[QUOTE=wombatman;361128]It was actually SNFS--as I recall the SNFS difficulty was slightly less than the GNFS difficulty.

Edit: Just found the poly file and confirmed that it was SNFS.[/QUOTE]Ok, I'll change it. Thanks.

Paul

Hello,

I got a load of badsched messages from lasieve4I11e when trying to factor 16^123+3^123 with SNFS. It's (16^123+3^123)/5074333684812894932003193739198849284459243849862123 in factordb. Have I missed an algebraic factor because 16 is a power? Or found a bug in lasieve4I11e?

The poly (generated by phi) was:
[code] n: 2519874106892870880613481828472591962375644104185293584477116742151028089507770472800630928489201
# 16^123+3^123, difficulty: 96.33, skewness: 0.43, alpha: 0.00
# cost: 2.25408e+12, est. time: 0.00 GHz days (not accurate yet!)
skew: 0.433
c4: 256
c2: -48
c0: 9
Y1: -3486784401
Y0: 1208925819614629174706176
m: 1240159616180673564011095568765000085925851664331848387212152397605756568130735823836381453524865
type: snfs
[/code]
Thanks to anyone who can shed any light on this.

Chris

badsched messages from lasieve4I11e (or 12e, 13e, 14e) are original - from the K+F code, as is. It is possible that for smaller sievers the "expected [I]schedule [/I]size" calculations are more frequently violated (by the randomly distributed number of factors, for which the estimate is in the code). Only for 15e and 16e sievers these estimated limits were tightened. For lesser sievers, there's no problem with the memory needed for those [I]schedules[/I]; any modern PC has enough.

That said, there's nothing wrong with having badsched messages; the sieving will go on fine. Just a few q0s are skipped. In the latest code, the warnings are completely switched off.

Your poly is fine (256 x^4 - 48 x^2 + 9). You could have used that 256 = 4^4, and quadruple the Y0, and the poly would have been (x^4 - 3 x^2 + 9), but this wouldn't have mattered much. Well, the skew would have been better.

[QUOTE=chris2be8;361481]Hello,

I got a load of badsched messages from lasieve4I11e when trying to factor 16^123+3^123 with SNFS. It's (16^123+3^123)/5074333684812894932003193739198849284459243849862123 in factordb. Have I missed an algebraic factor because 16 is a power? Or found a bug in lasieve4I11e?

The poly (generated by phi) was:
[code] n: 2519874106892870880613481828472591962375644104185293584477116742151028089507770472800630928489201
# 16^123+3^123, difficulty: 96.33, skewness: 0.43, alpha: 0.00
# cost: 2.25408e+12, est. time: 0.00 GHz days (not accurate yet!)
skew: 0.433
c4: 256
c2: -48
c0: 9
Y1: -3486784401
Y0: 1208925819614629174706176
m: 1240159616180673564011095568765000085925851664331848387212152397605756568130735823836381453524865
type: snfs
[/code]
Thanks to anyone who can shed any light on this.

Chris[/QUOTE]

It looks like Serge has already answered your question about the badsched messages, but yes you did miss an algebraic factor (and therefore using NFS on this number will waste your time). It has an Aurifeullian factorization:

16^123 + 3^123 = (16^41+3^41) * (16^41 - 4^41*3^21 + 3^41) * (16^41 + 4^41*3^21 + 3^41)

The primitive parts of the Aurifeullian factors are:

(16^41 - 4^41*3^21 + 3^41)/(16 + 4*3 + 3)
and
(16^41 + 4^41*3^21 + 3^41)/(16 - 4*3 + 3)

I believe these are primes of 48 and 49 digits, respectively.

Sharp eye! And that would explain why the siever would find twice as many factors and would be overflowing schedules most of the time. (Even though it would still work.) There was a situation [URL="http://mersenneforum.org/showthread.php?p=295174#post295174"]similar to this, before[/URL]. Both have the same reason.

[QUOTE=Batalov;361538]Sharp eye! And that would explain why the siever would find twice as many factors and would be overflowing schedules most of the time. (Even though it would still work.) There was a situation [URL="http://mersenneforum.org/showthread.php?p=295174#post295174"]similar to this, before[/URL]. Both have the same reason.[/QUOTE]

It also illustrates the danger behind something that I have been criticizing:

Running black box code without understanding the math behind it.

