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 but it is not listed as a record. —Preceding unsigned comment added by 18.104.22.168 (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 .
- 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)?