Wikipedia:Reference desk/Archives/Mathematics/2024 January 29

= January 29 =

List of factorization of 2n-1
Is there a list of factorizations available of 2n-1 for n up to about 175? Bubba73 You talkin' to me? 04:00, 29 January 2024 (UTC)


 * Funny enough, I found such a list embedded in somebody's Python file on Github. Here ya go. GalacticShoe (talk) 04:38, 29 January 2024 (UTC)
 * Thanks a million! It is missing a few, starting at n=193, but I believe that is sufficient for my needs.  Bubba73 You talkin' to me? 04:47, 29 January 2024 (UTC)
 * For future reference, the missing values of $$n$$ (up to 256) are 193, 211, 227, 229, 251, 253; attempting to factor them with WolframAlpha shows that indeed the composite numbers that need to be factored are very large. GalacticShoe (talk) 05:18, 29 January 2024 (UTC)
 * Yes, apparently they were using their own program to factor them, until they got to a certain size, then they switched to using Wolfram Alpha, which did most of the rest, except for ones that took too long.


 * I also found this page with a list up to 263: . It has a dead link for "more data", but you can find it on the Wayback Machine: . This page has some very extensive data products such as with an explanation of the format . For 193 it lists:

M( 193 )C: 13821503 M( 193 )C: 61654440233248340616559 M( 193 )D
 * The text on the page notes that "the largest prime factor is almost always implied, as some of them are _very_ large". --Amble (talk) 17:31, 29 January 2024 (UTC)


 * Thanks, I'll look at that. Bubba73 You talkin' to me? 00:37, 30 January 2024 (UTC)
 * See the Cunningham table:, also this list 210.244.72.152 (talk) 03:00, 3 February 2024 (UTC)

Followup remark: I implemented this in a program, to look up these factorizations rather than factor them each time. I did a test and it was 62x faster, so it can do in a minute what would take an hour, etc. Bubba73 You talkin' to me? 10:39, 1 February 2024 (UTC)
 * http://factordb.com has a database with billions of known prime factors of various numbers. It accepts expressions like 2^253-1. You can also enter 2^n-1 and get a list of factorizations. Composite factors are blue. 2^1277-1 is the smallest without a known factor so the whole number is listed in blue. I don't know whether there are smaller numbers with a partial but not full factorization. PrimeHunter (talk) 17:59, 1 February 2024 (UTC)
 * Thanks, I didn't know about that. I needed a table of complete factorizations for four types of numbers.  I got what I need with my own program on three of them, but 2^n-1 bogged down about n=139.  But I got it up to n=192 from the source somewhere above, which I think will be sufficient.  But if it turns out that I need more, I can use this.  Bubba73 You talkin' to me? 20:53, 1 February 2024 (UTC)

At factordb.com, can you enter a series and loop on that? That is, if $$f_n$$ is the sum of a series up to n, can you get the factors of $$f_n$$, for n = 1 to x? Bubba73 You talkin' to me? 05:31, 3 February 2024 (UTC)
 * I don't think so. PrimeHunter (talk) 10:41, 3 February 2024 (UTC)