Update 2013-12-28
 

A total of 15 new factors have been reported during the last month, all found by SNFS. One, by Bob Silverman, was a three way split so only 14 more composites have been completed. There are now 368 composites remaining.

The new factors are[code]

7+4 257 C217 73957602966199549936755024385676013552205559546509308687925129308357665462379661898067365712766461367. P116 R Smith SNFS 2013-12-05
11+3 202 C202 17944116667299591390705224290388619064127117684886703863303515321. P138 R Silverman SNFS 2013-12-06
7+5 239 C164 840177122571122653375849738316984484083698503140819868593002222383607. P95 R Silverman SNFS 2013-12-12
11+4 202 C159 6416627295211466033998948760328898174578914914894200910316477829622201. P90 R Silverman SNFS 2013-12-13
11-7 235 C181 3771161972433866922169452949917635577399128050425737243576647605902634218281. P105 J Becker SNFS 2013-12-18
11+6 202 C184 19275044322278775085296659607057368474715830077982400065621. C126 R Silverman SNFS 2013-12-11+6 202 C126 353924918521802745998422257102829286840698982836141122689859809. P63 R Silverman SNFS 2013-12-20
20
11+8 235 C184 914247670296450607843721050334638371057311462705998814829542122001013665972931631. P103 J Becker SNFS 2013-12-20
11-5 235 C192 29695721205916055436181128572672700600088852282726336145069447372970928919031489742349493811. P100 J Becker SNFS 2013-12-21
7-2 299 C209 3821452525211246433086736069714488526482524843835391132083465124659730518002985107. P127 T Womack SNFS 2013-12-22
7+2 290 C158 775583452412019876067469355136213243324536190643119629345261626449164360822961. P81 J Becker SNFS 2013-12-23
7+6 239 C176 926250561957955566657284495229990066919104196917413382839. P119 R Silverman SNFS 2013-12-24
5-2 355 C181 931914847236004735481465493267169191990633418182780158254061081177753441. P109 J Becker SNFS 2013-12-25
11+2 206 C166 745433310568040142270803533137743926948973838588525658063577. P106 R Silverman SNFS 2013-12-27
7-2 295 C161 2735593647782548954808750039524283629648228102207859964567271. P101 J Becker SNFS 2013-12-27
[/code]
and the first hole in each table is[code]

3+2_499 C184
3-2_515 C164
4+3_358 C152
4-3_359 C151
5+2_307 C165
5-2_311 C181
5+3_304 C187
5-3_323 C164
5+4_302 C205
5-4_311 C189
6-5_263 C185
6+5_268 C161
7-2_241 C161
7+2_244 C162
7+3_251 C199
7-3_251 C180
7+4_241 C189
7-4_269 C194
7-5_251 C157
7+5_254 C157
7+6_256 C182
7-6_257 C195
8+3_226 C166
8-3_227 C191
8-5_223 C160
8+5_229 C157
8-7_227 C154
8+7_236 C199
9-2_223 C188
9+2_229 C182
9+5_223 C199
9-5_227 C193
9+7_212 C158
9-7_227 C206
9+8_212 C185
9-8_233 C193
10+3_202 C158
10-3_211 C199
10+7_211 C184
10+9_211 C203
10-9_211 C169
11-10_211 C213
11+10_214 C189
11-2_211 C163
11+2_214 C214
11+3_206 C155
11-3_227 C185
11+4_211 C183
11-4_223 C232
11+5_211 C181
11-5_223 C162
11+6_212 C194
11-6_227 C214
11+7_214 C190
11-7_229 C234
11+8_212 C202
11-8_223 C191
11+9_211 C167
11-9_211 C199
12+11_206 C191
12-11_221 C165
12+5_202 C181
12-5_223 C218
12+7_211 C222
12-7_211 C213
[/code]

As always, please let me know of any omissions and errors you may find.

Here's wishing for a productive 2014.


