#15443: Random time outs in ecm.py
-------------------------------------+-------------------------------------
Reporter: vbraun | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: Volker Braun | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vbraun/ecm_cleanup | 998126dbd22d30eb34b46a0f122f9d62a9f861c9
Dependencies: | Stopgaps:
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Comment (by vbraun):
Reconstructed ECM output:
{{{
GMP-ECM 6.4.4 [configured with MPIR 2.6.0, --enable-asm-redc] [ECM]
Input number is 602400691612422154516282778947806249229526581 (45 digits)
Using B1=2000, B2=147396, polynomial x^1, sigma=4179203867
Step 1 took 2ms
Step 2 took 3ms
Run 2 out of 1000000000:
Using B1=2399, B2=2399-186156, polynomial x^1, sigma=4164584203
Step 1 took 2ms
Step 2 took 4ms
Run 3 out of 1000000000:
Using B1=2806, B2=2806-224406, polynomial x^1, sigma=3854196504
Step 1 took 3ms
Step 2 took 3ms
Run 4 out of 1000000000:
Using B1=3221, B2=3221-294786, polynomial x^1, sigma=3420982637
Step 1 took 3ms
Step 2 took 5ms
Run 5 out of 1000000000:
Using B1=3644, B2=3644-294786, polynomial x^1, sigma=1430191020
[...]
Using B1=22052, B2=22052-5026572, polynomial x^1, sigma=1562069045
Step 1 took 20ms
Step 2 took 26ms
Run 38 out of 1000000000:
Using B1=22779, B2=22779-5026572, polynomial x^1, sigma=1306733316
Step 1 took 21ms
Step 2 took 25ms
Run 39 out of 1000000000:
Using B1=23516, B2=23516-5031192, polynomial x^1, sigma=2409042976
Step 1 took 22ms
Step 2 took 25ms
Run 40 out of 1000000000:
Using B1=24263, B2=24263-5031192, polynomial x^1, sigma=518178309
Step 1 took 22ms
Step 2 took 26ms
********** Factor found in step 2:
602400691612422154516282778947806249229526581
Found input number N
}}}
So it seems that the "Found input number N" output doesn't imply that it
is probably prime. Some documentation would have been nice, too. Though
that leaves the question: how should we decide to give up? If the number
is actually prime then it always ends in "Found input number N", so we
can't just repeat until we find a factor. The readme says
{{{
5 - if no factor is found, either increase D by 5 digits and go to 0, or
use
another factorization method (MPQS, NFS)
}}}
but doesn't give any probability estimate in that case. Also, one of the
factors in question is only 17 digits so the B1-values tried should have
been just fine.
--
Ticket URL: <http://trac.sagemath.org/ticket/15443#comment:24>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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