ECM on small Generalised Fermat numbers - Page 3

jyb · 2010-09-13, 06:37

Quote:

Originally Posted by geoff

Thanks, I didn't know about that project. So it looks like two projects have been working independently on some of these numbers :-(

Well yes, but not very many of them. I think 128 is too small an exponent to have any remaining composites in the Homogeneous Cunningham tables, so it's only 256 that might be an issue, given the current table limits (except for 3^512+2^512, which happens to be fully factored). And even that's too big an exponent for quite a few of the tables. So there are really only a handful of composites that would currently intersect with work being done on numbers of the form a^2^n + b^2^n (apparently 6, including the C149 from 8^256+5^256).

geoff · 2010-09-13, 23:50

I have checked the overlap between the Homogeneous Cunningham and Generalized Fermat tables, it turns out there were 11 factors found independently by both projects, 2 in the Homogeneous Cunningham tables but not in the Generalized Fermat tables (6^2^8+5^2^8, 8^2^8+5^2^8, reported to Wilfrid keller), and 1 in the Generalized Fermat tables but not in the Homogeneous Cunningham tables (9^2^8+7^2^8, reported to Paul Leyland).

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2010-09-13, 23:50	#24
geoff Mar 2003 New Zealand 13×89 Posts	I have checked the overlap between the Homogeneous Cunningham and Generalized Fermat tables, it turns out there were 11 factors found independently by both projects, 2 in the Homogeneous Cunningham tables but not in the Generalized Fermat tables (6^2^8+5^2^8, 8^2^8+5^2^8, reported to Wilfrid keller), and 1 in the Generalized Fermat tables but not in the Homogeneous Cunningham tables (9^2^8+7^2^8, reported to Paul Leyland).