Trial Factoring - Factor Confirmation?

[butera]

Quick question on something I've thought about for a while.

When I report trial factoring results to PrimeNet, it's either no factor (which doesn't affect anything since more TF and a primality test are in that exponent's future), or a found factor.

Does PrimeNet do any verification that these factors are indeed genuine? I could imagine a situation where a copy/paste into the manual results could lead to an incorrect factor or a correct factor applied to the wrong exponent.

[kruoli]

Short answer:

Yes, since a factor can be checked quite quickly. In fact, one does not need to execute a large division. You (and the server) can do something like what's described in http://www.mersenne.org/various/math...rial_factoring.

[ixfd64]

Yes, the PrimeNet server always verifies the factor before adding it to the database. So you don't need to worry about submitting a bad factor.

[butera]

Originally Posted by ixfd64

Yes, the PrimeNet server always verifies the factor before adding it to the database. So you don't need to worry about submitting a bad factor.

That answers my question, thanks!

[tuckerkao]

Here was a factor I found back several months ago, I submitted to M103,373,321 at first, the server immediately recognized the error -
https://www.mersenne.org/report_expo...exp_hi=&full=1

[ewmayer]

A more interesting question is what the server does with the following kind of thing: A p-1 run found the following factor of M(109228331): 67043584777242522312784510096836476580550779917618449.

It is indeed a factor, but it's composite, as the same kind of base-2 modular binary exponentiation used in TF and to quickly verify reported factors, modified into a base-2 PRP test reveals.

I expect the server has some kind of quadratic-sieve code it uses to split such large-but-not-NFS-worthy composites - the result appears on the exponent status page.

[kriesel]

Originally Posted by ewmayer

A more interesting question is what the server does with the following kind of thing: A p-1 run found the following factor of M(109228331): 67043584777242522312784510096836476580550779917618449.

It is indeed a factor, but it's composite, as the same kind of base-2 modular binary exponentiation used in TF and to quickly verify reported factors, modified into a base-2 PRP test reveals.

I expect the server has some kind of quadratic-sieve code it uses to split such large-but-not-NFS-worthy composites - the result appears on the exponent status page.

Yes, the server is effective at dashing the hopes of a record large P-1 factor in such a case.

It took Alpertron's online ecm calculator 1.2 seconds to factor that to

3 258278 300321 182416 433937 × 20576 383782 390150 543028 926977