20220420, 20:19  #1 
Dec 2021
17 Posts 
OEIS A242274 Question
Hello. I am researching OEIS sequence A242274. I have validated all of the known terms, but between a(31)=549 and a(32)=804 I have found a candidate whose semiprime status appears to be unknown when I look in factordb.com  k=560. However, factordb.com indicates "Autogenerated SNFSPolynominal available!" I have taken Yafu ecm to t40 so far with no factors.
My question: Is there something I am missing about this number to indicate that it is not semiprime? I assume the existence of an autogenerated SNFS polynomial says nothing about the number of factors for the number (other than being not prime). And, my assumption is that at C270 a SNFS polynomial is of no practical use. I would like to ensure either the OEIS sequence is correct (i.e. k=560 is somehow known to be semiprime) or needs to modified to account for this apparently unknown term before 804. But, I was afraid there was something I might be missing and I don't want to mistakenly question another researcher. Thanks.  Kevin 
20220420, 20:43  #2  
Aug 2005
Seattle, WA
5×367 Posts 
Quote:


20220420, 20:49  #3  
Dec 2021
17 Posts 
Quote:


20220420, 20:59  #4 
Apr 2020
2·11·37 Posts 
These are generalized Woodall numbers. Paul Leyland maintains a page dedicated to factorizations of generalized Cullens and Woodall numbers, or GCWs for short, here. 560*3^5601 is listed as a C270 with no known factors there.
NFS@Home has run GCW factorizations in the past, so I think this number is of sufficient interest that it would be a suitable candidate. However, it may need further ECM before it is ready for SNFS. Last fiddled with by charybdis on 20220420 at 20:59 
20220420, 21:05  #5 
"Oliver"
Sep 2017
Porta Westfalica, DE
2100_{8} Posts 
How much ECM is left to be done? I assume we could get ECM done quickly.

20220420, 21:08  #6 
Dec 2021
17 Posts 
ECM is currently working its way from t40 to t45.

20220420, 21:12  #7 
Apr 2020
2·11·37 Posts 
Sam Wagstaff has probably done at least t50. Paul (xilman on mersenneforum) may have a precise count.

20220420, 21:22  #8 
Dec 2021
17 Posts 

20220420, 21:24  #9 
"Oliver"
Sep 2017
Porta Westfalica, DE
2100_{8} Posts 
If t50 is already done, you should skip to t50 since t40t45 is now way less efficient.

20220420, 21:25  #10 
Apr 2020
2×11×37 Posts 

20220420, 21:25  #11 
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{6}×17 Posts 
Okay, I will start at t55, too.

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