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Old 2022-04-20, 20:19   #1
nivek000
 
Dec 2021

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Default 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 "Auto-generated SNFS-Polynominal 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 auto-generated 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
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Old 2022-04-20, 20:43   #2
jyb
 
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Quote:
Originally Posted by nivek000 View Post
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 "Auto-generated SNFS-Polynominal 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 auto-generated 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
I'm afraid I have little insight into the question you're asking: I know of nothing that would indicate that this number is not a semi prime, but I am not an expert in this area. However, I did want to address your stated assumption above. The given SNFS polynomial is very much of practical use. This is a job with SNFS difficulty 270, and such jobs are done with some frequency. It would be a hard job for an individual to do (though certainly not impractical, if you have a lot of patience), but NFS@Home does jobs at this level all the time. Try posting in the NFS@Home sub-forum and see if you can get any interest.
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Old 2022-04-20, 20:49   #3
nivek000
 
Dec 2021

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Quote:
Originally Posted by jyb View Post
I'm afraid I have little insight into the question you're asking: I know of nothing that would indicate that this number is not a semi prime, but I am not an expert in this area. However, I did want to address your stated assumption above. The given SNFS polynomial is very much of practical use. This is a job with SNFS difficulty 270, and such jobs are done with some frequency. It would be a hard job for an individual to do (though certainly not impractical, if you have a lot of patience), but NFS@Home does jobs at this level all the time. Try posting in the NFS@Home sub-forum and see if you can get any interest.
Agreed. I was definitely speaking from an individual perspective with respect to factoring the C270 SNFS.
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Old 2022-04-20, 20:59   #4
charybdis
 
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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*3^560-1 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 2022-04-20 at 20:59
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Old 2022-04-20, 21:05   #5
kruoli
 
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How much ECM is left to be done? I assume we could get ECM done quickly.
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Old 2022-04-20, 21:08   #6
nivek000
 
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ECM is currently working its way from t40 to t45.
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Old 2022-04-20, 21:12   #7
charybdis
 
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Sam Wagstaff has probably done at least t50. Paul (xilman on mersenneforum) may have a precise count.
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Old 2022-04-20, 21:22   #8
nivek000
 
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Quote:
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ECM is currently working its way from t40 to t45.
But... I am doing ECM by CPU (on 40 threads). If someone wants to take over with GPU, have at it...
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Old 2022-04-20, 21:24   #9
kruoli
 
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If t50 is already done, you should skip to t50 since t40-t45 is now way less efficient.
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Old 2022-04-20, 21:25   #10
charybdis
 
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Quote:
Originally Posted by nivek000 View Post
But... I am doing ECM by CPU (on 40 threads). If someone wants to take over with GPU, have at it...
I say keep going even if someone does want to run GPU curves - nothing wrong with more than one person running ECM! Just make sure you move up to the t55 level.
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Old 2022-04-20, 21:25   #11
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Okay, I will start at t55, too.
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