I'm working on sigma(15251867^18).

Chris K

More small factors:[code]47570965596691129321998577319726635181355713928656324509740429454112155941345332231525290994149
prp44 factor: 33370253237879562210469672002454924615366609
prp52 factor: 1425550032766665317711062469995038169054313749359061

65041070278606301966580888210532503093975162817899605924603856514207690185169892502252157539583
prp41 factor: 29698220902492250849011767714446975352919
prp55 factor: 2190066216160043027357373834534068629814437632915752857

65353543734719806555209525029083829248391122117534211479528265147346526121056513138376495109973
prp42 factor: 447940668549715373818007861992293532348177
prp54 factor: 145897767993053849005946800410291059341764651845970949

73605860652530947393034679444214660893657873359244122279098692352097184681331592775106382071021
prp40 factor: 4631778309164973994527459288622496745811
prp56 factor: 15891490425369852203469641872296650318902111214790226111[/code]

[CODE]sigma(843714919^18)
prp57 factor: 629017442410402196436312814976034338231077906322700303949
prp98 factor: 36803168713931906785490293217387052832672744579993358434451414615501784387720981520154565951962387

sigma(2387363771591^12)
prp57 factor: 162458277288529987020436379430524091071139910744206899381
prp91 factor: 2670879253375756529533790688504170460953151631496429982580156561866558519152093533176448067
[/CODE]

Working on sigma(911^60)

[CODE]sigma(911^60)
prp57 factor: 156031270890159168019131653668709775167811623705826546487
prp122 factor: 23898352196256784691638349257955903536104529176607643282172103673277048222055947084616949982025439540284587151243481817703
[/CODE]
working on sigma(181^78) and sigma(169299992707751^12)

[quote=chris2be8;206669]I'm working on sigma(15251867^18).
[/quote]

r1=8378269240138186520522800712958060425119306384281001007 (pp55)
r2=152578428905106285990457072254744045389712075877418195906941 (pp60)

I'll do 45319^36 and 398581^30 next, they should only take a few days each. That clears t370.txt.

Is there a way to generate a SNFS poly for sigma(p^2) ie p^+p+1 where p is a large prime? I can't see a way to produce an equation with a large enough degree.

Chris K

[QUOTE=chris2be8]I'll do 45319^36 and 398581^30 next.[/QUOTE]
These two were already reserved, sorry.
Remember all the refresh button on my pages and this thread,
as things are changing rather fast.
It is time to add the file [url]http://www.lri.fr/~ochem/opn/t380.txt[/url]

[quote=Pascal Ochem;206822]These two were already reserved, sorry.
[/quote]

Sorry, glad I found out before wasting too much time.

I'll do the following (the first 10 sorted by SNFS difficulty), I should be able to script a job to do them in sequence:
9263420619893880611 6
9736529984267551639 6
126860821 16
4689632444309897463803449841 4
5342436683061058354198492453 4
7780457401386385640670987149 4
98419048214671022611 6
134692190916827758099 6
145406578159655383969 6
154734729607724347493 6

Also the following to test my code to generate SNFS polys:
11124772385569 10
129994124149 12

Chris K

Results so far:

sigma(9263420619893880611^6)
r1=1544447665661034976657558931538875307862799087971 (pp49)
r2=13521161864666081331055609685681597088288037725829349 (pp53)

sigma(11124772385569^10)
r1=51555417108733607537559975816689402518742568434774866036309 (pp59)
r2=4740690275675619499459417358429136407134344658938568830929114021 (pp64)

Chris K

Another result:

sigma(134692190916827758099^6)
r1=6555200433808397137037178662946940295578711 (pp43)
r2=12856257444302786691725689142756271998389722520662109056191630839 (pp65)

I've also nearly finished my script to generate SNFS/GNFS parameter files for composites. Here are a set of .poly and .n files for every number in t1000.txt with SNFS difficulty less than 200. Note I've only tested a sample of them though.

The only case I can't handle yet is if the exponent is 2. Is there a way to use SNFS to factor p^2+p+1 when p is a large prime?

I'm also reserving the following (none should take me long):
sigma(3869481297007413264839989^4)
sigma(15251867^18)
sigma(234414539125735760881^6)
sigma(252983942118045608479^6)
sigma(314756901565756922317^6)
sigma(48324254338285998810553779811^4)

I'm leaving the GNFS candidates to someone with a GPU to find the polynomials.

Chris K

[QUOTE=chris2be8;206881]The only case I can't handle yet is if the exponent is 2. Is there a way to use SNFS to factor p^2+p+1 when p is a large prime?[/QUOTE]

It might be worth back tracking. For example, the first case of an exponent 2 in t500.txt is for base

5502997992185822133325044025114218231630382402194049024447

Looking in checkfacts.txt, we see that this prime is most of

sigma(1785003035704867089959419277971^2)

and 1785003035704867089959419277971 is itself most of

sigma(27282710017315537^2)

and 27282710017315537 is a pretty large factor of

sigma(108541^6)

So you might find good SNFS polynomials by re-expressing in terms of one of these back-tracked bases.

