Polynomial selection for 2,2246M c221

[charybdis]

Originally Posted by Gimarel

I think, that the parameters for cado have to be reconsidered. For about 16h I run

polyselect -d 6 -n 24023387191766184217094927222587025087468868508838209688355658860897738047963529318736265313199625192712082581481439831563094403250831892547179972207284600405234081309183045488404642574713121441527058807512178264038863337 -P 5000000 -admin 1260 -admax 126001 -incr 420 -sopteffort 1 -t 32 -v -nq 279936

This isn't complete yet.

Running msieve rootsieve on the resulting size-optimized polys gives a best score 3.097e-16. Cados ropt with ropteffort 1 gets a score 2.875e-16 on the same size-optimized poly but ropteffort 10 gets only 2.760e-16.

Turns out this is not a bug, it's just unlucky. Running with -ropteffort 1 will not be better in general.

Originally Posted by Shi Bai

I think this is not totally unexpected. The quick answer is the
candidate polynomial got discarded during the test root sieve
procedure. For convenience, I will denote the polynomial generated
from "-ropteffort 1: 2.026e-09" as the "BestPoly".

The ropt code starts with generating many sublattices of linear
rotation of the form (a, b) (mod M) where M is a product of small
prime powers. They denote f + (a*x + b)*g. The best sublattices are
recorded in a global queue using the rough E-score (this is lognorm +
alpha). Then it starts some short test root sieve on these (a, b) (mod
M) to filter out some good (a, b) (mod M) in terms of MurphyE-score.
Note there will be some discrepancies between the E-score and
MurphyE-score, e.g. good polynomials with E-score may have worse
MurphyE-score during the test root sieve.

The BestPoly was generated by a rotation of (-159023*x -
1150894624933)*g(x) + f(x) from the original polynomial f(x), g(x),
together with some minor size-optimization in the end. For such
rotation, it sits on the sublattice:

# Info: tune [ 363], E: 55.36, lat (0, 506257, 523547) (mod 665280)

This sublattice is found in both cases (ropt = 1 and/or 10). However,
when ropt = 10, there are many sublattice candidates whose MurphyE
score is better than this BestPoly (during the test root sieve). Thus
the sublattice for this BestPoly was discarded (before entering the
actual root sieve) when ropt = 10.

[EdH]

i wonder if this explains why my spin script sometimes loses the best scoring poly I start with. . .

[swellman]

Originally Posted by VBCurtis

There's no harm in waiting for your last run, but I can say I won't be giving this a shot after all- that "4" is plenty to declare victory and move to test-sieving. If Greg would like someone else to test-sieve for him, I can take it on this week.

My last CADO run finished with a 2.8 handle, so nowhere near Gimarel’s top poly. I have finished searching.

Onward!

[swellman]

Originally Posted by VBCurtis

There's no harm in waiting for your last run, but I can say I won't be giving this a shot after all- that "4" is plenty to declare victory and move to test-sieving. If Greg would like someone else to test-sieve for him, I can take it on this week.

Bump. Are you still willing to test sieve this? Assuming of course that Greg is still willing to sieve it.

[VBCurtis]

Ya, sure- I'll have time sometime this week.