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These words seem to be used interchangeably in the article. For example "...factorised using GNFS..." vs, a few sentences later, "...the same team factored...". Personally I've never heard "factorised". Numbers are factored, not "factorised". But whichever one is settled on, it should be consistent
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2) The factorization is not "dominated" by one prime factor far larger than the others. This eliminates easy cases where you can find a few small prime factors, divide by them, and then be left with a prime.
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3) The number is not of a form where there is a known specialized prime factorization algorithm which is faster than methods for arbitrary numbers. This eliminates for example 2-1.
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a paragraph from the article after it was pointed out to me by a off-wiki friend who was much more knowledgeable in this area. The two main sources in the section was
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1) The number is not "constructed" in a way which makes all or some of the prime factors or divisors known without having to search for them. This eliminates
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Could someone explain what forms of numbers we are talking in the article? For example every mathematician knows what is the prime factorization of
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so I've removed the whole thing for now and putting it here for review, anything worth saving? Was removing the whole thing correct?
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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have made definitions, but here is my rough understanding: "Numbers of a general form" are numbers which satisfy these 3 conditions:
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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Maybe even name the page "NFS factorization records"? Or we could add (history of) P-1 and ECM records (
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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before doing mass systematic removals. This message is updated dynamically through the template
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before doing mass systematic removals. This message is updated dynamically through the template
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Factoring integers with sublinear resources on a superconducting quantum processor Yan et al.
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https://web.archive.org/web/20070823181923/http://ftp.cwi.nl/herman/SNFSrecords/SNFS-244
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https://web.archive.org/web/20071128061126/http://ftp.cwi.nl/herman/SNFSrecords/SNFS-233
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565:, "External links modified" talk page sections are no longer generated or monitored by
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If you found an error with any archives or the URLs themselves, you can fix them with
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If you found an error with any archives or the URLs themselves, you can fix them with
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I think the page needs a bit of clarification that these are GNFS and SNFS records.
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https://web.archive.org/web/20071213020640/http://www.boo.net/~jasonp/qs.html
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We did a thorough review / study of the
Schnorr-related quantum methods at
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Fast
Factoring Integers by SVP Algorithms, corrected (Schnorr)
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which appeared to be an preprint that never got published
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for additional information. I made the following changes:
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for additional information. I made the following changes:
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Thanks for removing that paragraph, it's an improvement.
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specify these are NFS records, maybe add ECM records?
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227:This article has not yet received a rating on the
385:http://www.loria.fr/~zimmerma/records/top50.html
561:This message was posted before February 2018.
441:This message was posted before February 2018.
553:http://ftp.cwi.nl/herman/SNFSrecords/SNFS-244
543:http://ftp.cwi.nl/herman/SNFSrecords/SNFS-233
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