William

[CODE]sigma(181^78)
prp80 factor: 25739015320855150499051264182961484208776659427641652489496171841849540757226649
prp89 factor: 13929880124146459040031779037654780622978168009938988043567649525197059383426241053734839

sigma(169299992707751^12)
prp60 factor: 752357879523670823657981724176526882497854840790019051297737
prp100 factor: 5794881953518279201322140572323144055996232952497935850722729445078483884519593152127443650118974053
[/CODE]

I'd like to reserve:
sigma(70841^36)
sigma(11807^42)
sigma(3169^52)


I've also been running ecm (1 curve with B1=3e6) against t900.txt and found a few factors. I'm about 60% done so far. I've factored the composite factors that were small enough and I'm running 2440 curves with B1=3e6 against the larger composite factors.
[CODE]
sigma(2505051879696101784446736308957057983399568618014258494724914460625463048799405009853287874873101^2)
Input number is 28317631169084198069030194037169909368028340458267457921839380259778804847407928468507273218386875476056127060054059527167 (122 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=917352573
Step 1 took 11033ms
Step 2 took 4164ms
********** Factor found in step 2: 1098016270233373573416364011899167
Found probable prime factor of 34 digits: 1098016270233373573416364011899167
Probable prime cofactor 25789810166533814578846380733984111214335321834799718281262105195138784232248993552884001 has 89 digits

sigma(550759634197315156413248874276230891^4)
Input number is 558711080864816989295870729411276510793816999383191244574831742885891713251236332381288821178844568498477062924734011580491 (123 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3199072956
Step 1 took 11097ms
Step 2 took 4208ms
********** Factor found in step 2: 60911175292735538034472124230954741
Found probable prime factor of 35 digits: 60911175292735538034472124230954741
Composite cofactor 9172554595764804808872766461663247341887451960833739796545964478431741294008289454770751 has 88 digits
# PRP38 = 15235357552515917516194845440593795931
# PRP51 = 602057061289649805601401385743985960100132589770221

sigma(217520163329371849510392496855978675988198225914501460305274507152079405801^2)
Input number is 1526291014672148577248706692583083236187593407450195798971736025157551675928839453331551121662974540156757382100020860475916795643220980320558447013 (148 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1580707850
Step 1 took 12973ms
Step 2 took 4965ms
********** Factor found in step 2: 925083184012802281
Found probable prime factor of 18 digits: 925083184012802281
Probable prime cofactor 1649895967248525993588079605582112108554512476861733145962089090656231187143948675725545026518132269766909741153933976890911540573 has 130 digits

sigma(55117948583087760771307531091116280962177468328828269471177812599347636181^2)
Input number is 3037988256007906095250073542674622617067379181646724789920562105917007761756898910474518394184604036950513944309995439514789692959998752351687900943 (148 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3401718988
Step 1 took 12813ms
********** Factor found in step 1: 995431947218694886853263
Found composite factor of 24 digits: 995431947218694886853263
# PRP11 = 17003492449
# PRP14 = 58542793499887
Composite cofactor 3051929631650112882877197310381271428584755278493658582552986062933065862953718019388528657737368834980130410579541569471361 has 124 digits
# 69064481778243140560311626407
# PRP43 = 1686491313836425845928986575296433525508571
# PRP53 = 26202072844438023130588680496144608149906016229338613

sigma(13632086608718780267983^10)
Input number is 19559818631198182171021131090593832007260894685356211694700896383756890568850816704857093004377195126107300576871069059287123536527845\
16787425734523744936385560730440641881651655082482420970277685180884403 (205 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2496690053
Step 1 took 20957ms
Step 2 took 7105ms
********** Factor found in step 2: 3843714342360297616842114881
Found probable prime factor of 28 digits: 3843714342360297616842114881
Composite cofactor 50887805099447493438770835214970594469683255008315829811490225925432912633483612508510251458759023197428698383152506916410029284626\
5423858173735279653999517674293691621934334963 has 177 digits

sigma(3381863410579^22)
Input number is 12656758864462610091975767150348257513324473268272327996606165409031928356342622699212838382441461570935203153014034964406057423875781\
651566932350165441072805517476237223710504276066886276533242248400744956384208191415182123501 (227 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3292291084
Step 1 took 22981ms
Step 2 took 7789ms
********** Factor found in step 2: 1357825728497321152826888922379
Found probable prime factor of 31 digits: 1357825728497321152826888922379
Composite cofactor 93213426427481194574844828414762862757812960471585215848233949748312690482817958938636933363436377173509304236340895653727174966165\
05563119835697380639709030933054023264286287189639855818951327719 has 196 digits
[/CODE]

How much ecm has been done against the roadblock numbers? I'd like to work on them, but I don't know where to start. I checked a couple in factordb, but I didn't see any data yet.