Paul

Update 2014-01-29
 

Ten new factorizations have been reported in the last month by JOn Becker and Bob Silverman. There are now 358 composites remaining.
[code]

7-6 295 C156 198172801723939989218024415081485491099447144008231082679128411198419161. P84 J Becker SNFS 2013-12-30
7+6 295 C162 367849978455190166510669162249852969440755919574267616247573509066310661406485231. P82 J Becker SNFS 2014-01-03
12+5 217 C168 77723606963611265620855504191221417317567818915909061. P115 J Becker SNFS 2014-01-10
12+5 202 C181 6852684146176673252491768734744046353006144423366147279275032842059519124529. P105 R Silverman SNFS 2014-01-13
11+3 206 C155 571950907689059512618260100302740279687949761183356444017520634177. P89 R Silverman SNFS 2014-01-20
12-7 217 C173 32114853298765120648993968836412156807173881027508040164286151671361. P106 J Becker SNFS 2014-01-21
6+5 301 C158 716559449753822290311200565076298690057993301984088712314534287346879969949. P83 J Becker SNFS 2014-01-26
7+4 241 C189 2978245172157205511932954932756841233795941469142427842112310187621546043. P116 J Becker SNFS 2014-01-27
8-5 223 C160 6434259230036039487905135301371715812938888592620281281169506971348553860325827. P82 J Becker SNFS 2014-01-27
9+7 212 C158 669335211634454725620546803457187350939798329324833. P107 J Becker SNFS 2014-01-28
[/code]

Update 2014-02-22
 

Eleven more numbers factored in the last month, one being a three-way split. There are 347 composites left to be done.

[code]

9+8 212 C185 3444386205778228293891460045073797841456349324470548577. C130 J Becker SNFS 2014-01-29
9+8 212 C130 60365316489708415609396003708117856456996577084161948561. P74 J Becker SNFS 2014-01-29
4+3 392 C191 2814404693768822743236126616936776084561615690598258273417920359083091777904715291009. P107 J Becker SNFS 2014-01-30
8+3 226 C166 9233775726392885620531273399039585716863773316125497771392237866598542333. P93 J Becker SNFS 2014-01-31
10+3 202 C158 99229531281892093011752365432366844987772549407029. P108 R Silverman SNFS 2014-02-01
3-2 515 C164 149280929703677076760068717888423520999207938562884490846164941682812062368221. P87 R Smith SNFS 2014-02-08
12+11 206 C191 4191811699141774598872486291900509546989017080729394996278280517. P127 R Silverman SNFS 2014-02-10
12+11 208 C177 6270563998817211156963254638490615560433781783324331733703854457848121375309508914049. P92 R Silverman SNFS 2014-02-10
7-2 241 C161 215291543240684229582533531992071344797912343591262140750360175777611. P93 R Silverman SNFS 2014-02-10
11+5 212 C194 1144841347458644071340571010539906425877779825356683527713. P137 J Becker SNFS 2014-02-11
4+3 374 C193 4202031003356608106699434895309154347790052079049572621. P139 J Becker SNFS 2014-02-15
10-3 211 C199 733902232094098959988928236771645189215575861292761364295334380428298829111245087908529. P112 R Silverman SNFS 2014-02-20
[/code]


Paul

It's been pointed out, rightly, that I've not posted an updated here for far too long. Turns out to have been five months. :redface: Mea culpa.

Anyway, the number of composites has now fallen below 300. As before, when it drops below 50 I'll extend the tables again. I suspect that might be quite a while yet.

