7- table

[garo]

Size	Base	Index	Mod	Diff	Ratio
299	7	389	-	328.7	0.909
220	7	395	-	267.0	0.823	/5q
214	7	419	-	354	0.60		/gnfs
305	7	421	-	355.7	0.855	
221	7	425	-	287.3	0.767	/5q
315	7	431	-	364.2	0.863	
342	7	433	-	365.9	0.933		
341	7	439	-	370.9	0.917

[geoff]

7,259- C175 = P69 * P106
P69 = 357708888729481429441295130414301389734167320382217282028474835603757
P106 = 4105565335483009892405469384537186162336640263688626513538197586407434630567675699756450562264314334763133

This was done using ggnfs.

[akruppa]

2300 curves at B1=11M on 7,263- 7,281- 7,387- 7,361- 7,373- 7,389- 7,391-. Adds 0.50108 to p45 and 0.06662 to p50 for each.

Alex

[akruppa]

8394 curves at B1=44M on 7,379- c320. Adds 6.47185 to p45, 1.09425 to p50 and 0.16726 to p55.

Alex

[R.D. Silverman]

Originally Posted by akruppa

8394 curves at B1=44M on 7,379- c320. Adds 6.47185 to p45, 1.09425 to p50 and 0.16726 to p55.

Alex

Hi,

What criteria do you use to select your ECM candidates?

[akruppa]

Mostly base 3, where 3,487- just started the matrix job. I'll do others soon. Besides base 3, p,q- with p,q prime and no/few known primitive factors are high on my list, too. Currently ECM is running on 11,239- c246.

Alex

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
7	347-	C263	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	
33026113620772114208766604063467661003723471054258542654638480163235395066667816968649454626706486286757449262870499223580340566358988528768748899525538521074418576135045990723823283809539231151245039475832681824086824878451971862643338135772425108809320687434713
...

p50 = 89823582672830825295829211905814036272016809423171

nearing half-way through the last run on the last large incomplete range for
testing to p50, 2100 curves/7830 left to go on the generic c251-c299 list
(not 2- or 2+ with n < 1200). The only other, smaller range left having
been updated on the 2- discussion thread.

I'm assuming this one's complete, but Paul notes that he has
the 213-digit cofactor listed as "prp213", with the comment

PS: note that I write 'prp213' and not 'p213', since one of the major computer
algebra systems (which I am using) says (courtesy Richard Pinch):

> ifactor(381707*293621*29363);

(3290922560713061)

> isprime(2432870015941);

true

> ifactor(2432870015941);

(1213) (551461) (3637)

-bd (factor reported May 14th)

[fivemack]

(7^35201-1)/6 is a base-3 pseudoprime.

At 29749 digits it's much too big for ECPP (20562 digits took six K8/2400-years, 15071 digits took two Xeon/2600-years); 35200 looks splendidly composite, so I suppose I should start hunting cyclotomic factors.

[bdodson]

Originally Posted by fivemack

(7^35201-1)/6 is a base-3 pseudoprime.

At 29749 digits it's much too big for ...

Not to mention being a bit beyond the limit for the Cunningham
Tables. -bd

[R.D. Silverman]

Originally Posted by fivemack

(7^35201-1)/6 is a base-3 pseudoprime.

At 29749 digits it's much too big for ECPP (20562 digits took six K8/2400-years, 15071 digits took two Xeon/2600-years); 35200 looks splendidly composite, so I suppose I should start hunting cyclotomic factors.

Indeed. The cyclotomic factors will not help ECPP, but they can greatly help
APR-CL.

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
7	317-	C202	5215(1.40359)	0(0.203361)	165(0.00921839)	0(0.00148122)
4817387775478910748337470675295461658412305210077087712511098562369825581753381999542716517188369317201504120140218066670989302797199195269475798377529788582602272660294198048152636381680533617071470639
...

This short table's now one shorter, after 7,317- c202 = p51*p151, with

p51 = 399676211948778347375576150888294069325575626336229

The 3rd cure2 duo factor (from the B1 = 260M run; on the part of
c190-c209 above difficulty 250). PaulZ's c120-355 file lists this as
entering ecmnet files as a c249, with what looks like a p47 found by
Philip McLaughlin 20.02.05. -Bruce