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

fivemack · 2013-02-03, 09:53

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?

Batalov · 2013-02-03, 10:12

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).

ET_ · 2013-02-03, 10:34

Quote:

Originally Posted by fivemack

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?

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

Luigi

fivemack · 2013-02-03, 15:16

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.

Stargate38 · 2013-02-03, 18:02

I think this thread should be in the FactorDB forum.

fivemack · 2013-02-04, 23:49

For example, when I ask for http://www.factordb.com/listtype.php...=10&start=1234 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.

gd_barnes · 2013-02-04, 23:54

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.

kosta · 2013-02-27, 13:04

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).

2013-02-03, 09:53	#1
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²·131 Posts	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 2^397111-1. These forms don't seem to have been searched very far (2^126111-1 had no factors in the db); is there someone particularly interested in them?

2013-02-03, 18:02	#5
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 3·13·17 Posts	I think this thread should be in the FactorDB forum. Last fiddled with by Stargate38 on 2013-02-03 at 18:02 Reason: forgot period

2013-02-04, 23:54	#7
gd_barnes May 2007 Kansas; USA 10395₁₀ Posts	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. Last fiddled with by gd_barnes on 2013-02-05 at 00:02 Reason: edit

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2013-02-03, 10:12	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10010100000110₂ Posts	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).

2013-02-03, 15:16	#4
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²×131 Posts	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.

2013-02-04, 23:49	#6
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²·131 Posts	For example, when I ask for http://www.factordb.com/listtype.php...=10&start=1234 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.

2013-02-27, 13:04	#8
kosta Jan 2013 2³·7 Posts	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).