20210102, 17:43  #1 
Oct 2012
13 Posts 
Trial Factoring  Factor Confirmation?
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. 
20210102, 18:03  #2 
"Oliver"
Sep 2017
Porta Westfalica, DE
494_{10} Posts 
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. 
20210102, 18:54  #3 
Bemusing Prompter
"Danny"
Dec 2002
California
2·3·397 Posts 
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.

20210102, 23:43  #4 
Oct 2012
15_{8} Posts 

20210401, 03:37  #5 
Jan 2020
239_{10} Posts 
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 
20210402, 20:32  #6 
∂^{2}ω=0
Sep 2002
República de California
11627_{10} Posts 
A more interesting question is what the server does with the following kind of thing: A p1 run found the following factor of M(109228331): 67043584777242522312784510096836476580550779917618449.
It is indeed a factor, but it's composite, as the same kind of base2 modular binary exponentiation used in TF and to quickly verify reported factors, modified into a base2 PRP test reveals. I expect the server has some kind of quadraticsieve code it uses to split such largebutnotNFSworthy composites  the result appears on the exponent status page. Last fiddled with by ewmayer on 20210402 at 20:32 
20210402, 21:34  #7  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2×2,549 Posts 
Quote:
It took Alpertron's online ecm calculator 1.2 seconds to factor that to 3 258278 300321 182416 433937 × 20576 383782 390150 543028 926977 

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