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Old 2007-02-11, 10:13   #12
smh
 
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Default 7,369+

The factorization of 7,369+
Code:
N=1220405226285619945756348670137067016231858382388759093946808065079087837263798689004423784126614304877916794166585153080165576904203292081334513511883636679 ( 157 digits)
SNFS difficulty: 207 digits.
Divisors found:
 r1=6142066474055855232929203714385784449474893513223804175646566504462164839 (pp73)
 r2=198696193120120523724484570554803032601480192693797052471947352941452314336611558561 (pp84)
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Old 2007-02-16, 11:41   #13
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Quote:
Originally Posted by garo View Post
Code:
Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
7	268+	C185	0(2.09174)	1500(0.38003)	590(0.0622008)	0(0.00529647)	24891507626244406120480497383985472681305924731801184706322368928780665216062688549532304713344794061905695890812821414304746944292502195893893185976748433282143972451856610060708867729
7	277+	C165	0(2.63512)	2160(0.477957)	0(0.0754361)	300(0.0068697)	764169214984901399630692275650584231425025348355149686578046847318220645141189717081771327184620438521905751313557954868835605128206993730879714642532855451764280301
7	281+	C193	0(1.05135)	40(0.20483)	630(0.0359772)	0(0.00565555)	2516294595449137842681508585485646837421570643438650885148026245098763672561537469456681219103325978671874012513114729395154498555009442701679972794303854947056828213099044731024785693598408501
7	293+	C187	0(1.05135)	40(0.20483)	630(0.0359772)	0(0.00565555)	6296364125172606494267021976455542556266929629924116599358890439755079922316658752809164765449896438043177976128556281990307165213790485254119081954628526897773640579224973494810677036269
7	296+	C190	0(1.05135)	40(0.20483)	630(0.0359772)	0(0.00565555)	1356163416951937876557001505933169803564430235101416990157506017350642263591410041280066882747594949410315805897987731453297466481423216502839776429178903315292221210239889451723850810964257
7	304+	C244	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	2444756019389824513591272721991134305364953743492866519256843340420013724341177902164948004866527943007948233639179864459205849358076675807034493021066454057004034303391102438349978163218356955457540716772277033528913230339448832563811936086401
7	305+	C164	0(1.63512)	2160(0.277957)	0(0.0421028)	0(0)	75616255520827784675782015796854048051769404859904095192646831803878044120314513038381693106305370967157805847566363027340927138519266608440018492169637221447988951
7	307+	C225	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	191912678714182028163799292265823724290963938738177834817041179664820956801451825525439208941243720035272266390410319027738756014542712420537696645251879152105341147064324645423200289882795054112774329399346966019509458778229
7	308+	C174	0(1.63512)	2160(0.277957)	0(0.0421028)	0(0)	
113648287310696143244647281716667420823547572687234153853394539553946851107682429176795021396914248864362792187795043899718017220825724024870865285822705603499137955179952529
...
Another Opteron factor from the c170-c189s of difficulty above 220,
but fairly low index (exponent?) on the 7+ list,

p53 = 14851094996429691600490236339835792528652136238327153

finishes 7, 308+ c174, difficulty 228. -Bruce
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Old 2007-04-05, 15:31   #14
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Quote:
Originally Posted by garo View Post
Code:
Base    Index    Size    11M(45digits)    43M(50digits)    110M(55digits)    260M(60digits)    Decimal
...
7    749L    C238    10(0.269602)    0(0.0525876)    165(0.00921839)    0(0.00148122)    
4497456...
7    749M    C237    20(0.27178)    0(0.0528773)    165(0.00921839)    0(0.00148122)
164959124809893472329424757751655148079565633455466027673906621412458337002020504067030885791639519072226444034314933019574901067324842075319267094661693225359034747178675710203878229024745847824322518524989430516136746304188339946056499
7    763L    C232    9(0.269384)    0(0.0525586)    165(0.00921839)    0(0.00148122)    
7    791M    C267    5000(1.35675)    0(0.197133)    165(0.00921839)    0(0.00148122)
A short list of composite 7LM's above 400; one shorter now, with a
nice/clean factorization of 7, 749M C237 by

p54 = 560083796201478625264978113443563586587662087342132809

just three large non-algebraic factors. Another xp/condor_grid factor,
500 curves short of t50 on the first part of c234-c250, 900 short on
the rest of the (next-to-last) pass; b1 = 43M, with t50 = 7830 curves.

