Talk:Integer factorization records

Could someone explain what forms of numbers we are talking in the article? For example every mathematician knows what is the prime factorization of $10^{10000000000000}$ but it is not listed as a record. —Preceding unsigned comment added by 81.197.84.247 (talk • contribs)

I don't know whether reliable sources have made definitions, but here is my rough understanding: "Numbers of a general form" are numbers which satisfy these 3 conditions:

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 $10^{10000000000000}$.

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.

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 2ⁿ-1.

"Numbers of a special form" satisfy 1) and 2), but not 3). PrimeHunter (talk) 17:18, 13 September 2008 (UTC)

specify these are NFS records, maybe add ECM records?

I think the page needs a bit of clarification that these are GNFS and SNFS records.

Maybe even name the page "NFS factorization records"? Or we could add (history of) P-1 and ECM records (http://www.loria.fr/~zimmerma/records/top50.html)?

VictordeHollander (talk) 00:58, 29 January 2015 (UTC)

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External links modified (January 2018)

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Factored or Factorised

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 in the article. 66.76.242.44 (talk) 15:36, 6 May 2019 (UTC)

I searched a little, and this might just be a difference in US vs UK use of the words. 66.76.242.44 (talk) 15:42, 6 May 2019 (UTC)

Removal of paragraph

Hiya, I've removed 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

Fast Factoring Integers by SVP Algorithms, corrected (Schnorr) which appeared to be an preprint that never got published

and Factoring integers with sublinear resources on a superconducting quantum processor Yan et al. which appears to be questioned by various academics (in blogs but quite harshly)

so I've removed the whole thing for now and putting it here for review, anything worth saving? Was removing the whole thing correct? Justiyaya 12:03, 13 November 2023 (UTC)

Thanks for removing that paragraph, it's an improvement.

We did a thorough review / study of the Schnorr-related quantum methods at https://arxiv.org/abs/2308.07804, and found the rebuttals to be quite correct. The claim that a 48-bit number was "factored on a quantum computer" isn't really what happened - it's a massively parallel process, and just one or two of these parallel jobs were run on quantum computers, supplemented with millions of classical jobs. And there are better classical alternatives. Dominic Widdows (talk) 22:04, 23 February 2024 (UTC)