# 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 ${\displaystyle 10^{10000000000000}}$ but it is not listed as a record. —Preceding unsigned comment added by 81.197.84.247 (talkcontribs)

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 ${\displaystyle 10^{10000000000000}}$.
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)