We're stackin-up a nice backlog of top10 factors for Paul_Z's return;
now three p6x's (well, two p61's and a p60); three p55's (including CWI's
most recent) and now three p54's (the above being largest of the three).
That leaves just one p53 on the list, with p53 = 9585... just an epsilon
below 10^53 = c54; well 3 epsilon, maybe. Not sure anyone else is keeping
track, but we went from a bunch of p53/p52's on the March/April version
on the top10 just a short time ago to a 2007 top10 that's past the final
top10's of all but 2005 and 2006. Only one thing missing ...

-Bruce
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Old 2007-04-16, 16:32   #15
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Default New C147 Cunningham

Quote:
Originally Posted by garo View Post
Code:
Base    Index    Size    11M(45digits)    43M(50digits)    110M(55digits)    260M(60digits)    Decimal
7    553L    C162    0(1.63512)    2160(0.277957)    0(0.0421028)    0(0)    12143...
7    623M    C201    0(0.290133)    30(0.0561584)    165(0.00980315)    0(0.00148122)    
572764160374062390778582132462392970530521669223110869105995125704637960227591144170886210619166786406559269065650312403149475510996471848580728879471105061333261902489032610186738765642929594779933683
...
Looks like maybe we lost a line-feed; now that I'm editing, I see this
number didn't get lost (just a bit misplaced). Anyway, both cunningham.in
and Sam's page (main table) list this as still unfactored. I'm not changing
that, but the cofactor is now much more tractable after

p55 = 1563041865860853068488258202876043117290282825594727101

leaving a c147. This is the first factor from the new Opteron run with
B1 = 260M on the c190-c233's, starting with difficulty 220-249, looks like
112 numbers. They've already had a t50, so this is a 2nd t50 pass, to
2*t50. I expect to finish that 2nd t50 on the cofactor later today, if
anyone wants the cofactor? -Bruce
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Old 2007-04-20, 16:56   #16
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Quote:
Originally Posted by garo View Post
Code:
Base    Index    Size    11M(45digits)    43M(50digits)    110M(55digits)    260M(60digits)    Decimal
...
7    394+    C299    0(0.162075)    0(0.0316957)    100(0.0055869)    0(0.000897706)    12597028391758707504505871707118986227194005702805319652483887202035568850815397573894571692409830968120825756560491226356198519538904322513970168020768815379035312961479032215147567288259053215927891508984829255359238697015609275517141332802378973982340074177639109330225369216355441930060384311093
...
Seems like I can report TWO factors of this one since Garo's Jan '05
list was posted. The first, from Oct '05 was

p51 = 761117931894801857861437085827656037712705972978693 then
p52 = 1386615940613328186240837612222334356638972207862241

from today. Still with a composite cofactor, c299 --> c248 --> c197,
still hard. Ah. Sam's main tables give just one other non-algebraic
factor,

p34 = 1477031145181238990102844609682429, with (2) = 2*.5.5
for the algebraic factor (not sure what that 2* is, 7^2+1 = 50 is
just 2.5.5). That's a lot on non-algebraic factors, over 135-digits;
I wonder whether the snfs difficulty ... ah, this is bizzare, the exponent
(index) is 394 = 2*197, with a c197 cofactor, 197 prime. Ah!, judging
by the difficulty of 7, 334+ at 2*167, the 167 seems not useful, and
the difficulty is just log[10](7^334) = 282.26; so 396 looks likely
to give difficulty 332.96, nearly 333. So here's a case where the
p51 wasn't enough to be useful, but combined with the new p52,
gnfs on the new c197 sounds easier(!) than the snfs. Substantially.

Anyway, this was an xp factor, on the very last 500/7830 curves
needed for t50, working on the 2nd quarter of the 96 numbers from
c251-c299 (generic). So the c197 will finish its t50 test in a few
hours; but seems to be a candidate for a substantial portion of
a t60 before the gnfs(!) sieving. -Bruce
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Old 2007-04-20, 17:10   #17
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Quote:
Originally Posted by bdodson View Post

p34 = 1477031145181238990102844609682429, with (2) = 2*.5.5
for the algebraic factor (not sure what that 2* is,

The asterisk denotes an intrinsic prime factor.
2 is not an algebraic factor, but 7^n + 1 is always even and hence
divisible by 2.
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Old 2007-07-12, 14:34   #18
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Quote:
Originally Posted by garo View Post
Code:
Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits) Decimal
...
7	344+	C249	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	
848402433198325396544787562962163036757591093009878091095664122763186887365957852245987878869995374756552396332634029551986017530299072028798210185348536984869847949751858614721498000420473967556746187843672785351360202727393688033851063761979531489
...
Two prime factors today, both p52's, both from c249's, both with a
198-digit cofactor, but this one is complete, with a p198.