A total of 58 factors has been reported in the interim. This list gives them all, together their dates of discovery and by whom:
[code]
10+7 211 C184 1799606819198122234048339948739487234113485490970639787. P130 R Silverman SNFS 2014-02-27
10-9 211 C169 5154437354998938604043908799401406356271220866994513553424136659719. P102 R Silverman SNFS 2014-03-07
4+3 358 C152 1109101656258342333721616067827492612344708914014509612194450365497. P86 R Smith SNFS 2014-03-10
10+3 211 C206 44294182405576462258418473957035755971131485730027286804343. P147 R Silverman SNFS 2014-03-12
10+9 211 C203 7281867508323681750250963199024956243665914058096726070545136786447125726426883815672446426321. P109 R Silverman SNFS 2014-03-14
9+5 232 C150 295480994406910578726040928176457694875593004859398781572273. P90 S Wellman GNFS 2014-03-15
11-2 211 C163 350340299352252693830170865967573579975105687941978160077. P106 R Silverman SNFS 2014-03-24
8-7 227 C154 269620963486428574738135684293528466206753766651333. P104 R Smith SNFS 2014-03-24
11+5 211 C181 43270616152144098830508474138367047521373238271770486104033277. P119 R Silverman SNFS 2014-04-01
6-5 263 C185 2442997798112271198606374519194387018066019311367204631778626709786865876598943383612967. P98 R Silverman SNFS 2014-04-03
8-3 227 C191 19033014922246122414254311104977176791679483687681583. P139 R Smith SNFS 2014-04-07
11-9 211 C199 5949484370671334765423216264605582874182394969790411084778892211299412409911732477417017. P111 R Silverman SNFS 2014-04-15
5+4 343 C160 119277139310815680377554129695932725252372252349297286721328813436385291465121. P83 R Smith SNFS 2014-04-22
11+9 211 C167 485408510141466544829694137564782723677988414778893. P116 R Silverman SNFS 2014-04-23
9+7 218 C198 1441134542533885277328969873480595222190843810763281367100575022924014393484177. P119 J Becker SNFS 2014-05-03
7+2 244 C162 2020174347339967246332189326706542079698652264585605746777. P105 R Silverman SNFS 2014-05-04
11-10 211 C213 2923611324546669813125120093375640794514176858486596126779869. C152 R Silverman SNFS 2014-05-05
11-10 211 C152 2203254555890006183747570726850710873225947944124325157909415582512014525737. P77 R Silverman SNFS 2014-05-05
5-2 343 C166 807200141672441154171099747263862011639277721222036603231761222674641. P97 R Smith SNFS 2014-05-08
8+5 229 C157 31544119506341825149797562194066039799177126494400525786084331. P96 J Becker SNFS 2014-05-08
10+7 212 C208 290266391659366517545986534766285416763074431700699272304999288234915164497. P134 R Silverman SNFS 2014-05-09
7+3 287 C193 3652747559733823919752839135105185714808727284692621911223025218533. P127 J Becker SNFS 2014-05-12
5+4 302 C205 4760254712727761783001493379619092116814877180639066491626409639205645458790244639766957. P118 J Becker SNFS 2014-05-12
10+9 212 C159 52906451823237936685629533390579733945706199229943886349761. P100 R Silverman SNFS 2014-05-19
10+3 212 C172 121133659509085405710961447724652131155990487029265215374202950847353255075485089. P92 R Silverman SNFS 2014-05-23
9-8 259 C188 2007080186348373556359862243413293338231095468474678206907306322239007. P118 J Becker SNFS 2014-05-24
8-5 229 C167 18014247613185028576663972008376934023393005116945826751. P112 R Silverman SNFS 2014-05-26
6+5 268 C161 85724875772908480879927300707761089302782582830782318537097. P102 R Smith SNFS 2014-05-27
9+5 259 C198 108409063656379943998132929530646141485724742960580462026189. P139 J Becker SNFS 2014-05-27
7-3 251 C180 9677955284486842730394978022862794783303900115873678483544677. P119 J Becker SNFS 2014-05-29
11+3 211 C152 450441119933643241231914635773349224595334396470420846710619. P92 R Silverman SNFS 2014-06-02
11+4 211 C183 2201544582765543560399629381338437282593404233456738346198721847129929566915031. P105 R Silverman SNFS 2014-06-08
11+4 221 C198 735006920316357930137654415505118925425061454919100686316332036652681017333400349191635495845639. P102 R Silverman SNFS 2014-06-10
11+10 221 C183 681301911415681466861388903040317129449982770398373730701100340572878652556596209. P102 R Silverman SNFS 2014-06-16
7+4 251 C183 412352557926471129192909975971589432706581997390341208804493016239043936141803303. P103 J Becker SNFS 2014-06-15
7-5 251 C157 3111000189503632136024901408434425270345480789444856981. P102 J Becker SNFS 2014-06-18
9-5 259 C206 80749563062119613692414045426316196143205422345163664256408394964514200448346257252836627707451. P111 R Smith SNFS 2014-06-18
11+2 221 C150 148074351512945983206944705845865761221177131304743. P100 R Silverman SNFS 2014-06-20
7+3 251 C199 27319969991003684980959050090547509854002985313564642026886191708333807403. P125 J Becker SNFS 2014-06-20
11+3 221 C195 36117242265606704734920339303534856450360402778039726538077953. P133 J Becker SNFS 2014-06-21
5+3 304 C187 31459625209404492817565167877270335492295921424917412265889. P128 J Becker SNFS 2014-06-23
9-2 223 C188 125011407662402148713308141737450344675045644048615948887262634819337595213548847. P108 J Becker SNFS 2014-06-25
11-10 221 C189 746193837597400194961269701447723094836320914936196626289788460312620197339882837. P108 R Silverman SNFS 2014-06-25
9+5 223 C199 195448484246209268822070448577664235342879060499633752165169763403546793912125764874597280403279581. P100 J Becker SNFS 2014-06-26
8+7 236 C199 174566719779500159964972081381121533226056882516489793. C146 J Becker SNFS 2014-06-30
8+7 236 C146 109945892145191425533621909103078403019115802800723618701113. P87 J Becker SNFS 2014-06-30
7-3 253 C154 57350904070379655235952829697861957843470057632778132121835796275642489. P83 J Becker SNFS 2014-06-30
7-2 251 C203 1713508938798681067790104842992131118127428345676304091. C149 R Silverman SNFS 2014-07-02
7-2 251 C149 36382105696689425231505442811730691733427879080281715448658903. P87 R Silverman SNFS 2014-07-02
4-3 377 C165 199995668829649308746187817731578438704174683765578105899045416541. P99 J Becker SNFS 2014-07-02
10+3 214 C182 8231065656074719785378319850071856250095871136702367359163918110616837. P112 J Becker SNFS 2014-07-07
5+2 307 C165 6594569454290661347643658521338051635988810785747665607. P111 J Becker SNFS 2014-07-07
6-5 299 C179 13906197108233559443423525235333303871757546413914766853309390752306762787. P106 J Becker SNFS 2014-07-10
7+5 254 C157 39929857890512157344562478700873077141413862876768404929800913. P95 J Becker SNFS 2014-07-12
11+8 212 C202 234698627390111656200178822786345028681367674003818169. C149 R Silverman SNFS 2014-07-14
11+8 212 C149 55220696071318497234909566133960365166760491361654764834737940186577. P81 R Silverman SNFS 2014-07-14
7+2 254 C213 1875539232188775893671872454498540361084613547528712029947637. P153 J Becker SNFS 2014-07-14
11+2 238 C158 26807753504234513023960208043246055653810057889967172246538516949. P93 R Smith SNFS 2014-07-17[/code]

