... and another one
 

[CODE]ECM found a factor in curve #10, stage #2
Sigma=7210635612416542, B1=250000, B2=25000000.
2^35677+1 has a factor: 1174478776290172030409 (ECM curve 10, B1=250000, B2=25000000)
ECM found a factor in curve #38, stage #2
Sigma=1699163987306510, B1=250000, B2=25000000.
2^35677+1 has a factor: 4519369329719894060013787 (ECM curve 38, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus (2^35677+1)/3 = 1174478776290172030409 · 4519369329719894060013787 · PRP10694

[QUOTE=axn;500831][CODE]ECM found a factor in curve #10, stage #2
Sigma=7210635612416542, B1=250000, B2=25000000.
2^35677+1 has a factor: 1174478776290172030409 (ECM curve 10, B1=250000, B2=25000000)
ECM found a factor in curve #38, stage #2
Sigma=1699163987306510, B1=250000, B2=25000000.
2^35677+1 has a factor: 4519369329719894060013787 (ECM curve 38, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus (2^35677+1)/3 = 1174478776290172030409 · 4519369329719894060013787 · PRP10694[/QUOTE]

Congrats :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^35677+1)/3/1174478776290172030409/4519369329719894060013787" | ../../coding/gwnum/hybrid - 1 2 35677 1

Testing (x + 2)^(n + 1) == 7 (mod n, x^2 - x + 1)...
Likely prime!

real 0m1.115s
user 0m0.900s
sys 0m0.036s
[/CODE]

... and another one
 

[CODE]ECM found a factor in curve #2, stage #1
Sigma=461605036619020, B1=250000, B2=25000000.
2^35851+1 has a factor: 54919454473787 (ECM curve 2, B1=250000, B2=25000000)
ECM found a factor in curve #111, stage #2
Sigma=2529484593925455, B1=250000, B2=25000000.
2^35851+1 has a factor: 1383891629171890065880777 (ECM curve 111, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
(2^35851+1)/3 = 1184732147 · 54919454473787 · 1383891629171890065880777 · PRP10745

[QUOTE=axn;500843][CODE]ECM found a factor in curve #2, stage #1
Sigma=461605036619020, B1=250000, B2=25000000.
2^35851+1 has a factor: 54919454473787 (ECM curve 2, B1=250000, B2=25000000)
ECM found a factor in curve #111, stage #2
Sigma=2529484593925455, B1=250000, B2=25000000.
2^35851+1 has a factor: 1383891629171890065880777 (ECM curve 111, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
(2^35851+1)/3 = 1184732147 · 54919454473787 · 1383891629171890065880777 · PRP10745[/QUOTE]

Congrats again :toot: :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^35851+1)/3/1184732147/54919454473787/1383891629171890065880777" | ../../coding/gwnum/hybrid - 1 2 35851 1

Testing (x + 2)^(n + 1) == 5 (mod n, x^2 + 1)...
Likely prime!

real 0m0.703s
user 0m0.888s
sys 0m0.008s
[/CODE]

[QUOTE=axn;497976]
[CODE]ECM found a factor in curve #1, stage #2
Sigma=7791075725288429, B1=250000, B2=25000000.
2^29027+1 has a factor: 275322488297 (ECM curve 1, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus (2^29027+1)/3 = 578914489 · 275322488297 · PRP8718[/QUOTE]

[QUOTE=axn;498055][CODE]ECM found a factor in curve #390, stage #2
Sigma=7844702814691327, B1=250000, B2=25000000.
2^29437+1 has a factor: 24192412837755888627020059 (ECM curve 390, B1=250000, B2=25000000)
Cofactor is a probable prime![/CODE]

(2^29437+1)/3 = 1177481 · 24192412837755888627020059 · PRP8830[/QUOTE]
These two are now proven (long time back... waiting for factordb to upload it)

