 15:46   #905
CRGreathouse

Aug 2006

3·1,987 Posts

Quote:
 Originally Posted by Mini-Geek For this number the applet used the "Rabin probabilistic prime check routine" (the ProbabilisticPrimeTest method in the code), where it does a PRP test for N.bitlength()/2 bases (in this case, 1659 bases).
What an odd choice, testing more bases for larger numbers.

2010-09-22, 18:30   #906
axn

Jun 2003

2·32·269 Posts

Quote:
 Originally Posted by CRGreathouse What an odd choice, testing more bases for larger numbers.
It "proves" the numbers (I'm guessing, under RH), not just PRP tests them.

2010-09-22, 19:19   #907
CRGreathouse

Aug 2006

596110 Posts

Quote:
 Originally Posted by axn It "proves" the numbers (I'm guessing, under RH), not just PRP tests them.
That's not nearly enough bases for Miller's test. He proved that 70 log^2 x bases suffice under the ERH; I seem to remember a modern version lowering the 70 to 2 or 3. But even in the most generous interpretation that would take 10,582,599 tests, not 1659.

Edit: Actually, not all bases up to 70 log^2 x need be tested -- only those in A089105. But even if only the primes were included, that's 700,709 tests (and I'm pretty sure A089105 is a superset of A000040).

Last fiddled with by CRGreathouse on 2010-09-22 at 19:32

 2010-09-23, 09:59 #908 Andi_HB     Mar 2007 Germany 23·3·11 Posts Table 10^n+1 updatet till n=500 from Alfred Reich / Kamada`s Sites.
2010-09-23, 12:08   #909
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 Originally Posted by CRGreathouse That's not nearly enough bases for Miller's test. He proved that 70 log^2 x bases suffice under the ERH; I seem to remember a modern version lowering the 70 to 2 or 3.
2 log^2 x by a result from Eric Bach

2010-09-23, 13:53   #910
CRGreathouse

Aug 2006

596110 Posts

Quote:
 Originally Posted by R.D. Silverman 2 log^2 x by a result from Eric Bach
Yes, that's the result I was thinking of. He proved an auxiliary result with constant 3 and that result with constant 2; now it comes back.

Last fiddled with by CRGreathouse on 2010-09-23 at 13:53

 2010-09-24, 08:36 #911 schickel     "Frank <^>" Dec 2004 CDP Janesville 2·1,061 Posts What kind of connection do you have the DB on? If I wanted to automate the downloading of aliquot sequences to check on progress, do I need to worry about using up too much bandwidth or running too many connections to the DB too quickly?
2010-09-24, 08:39   #912
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2×1,061 Posts

Quote:
 Originally Posted by Syd I made a small change so you dont need to "POST" the factors anymore, simple "GET" will do now, too.
Can you give me an example of a GET string to upload a factor? I'm sure it's obvious, but I can't get it to work...

 2010-09-24, 14:44 #913 rekcahx   Oct 2009 Oulu, Finland 1E16 Posts If I know that 35735836391277091 is a factor of (10^3434*15+10^6869-1)/69 , what is correct GET string for that? Yes, I can upload factors by hand using normal web browser, but it requires too much manual work.

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