3+ table

[Mystwalker]

It's most likely 3,499+

[akruppa]

Probable prime factor 1 has 121 digits:
2283855864616538319188501894078270917939970969131804770999352122148044707782348310208944420760967216707417196548630820741
Probable prime factor 2 has 65 digits:
77104115792306847773969759123947639401032809855965933396877513801

SNFS.

Alex

[akruppa]

Original number had 148 digits:
2716918436044945949944823985296833001963640254044400521055021835008032938970965633698011438803715583581679641230797027386350590008225304699681611351
Probable prime factor 1 has 82 digits:
1580757464381207284516313971349868565603302273698715818718303979482761015420509531
Probable prime factor 2 has 67 digits:
1718744650754182976202528603042164953120336270744134393913100855221

GNFS.

Alex

[bdodson]

Originally Posted by R.D. Silverman

But he has not publically announced this.
He has also done a lot of work at the 50 digit level, but again, he has not
announced the precise nature of his level of effort.

The only reason I discuss this is that it is nice, for those of us doing NFS,
to know that numbers have been sufficiently tested to proceed with NFS.

I believe I resemble that remark. My July 4th post on v2.0, 2006, gives
a fairly thorough update. 50-digit testing is complete on c142 - c210
(except for the last 500 curves with b1=44M on 7 numbers from c16x,
being used to keep the old P3 cluster occupied). I'm looking at raising
that to 800-bits (c240 or c241), checking parameters on the first five
holes. That takes adding 1050 curves with b1=260M to the previous
report (loc. cit.). C217 3,509+ held on to near the end, then gave-up
a p47 twice on the last run. While my first reports (still) go to the
ecmnet page (where Paul Zimmermann forwards them to his ecmnet list),
for forum readers, here's

p47 = 19724128725821325379688781664270351435664812399,
Dodson/ecmnet (prime cofactor).

Bruce

[bdodson]

Originally Posted by bdodson

...
C217 3,509- held on to near the end, ..., here's

p47 = 19724128725821325379688781664270351435664812399,
Dodson/ecmnet (prime cofactor).

Bruce

Ooops, as Bob points out, the cofactor is a C171; presumably the
p47 isn't enough to keep snfs from being the method of choice. -bd

[R.D. Silverman]

Originally Posted by bdodson

Ooops, as Bob points out, the cofactor is a C171; presumably the
p47 isn't enough to keep snfs from being the method of choice. -bd

No, it isn't. But if the factor had been about 55-56 digits, then GNFS
would probably be faster....

[akruppa]

Probable prime factor 1 has 118 digits:
2863444844784765273769276357682225285846811932015816786957553211027268460554271639307645113153966178527393827051882261
Probable prime factor 2 has 64 digits:
1223967211946315524725505592278476748023592868457900490298056129

SNFS.

Alex

[akruppa]

Is anyone already working on 3,499+? If not, I'd like to reserve it, please.

Alex

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
3	499+	C238	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	
3030024316322494736865438923295276593168615418833468586695502986048383349298657957016542355248282398609014975211200321312737994293084422178582702576380168815001814270653970287510445236380484434164382530965846048227334032165844982948134167
...
3	538+	C235	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)
1873335149090657974519074645679022532290800810832951463238668268127625592079248192372920853463850211027388925100798482946180858269215704729756987725080328396710985809161560038857400789972464158809724384579200698052215692148831032586517
...

Ben a while since the last entry on this table. Nice factor, at

p58 = 4424817286530482826420459992414631518016054430795822455701

but at 3,538+ c235 = p58*c177, with snfs difficulty 256.69, this is
still somewhat better by snfs (than c177 gnfs) and still not-so-easy
to finish.

Looks fairly good on the 2007 top10, in 8th spot (would have been 3rd
on the 2006 list), and --- for the first time --- pushes the last p56 out
of the top10. -Bruce

[R.D. Silverman]

Originally Posted by bdodson

Ben a while since the last entry on this table. Nice factor, at

p58 = 4424817286530482826420459992414631518016054430795822455701

but at 3,538+ c235 = p58*c177, with snfs difficulty 256.69, this is
still somewhat better by snfs (than c177 gnfs) and still not-so-easy
to finish.

Looks fairly good on the 2007 top10, in 8th spot (would have been 3rd
on the 2006 list), and --- for the first time --- pushes the last p56 out
of the top10. -Bruce

For a while Arjen's students were finding 'top 10' factors on
a regular basis. It's been a while since we heard from them.
Does anyone know what they are doing???

[bdodson]

Originally Posted by R.D. Silverman

For a while Arjen's students were finding 'top 10' factors on
a regular basis. It's been a while since we heard from them.
Does anyone know what they are doing???

I don't expect further top10 factors this year from either epfl or CWI. -bd