26000-26500 done


[CODE]
2^26017+1 has a factor: 628295109713251741345216912537379 (ECM curve 399, B1=250000, B2=25000000)
2^26021+1 has a factor: 20056522540355505315086219 (ECM curve 45, B1=250000, B2=25000000)
2^26041+1 has a factor: 131880107821847253060288953 (ECM curve 137, B1=250000, B2=25000000)
2^26041+1 has a factor: 5133597786411701095883 (ECM curve 3, B1=250000, B2=25000000)
2^26053+1 has a factor: 185255101747907703065087656691 (ECM curve 77, B1=250000, B2=25000000)
2^26053+1 has a factor: 4197165704910243992819 (ECM curve 101, B1=250000, B2=25000000)
2^26083+1 has a factor: 1118283355318735860011 (ECM curve 18, B1=250000, B2=25000000)
2^26083+1 has a factor: 55421847303778673 (ECM curve 2, B1=250000, B2=25000000)
2^26107+1 has a factor: 859528261417318515403 (ECM curve 44, B1=250000, B2=25000000)
2^26107+1 has a factor: 859528261417318515403 (ECM curve 6, B1=250000, B2=25000000)
2^26119+1 has a factor: 33599180088532561 (ECM curve 110, B1=250000, B2=25000000)
2^26119+1 has a factor: 33599180088532561 (ECM curve 6, B1=250000, B2=25000000)
2^26119+1 has a factor: 4069121945248193970904063489 (ECM curve 55, B1=250000, B2=25000000)
2^26119+1 has a factor: 4069121945248193970904063489 (ECM curve 77, B1=250000, B2=25000000)
2^26141+1 has a factor: 12302651387100233 (ECM curve 3, B1=250000, B2=25000000)
2^26177+1 has a factor: 2209568257662624159233 (ECM curve 110, B1=250000, B2=25000000)
2^26177+1 has a factor: 6699363221022123855592841 (ECM curve 139, B1=250000, B2=25000000)
2^26183+1 has a factor: 6326277643729527361793969 (ECM curve 137, B1=250000, B2=25000000)
2^26189+1 has a factor: 21939023541432339273131 (ECM curve 76, B1=250000, B2=25000000)
2^26237+1 has a factor: 4940480327570136992401935019 (ECM curve 184, B1=250000, B2=25000000)
2^26249+1 has a factor: 61769675275297363243 (ECM curve 62, B1=250000, B2=25000000)
2^26263+1 has a factor: 27775488948006877565753 (ECM curve 70, B1=250000, B2=25000000)
2^26293+1 has a factor: 5178618228283053971 (ECM curve 15, B1=250000, B2=25000000)
2^26297+1 has a factor: 331056202075107398295261259 (ECM curve 28, B1=250000, B2=25000000)
2^26297+1 has a factor: 336250445903171 (ECM curve 2, B1=250000, B2=25000000)
2^26321+1 has a factor: 45467342717607470637587 (ECM curve 2, B1=250000, B2=25000000)
2^26393+1 has a factor: 182532853384830323 (ECM curve 2, B1=250000, B2=25000000)
2^26399+1 has a factor: 2527029406443001360675782573227 (ECM curve 515, B1=250000, B2=25000000)
2^26399+1 has a factor: 7913514683358829152208219 (ECM curve 3, B1=250000, B2=25000000)
2^26417+1 has a factor: 62150979840284417056493607362041 (ECM curve 231, B1=250000, B2=25000000)
2^26423+1 has a factor: 872930940764728645666579 (ECM curve 7, B1=250000, B2=25000000)
2^26431+1 has a factor: 4775290088417746293443 (ECM curve 7, B1=250000, B2=25000000)
2^26437+1 has a factor: 1287872173435586759323 (ECM curve 155, B1=250000, B2=25000000)
2^26437+1 has a factor: 1287872173435586759323 (ECM curve 98, B1=250000, B2=25000000)
2^26479+1 has a factor: 1504735026754535267 (ECM curve 18, B1=250000, B2=25000000)
2^26479+1 has a factor: 1504735026754535267 (ECM curve 287, B1=250000, B2=25000000)
2^26489+1 has a factor: 31055541621204479789435950003 (ECM curve 378, B1=250000, B2=25000000)
2^26489+1 has a factor: 5601166359596957819 (ECM curve 6, B1=250000, B2=25000000)
2^26497+1 has a factor: 442348719449699348137687049 (ECM curve 424, B1=250000, B2=25000000)

[/CODE]

