[QUOTE=Mini-Geek;230896]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.[/QUOTE]

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.

[QUOTE=kar_bon;230900]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.[/QUOTE]

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).

[QUOTE=Mini-Geek;230908]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).[/QUOTE]

What an odd choice, testing more bases for larger numbers.

[QUOTE=CRGreathouse;230914]What an odd choice, testing more bases for larger numbers.[/QUOTE]

It "proves" the numbers (I'm guessing, under RH), not just PRP tests them.

[QUOTE=axn;230951]It "proves" the numbers (I'm guessing, under RH), not just PRP tests them.[/QUOTE]

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 [url=http://oeis.org/classic/A089105]A089105[/url]. But even if only the primes were included, that's 700,709 tests (and I'm pretty sure A089105 is a superset of A000040).

Table 10^n+1 updatet till n=500 from Alfred Reich / Kamada`s Sites.

[QUOTE=CRGreathouse;230961]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. [/QUOTE]

2 log^2 x by a result from Eric Bach

[QUOTE=R.D. Silverman;231089]2 log^2 x by a result from Eric Bach[/QUOTE]

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.

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?

[QUOTE=Syd;230872]I made a small change so you dont need to "POST" the factors anymore, simple "GET" will do now, too.[/QUOTE]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...

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.