The web tables will be updated in the next couple of minutes assuming my ISP is on the ball.

Here are the 13 factors found by Jon Becker and Bob Silverman in the last six weeks or so. The number of composites has now dropped to 280.
[code]11+9 212 C195 1520900838410715627018456080820481158514652504785137663020788247569615708501061249089. P111 R Silverman SNFS 2014-07-24
11+6 212 C194 921989360328312677952130422162622645884923117050550180442132740763041767801. P119 R Silverman SNFS 2014-08-04
4+3 359 C183 450599519762644214258813688149681091909153287393691100683310368554283368617. P109 R Silverman SNFS 2014-08-07
4-3 359 C151 4824892217200794810317137067999718039504281963413937063959523445188647873. P78 R Silverman SNFS 2014-08-14
6+5 299 C178 18006320767077126443435263405055293033889159662505375331666695577742577981. P105 J Becker SNFS 2014-08-19
6+5 277 C171 4199596751468932240197449502173337209916566125605533134474833329153. P104 J Becker SNFS 2014-08-21
5+2 311 C186 62608460956354845733668663264163999024449571628605386820763743855162289. P115 R Silverman SNFS 2014-08-22
9+5 226 C214 190187623461183181272797588866108317230755985241344400664511780649835542893294991317. P131 J Becker SNFS 2014-08-24
5-2 311 C181 490237764753989880161152457427678614460281074695930341480589253755273238816158929. P100 R Silverman SNFS 2014-09-02
9-2 247 C207 316192789206149846592078148336115653567605562733010223518251213911801955185100785033681174451790439. P108 J Becker SNFS 2014-09-02
5-2 341 C152 724341148035986494846586104061457441261327758299323449645414686918397. P83 J Becker SNFS 2014-09-03
8+3 239 C208 2913398998086904002371920183790860073709075276472902578421984394759456656538323749. P126 J Becker SNFS 2014-09-04
8+5 239 C215 17847024861844446493976166730904693347020620602192682255671878909005575252016486320255074109451. P121 J Becker SNFS 2014-09-06
[/code]

Paul