OEIS A242274 Question

nivek000 · 2022-04-20, 20:19

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

jyb · 2022-04-20, 20:43

Quote:

Originally Posted by nivek000

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.

nivek000 · 2022-04-20, 20:49

Quote:

Originally Posted by jyb

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.

charybdis · 2022-04-20, 20:59

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.

kruoli · 2022-04-20, 21:05

How much ECM is left to be done? I assume we could get ECM done quickly.

nivek000 · 2022-04-20, 21:08

ECM is currently working its way from t40 to t45.

charybdis · 2022-04-20, 21:12

Sam Wagstaff has probably done at least t50. Paul (xilman on mersenneforum) may have a precise count.

nivek000 · 2022-04-20, 21:22

Quote:

Originally Posted by nivek000

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...

kruoli · 2022-04-20, 21:24

If t50 is already done, you should skip to t50 since t40-t45 is now way less efficient.

charybdis · 2022-04-20, 21:25

Quote:

Originally Posted by nivek000

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.

kruoli · 2022-04-20, 21:25

Okay, I will start at t55, too.

2022-04-20, 20:19	#1
nivek000 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 "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

2022-04-20, 20:59	#4
charybdis Apr 2020 2²·11·17 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. 5603^560-1 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*

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
k-tuples in OEIS	MattcAnderson	MattcAnderson	0	2021-08-24 14:20
zero sequence in oeis	MattcAnderson	Miscellaneous Math	4	2021-03-05 15:46
This one isn't in the OEIS	R2357	Puzzles	1	2021-01-12 23:14
OEIS account - quick question	mart_r	Lounge	3	2012-01-12 21:57
my misunderstanding of the OEIS	science_man_88	Miscellaneous Math	11	2011-05-18 15:04

2022-04-20, 21:05	#5
kruoli "Oliver" Sep 2017 Porta Westfalica, DE 3×7³ Posts	How much ECM is left to be done? I assume we could get ECM done quickly.

2022-04-20, 21:08	#6
nivek000 Dec 2021 10001₂ Posts	ECM is currently working its way from t40 to t45.

2022-04-20, 21:12	#7
charybdis Apr 2020 2²·11·17 Posts	Sam Wagstaff has probably done at least t50. Paul (xilman on mersenneforum) may have a precise count.

2022-04-20, 21:24	#9
kruoli "Oliver" Sep 2017 Porta Westfalica, DE 3×7³ Posts	If t50 is already done, you should skip to t50 since t40-t45 is now way less efficient.

2022-04-20, 21:25	#11
kruoli "Oliver" Sep 2017 Porta Westfalica, DE 10000000101₂ Posts	Okay, I will start at t55, too.