Next plausible Lucas/Fibonacci/similar milestones

[fivemack]

By Easter we should have finished the Fibonacci/Lucas numbers to 200 digits, and the Fibonacci/Lucas numbers with quartic polynomials to difficulty 250; the ones with sextic polynomials to difficulty 275 are already done.

This feels as if maybe I should move away from Q[sqrt(5)]; any ideas of a good direction to go in? Spending a year of my own compute time on a GNFS(210) isn't immediately appealing.

[Batalov]

Perhaps, a factorization catalog of Lehmer numbers?

[R.D. Silverman]

Originally Posted by fivemack

By Easter we should have finished the Fibonacci/Lucas numbers to 200 digits, and the Fibonacci/Lucas numbers with quartic polynomials to difficulty 250; the ones with sextic polynomials to difficulty 275 are already done.

This feels as if maybe I should move away from Q[sqrt(5)]; any ideas of a good direction to go in? Spending a year of my own compute time on a GNFS(210) isn't immediately appealing.

The Fibonacci's are complete to index 1400. Perhaps do the same for Lucas?

[xilman]

Originally Posted by fivemack

By Easter we should have finished the Fibonacci/Lucas numbers to 200 digits, and the Fibonacci/Lucas numbers with quartic polynomials to difficulty 250; the ones with sextic polynomials to difficulty 275 are already done.

This feels as if maybe I should move away from Q[sqrt(5)]; any ideas of a good direction to go in? Spending a year of my own compute time on a GNFS(210) isn't immediately appealing.

The GCW tables have had all the low-hanging fruit removed but there are still many which are much easier than GNFS(210).

An update to https://www.brnikat.com/nums/cullen_...utor_info.html is long overdue, given that both SSW and Rob Hooft have sent in factors recently, but a few G18x and S25x are still available. Note that the latter do not have particularly good polynomials but your rather impressive resources should be able to breeze through either class at a frequency approaching a microHertz.

I´m running CADO-NFS on 11,244-_C218 with a naive difficulty of S256.5 but that is one of the bad polynomials and it will take me several more months, not least because only two machines are running part time on it. I can provide CADO server details on request if anyone wishes to contribute.

[xilman]

Originally Posted by xilman

The GCW tables have had all the low-hanging fruit removed but there are still many which are much easier than GNFS(210).

Update now completed.

The smallest composite remaining to be factored has 184 digits. There are 13 composites with fewer than 190 digits and 88 with at least 1000 digits.

For those wishing to factor with the SNFS algorithm, this table contains the a and n values sorted by SNFS-difficulty (defined here as log10 (n.an) ) for those unfactored numbers which have SNFS-difficulty under 265. There are 68 entries in this table, some of which may have been reserved.

[R.D. Silverman]

Originally Posted by xilman

Update now completed.

And there are a lot of numbers from the Homogeneous Cunninghams that
are too big for lasieved. Many GNFS in the 175+ digit range, A lot of quartics
in the C220-250 range, etc. etc. Plus a bunch of SNFS in the (say) 255-280 digit
range...