Why is factordb filled with not-very-factored near-Cunninghams?
 

I have a small unreliable ARM board which has been doing ECM for the last week or so, on batches of 121-digit numbers extracted from factordb.

I keep finding factors of numbers of pseudo-Cunningham forms like 2^397*111-1. These forms don't seem to have been searched very far (2^126*111-1 had no factors in the db); is there someone particularly interested in them?

It may be that someone is creating them by entering some random stuff and then flipping a few pages?

For a test, I entered "1345*3^n-2" in the search form and flipped until n<=300 (with page size 100). Now, there's a few dozen of composites. Are they useful? I doubt it. But the engine makes this very easy, and someone must be doing that (cmd proudly posts about this all the time - but his messages are mostly deleted on arrival).

[QUOTE=fivemack;327308]I have a small unreliable ARM board which has been doing ECM for the last week or so, on batches of 121-digit numbers extracted from factordb.

I keep finding factors of numbers of pseudo-Cunningham forms like 2^397*111-1. These forms don't seem to have been searched very far (2^126*111-1 had no factors in the db); is there someone particularly interested in them?[/QUOTE]

I may throw some curves at them... How's the B1?

Luigi

I really don't think this is a calculation that's worth doing. I just wanted a job that I could run on a machine that wouldn't stay running for more than ten hours at a time and that might be of some utility, but I'm getting to think that the utility is low.

(for numbers, I was running 32 curves at B1=10^6 on each of the C121 numbers, and getting about one factor per three numbers)

I'm getting about the same ECM performance on the four Cortex-A9 cores that I have from one K10/1900 core on the large server.

I think this thread should be in the FactorDB forum.

For example, when I ask for [url]http://www.factordb.com/listtype.php?t=3&mindig=200&perpage=10&start=1234[/url] I get

225^94+5
717^71-1
627^102-1
1066^74+1
1017^95+1
42122428890929^17-1
724^79-1
244^93+7
726^73-1
167^109-6

These are perfectly reasonable forms, I suppose, but I'd rather extend a small-initial-element aliquot sequence than devote effort to any of them.

627^102-1 is now fully factored. FactorDB just needed the algebraic factor 627^51-1 added and it took care of the rest.

Edit: 1017^95+1 also had a 23-digit factor that came from 1017^19+1.

As others have pointed out most of these are junk. However, some of them are a bit more interesting. Factorization of Numbers of the form p^n - 1 with p prime is of great practical utility. It is a requirement and the greatest part of the work in checking whether some polynomial of order n is primitive in the finite field GF(p^n). As such mathematics and humanity in general can benefit from this.

See my requests for help in factoring M31^n - 1 and M61^n - 1 in another thread. Larger n's are of value, but it is fine to take n such that there is as many cyclotomic factorizations as possible. For example n=168 n=210 n=240 and so on.
(M31 and M61 are the 8th and 9th Mersenne primes in the factordb.com notation).