Ready SNFS targets

XYYXF · 2014-05-13, 19:41

Some ECM pre-factoring is necessary to remove small factors before running an SNFS job, stopping when the expected factor size is about 22% of SNFS difficulty.

There we collect targets which are ready for SNFS.

If you see a composite which survived enough ECM tests and has a small cofactor, feel free to add it there. A polynomial construction is also appreciable :-)

fivemack · 2014-05-15, 23:56

Quote:

Originally Posted by XYYXF

C250_128_89, 21000 curves at B1 = 260M, difficulty 250
(2¹⁰⁴)⁶ + 15842*(89²¹)⁶ = 6 * C250

C254_127_102, 21000 curves at B1 = 260M, difficulty 256
(127¹⁷)⁶ + 102*(102²¹)⁶ = 103 * C254

I'd expect these to take 15k - 25k thread-hours each (depending on the age of the machine you use), so they're non-trivial commitments unless you've got access to a cluster.

XYYXF · 2014-12-05, 22:45

C251_126_103, 20000 curves at B1 = 260M
Sextic (difficulty 254): 126*(126¹⁷)⁶ + (103²¹)⁶ = 635 * C251

XYYXF · 2015-04-13, 20:02

All are factored (or reserved) except for

Quote:

Originally Posted by XYYXF

C208_133_43, 7600 curves at B1 = 43M
Sextic (difficulty 218): 43*(43²²)⁶ + 133*(133⁷)⁶ = 16248239480 * C208

fivemack · 2015-06-16, 20:35

I'll take C208_133_43

XYYXF · 2015-06-21, 23:15

(reserved) C162_123_58, 7600 curves at B1=43M
Sextic (difficulty 217): 195112*(58²⁰)⁶ + 228886641*(123⁹)⁶ = 50002164960288875248029920622180294596898636638194696301 * C162

C162_144_37, 7600 curves at B1=43M, perhaps needs some curves at B1=110M
Sextic (difficulty 226): (37²⁴)⁶ + 144*(12¹²)⁶ = 18503369959822517532081459390273377279584717590723349144530544225 * C162

These two are currently the smallest composites in the project (except for C160_146_39 which is already under SNFS by Sean Wellman).

(reserved) C166_117_76, 7600 curves at B1=43M
Sextic (difficulty 220): 438976*(76¹⁹)⁶ + 257049*(3²⁵*13¹²)⁶ = 3687149743256520163799275205528985260542672222364271457 * C166

fivemack · 2015-06-22, 13:32

I'll take C162_123_58; however, it is definitely a GNFS number (polynomial from five minutes search sieves 60% faster than the SNFS sextic).

The other C162 is an SNFS number, since the coefficients of the SNFS polynomial are so much smaller than for 123_58

XYYXF · 2015-06-22, 19:39

That's how the coefficients affect the sieving speed :)

XYYXF · 2015-06-28, 06:53

C165_125_71, 18000 curves at B1=110M
Sextic (difficulty 234): (71²¹)⁶ + 8875*(5³⁵)⁶ = 705802046969421619725838846919055406138655378181220926249900100315924 * C165

Might be GNFS as well...

fivemack · 2015-06-28, 16:56

I will throw 100 CPU-hours at polynomial selection and report back if it gets good enough, but at the moment I suspect 125,71 is SNFS.

fivemack · 2015-06-30, 08:50

I'll take C165_125_71 for GNFS

2014-05-13, 19:41	#1
XYYXF Jan 2005 Minsk, Belarus 2⁴×5² Posts	Some ECM pre-factoring is necessary to remove small factors before running an SNFS job, stopping when the expected factor size is about 22% of SNFS difficulty. There we collect targets which are ready for SNFS. If you see a composite which survived enough ECM tests and has a small cofactor, feel free to add it there. A polynomial construction is also appreciable :-) Last fiddled with by XYYXF on 2016-02-14 at 19:39 Reason: updated

2015-06-21, 23:15	#6
XYYXF Jan 2005 Minsk, Belarus 2⁴·5² Posts	(reserved) C162_123_58, 7600 curves at B1=43M Sextic (difficulty 217): 195112(58²⁰)⁶ + 228886641(123⁹)⁶ = 50002164960288875248029920622180294596898636638194696301 * C162 C162_144_37, 7600 curves at B1=43M, perhaps needs some curves at B1=110M Sextic (difficulty 226): (37²⁴)⁶ + 144(12¹²)⁶ = 18503369959822517532081459390273377279584717590723349144530544225 C162 These two are currently the smallest composites in the project (except for C160_146_39 which is already under SNFS by Sean Wellman). (reserved) C166_117_76, 7600 curves at B1=43M Sextic (difficulty 220): 438976(76¹⁹)⁶ + 257049(3²⁵13¹²)⁶ = 3687149743256520163799275205528985260542672222364271457 C166 Last fiddled with by XYYXF on 2015-06-28 at 06:59

2015-06-22, 13:32	#7
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2×7×461 Posts	I'll take C162_123_58; however, it is definitely a GNFS number (polynomial from five minutes search sieves 60% faster than the SNFS sextic). The other C162 is an SNFS number, since the coefficients of the SNFS polynomial are so much smaller than for 123_58 Last fiddled with by fivemack on 2015-06-22 at 15:26

2015-06-30, 08:50	#11
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2·7·461 Posts	I'll take C165_125_71 for GNFS Last fiddled with by fivemack on 2015-06-30 at 10:04

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2014-12-05, 22:45	#3
XYYXF Jan 2005 Minsk, Belarus 2⁴×5² Posts	C251_126_103, 20000 curves at B1 = 260M Sextic (difficulty 254): 126(126¹⁷)⁶ + (103²¹)⁶ = 635 C251

2015-06-16, 20:35	#5
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 1100100110110₂ Posts	I'll take C208_133_43

2015-06-22, 19:39	#8
XYYXF Jan 2005 Minsk, Belarus 2⁴×5² Posts	That's how the coefficients affect the sieving speed :)

2015-06-28, 06:53	#9
XYYXF Jan 2005 Minsk, Belarus 110010000₂ Posts	C165_125_71, 18000 curves at B1=110M Sextic (difficulty 234): (71²¹)⁶ + 8875(5³⁵)⁶ = 705802046969421619725838846919055406138655378181220926249900100315924 C165 Might be GNFS as well...

2015-06-28, 16:56	#10
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 1100100110110₂ Posts	I will throw 100 CPU-hours at polynomial selection and report back if it gets good enough, but at the moment I suspect 125,71 is SNFS.