p52 = 1049139601018587804651174395448130408419345356019601

Another difference; this one was found in step 1. Both factors with
B1 = 110M from the 2nd t50 on c234-c250. (My previous post, on the 11+
thread refers to numbers with difficulty above 230, but all of c234-c250 has
difficulty above 230.) The other p52 today is over on the 10+ list. -Bruce
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Old 2007-12-26, 23:54   #19
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Quote:
Originally Posted by garo View Post
Code:
Base    Index    Size    11M(45digits)    43M(50digits)    110M(55digits)    260M(60digits)    Decimal
...
7    361+    C177    0(0.267423)    0(0.0522979)    165(0.00921839)    0(0.00148122)    198700916630605127701223302417616710723890394808792430178698164387815957298370406316846858692285240437599835481341431542746271266282813879623780207322460542450751768905195677371
...
Seems 2007 is still holding on. Another interesting factor,

p58 = 5907090586313286536313560574827695694485218120865194167761

to finish 7,361+. Just the 4th p58, this one the largest; 20th on the
alltime top50. This looks like an extension, according to PaulZ's c120c355
file [which goes to c384, after the extensions ... was c388]. There was a
previous p43 from Florek in 2002; then I had a p52 in May 2005, so this is
quite a victory for ecm. A _very_ hard number, Peter's file has the
difficulty at 305.08. From ATH's binary, with_redc, from the core2s. --Bruce
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Old 2007-12-27, 09:28   #20
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Quote:
Originally Posted by garo View Post
Code:
Base    Index    Size    11M(45digits)    43M(50digits)    110M(55digits)    260M(60digits)    Decimal
7    553L    C162    0(1.63512)    2160(0.277957)    0(0.0421028)    0(0)    121430320706697915049319571820938612339839103511203228365038712405864062286488014383780945081656956920914885455293777803715695798900704822793747578251532474132863 
7    623M    C147    0(0.290133)    30(0.0561584)    165(0.00980315)    0(0.00148122)    366441982703137439985118396104233562459088529655661907838220122467855202058232469698067258520663584377870441808818968429657039594037956291136054383
7    707M    C210    0(0.267423)    0(0.0522979)    165(0.00921839)    0(0.00148122)    472054059611270400983608549557558227905007021637244050204349363126183160481310453566945887867603039662152841534558489644637201992871925697296909407815438565792126797162200883356248382597290136842663663679579189
7    721L    C160    0(2.63512)    2160(0.477957)    0(0.0754361)    300(0.0068697)    5356881973409779315269107551188200510055896921691274696679942552605096584393647238262436468451711592080716697358800110922497064389662428524908532793335207245837
7    749L    C238    10(0.269602)    0(0.0525876)    165(0.00921839)    0(0.00148122)    4497456252499534106781967617970542206752003294281159107377213220466000015285312277935245611828453159674603865646982208112105747628199259750861770978253240911462140374843984254977992760423780508859874872130155423138521207959972157475310943
7    763L    C232    9(0.269384)    0(0.0525586)    165(0.00921839)    0(0.00148122)    6515180376319078685789959643925757754026899474823025887395003249390181392917101832152641091597852098563283044340856752407085554748844813645272052871719721240954131188185058106409464326290793323308382687421699124115819744405591668837
7    791M    C267    5000(1.35675)    0(0.197133)    165(0.00921839)    0(0.00148122)    226497099234038156560890108714990425463225062521934264892816001152819389875232252551541771614152227953368526412412903147468937823766214675300324742231416121917568661606217008948211113017371780018308597176578821819603354641098930095882776514443757030676483059941258021
is there an easy way to create such a table
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Old 2007-12-27, 14:12   #21
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Quote:
Originally Posted by henryzz View Post
is there an easy way to create such a table
Truly clueless.
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Old 2007-12-27, 16:10   #22
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Quote:
Originally Posted by bdodson View Post
p55 = 1563041865860853068488258202876043117290282825594727101
leaving a c147.
That's already finished by Irvine:
Code:
5550  7, 623M c147 22348792744766119486679460211348231845826672292165945209975680839. p83 Irvine gnfs

Last fiddled with by R. Gerbicz on 2007-12-27 at 16:11
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