35000-37000. Not all of it is reported to factordb.
[CODE]2^35023+1 = 113183376254043141161
2^35059+1 = 122100260976161936953
2^35059+1 = 5081250871604071390846834931
2^35081+1 = 42152949521270544720121
2^35083+1 = 46237943078921329470331
2^35099+1 = 1330412517631594162811
2^35107+1 = 9928924318289607289
2^35111+1 = 332188260769
2^35111+1 = 5020413836529499
2^35111+1 = 84114660640714864610704172014550771
2^35117+1 = 224034332481330219209
2^35117+1 = 370749342883
2^35129+1 = 40671179984315413051
2^35141+1 = 193910602584159151907
2^35149+1 = 1570482697579
2^35149+1 = 5552794488958059617
2^35149+1 = 94748900554963
2^35159+1 = 170014297293457
2^35221+1 = 212128656885735673
2^35221+1 = 2310054119427673
2^35221+1 = 77348454012545842284065592464509187
2^35227+1 = 522224860125658870711323721
2^35251+1 = 531468250524618163
2^35251+1 = 65905552225620396770969
2^35257+1 = 84237223139
2^35281+1 = 23561017638982590006455257074049
2^35281+1 = 2388708612307531
2^35281+1 = 723905516838433
2^35291+1 = 366926718925073711771
2^35311+1 = 20311032643556721673
2^35317+1 = 185952660922694115011
2^35317+1 = 57941635273
2^35317+1 = 7595806110725113
2^35317+1 = 808832383226407913382001
2^35317+1 = 924413349087665689963
2^35323+1 = 1158266403574290489148692787
2^35327+1 = 15861087845131
2^35327+1 = 339986992508954715068221152957883
2^35419+1 = 7123371688953535409899575162977
2^35423+1 = 120634278827563257315011
2^35437+1 = 1326826778122120195928088619
2^35447+1 = 166594150747018714502197187
2^35447+1 = 1829477324478848226067
2^35461+1 = 599811705298988911307
2^35509+1 = 330303349230688544092512209
2^35531+1 = 410890099257097
2^35533+1 = 286781794840618937
2^35573+1 = 198875338699
2^35573+1 = 76965173633
2^35591+1 = 59278826015269387547
2^35617+1 = 83719614027791626580103817
2^35671+1 = 3676508930160410422569353
2^35677+1 = 1174478776290172030409
2^35677+1 = 4519369329719894060013787
2^35729+1 = 11221428467401
2^35731+1 = 301454157409
2^35747+1 = 424807296153399643459
2^35753+1 = 9833561824259
2^35759+1 = 285651750017440388794327184819
2^35759+1 = 573620060003
2^35771+1 = 538309462516863571
2^35801+1 = 536982295291368094245580771510325003
2^35809+1 = 2039488914148187993
2^35831+1 = 10176242338242543169
2^35831+1 = 1056205199655132118582241
2^35831+1 = 1676614447177907
2^35837+1 = 17607815123702487186134209
2^35837+1 = 214243621506777271889947
2^35837+1 = 7053251225616658999496547429053194571
2^35851+1 = 1383891629171890065880777
2^35851+1 = 54919454473787
2^35869+1 = 9932173231867
2^35879+1 = 58508597140221097
2^35897+1 = 23665958656417027977414033521
2^35897+1 = 390126898730394569
2^35923+1 = 252955049935486907
2^35933+1 = 238587570463524141962563
2^35951+1 = 14154366526626523289
2^35951+1 = 457540284625947517811298761
2^35951+1 = 63641949967735689569
2^35963+1 = 32096378846064876121
2^35969+1 = 123351271295739759349144777
2^35969+1 = 679299672584947
2^35993+1 = 7409860505483353
2^35993+1 = 8529379072805540266448233
2^36011+1 = 325036680207277651
2^36011+1 = 34271946340058389293421577
2^36013+1 = 19836518047817753795657
2^36017+1 = 134275137380776133473249012507
2^36061+1 = 1228607914303348144264240427
2^36061+1 = 621725967557322227
2^36067+1 = 1439002616132767805892453953
2^36067+1 = 165532812644249
2^36073+1 = 150085079624224771457
2^36097+1 = 576403976273941124833
2^36107+1 = 93109339819051849
2^36131+1 = 516273598430455433
2^36131+1 = 70043565369613924747
2^36137+1 = 104062202277266472233
2^36151+1 = 158695587499
2^36161+1 = 164299973820272891
2^36209+1 = 22515145857367084547
2^36217+1 = 7112551120199282411
2^36229+1 = 1233776075773010201
2^36251+1 = 2536244699859780305881
2^36319+1 = 63907929223829294904575617
2^36341+1 = 1890670883762627
2^36341+1 = 25866531152475940335125831531
2^36341+1 = 4074672053346216578613068819
2^36373+1 = 308756722823171502965753
2^36389+1 = 10913417212344757619
2^36389+1 = 840498081116297
2^36433+1 = 5163870767108471777
2^36433+1 = 538347196747
2^36451+1 = 105553581258909331
2^36451+1 = 8279212954171
2^36457+1 = 21422791117896457
2^36467+1 = 3426110538122843
2^36473+1 = 232877752734045451
2^36473+1 = 39553477578619901169307219
2^36479+1 = 1656256823245894937
2^36479+1 = 33870616158305418891131
2^36551+1 = 64240001943585886102793
2^36559+1 = 10906743102656195102467
2^36571+1 = 1546411998474267593
2^36583+1 = 2407209361035002089
2^36599+1 = 335141857392877792552800320115523
2^36607+1 = 56109203446684836103966333390273
2^36629+1 = 374881991273
2^36629+1 = 86147123433826617641
2^36653+1 = 92624194046918357608861382805992497
2^36677+1 = 155494995915451821014690881
2^36683+1 = 297225455443920180251
2^36683+1 = 56429825731
2^36691+1 = 113599597854846121
2^36691+1 = 147611335469240199560209
2^36709+1 = 3563439321965963771
2^36713+1 = 21895318418062336952051
2^36713+1 = 63051090132131
2^36713+1 = 94130434511908956913
2^36739+1 = 13302000107046451
2^36761+1 = 27802425541811
2^36779+1 = 10694783157446139957212312283007241
2^36781+1 = 3107786068546457
2^36791+1 = 1697152292227030627081
2^36791+1 = 320299932830262659
2^36809+1 = 160239957139
2^36809+1 = 2895485669441367276097393
2^36821+1 = 3784645085803
2^36821+1 = 91194520656277173482107
2^36833+1 = 361414478796803
2^36833+1 = 9010185614956079339
2^36847+1 = 11989062800607888058633
2^36847+1 = 17455251492458150529131
2^36847+1 = 3973327193723
2^36857+1 = 6077049154912019783593585687283
2^36887+1 = 33899737186976594086855201
2^36899+1 = 10130794613281
2^36899+1 = 12632969385867659
2^36901+1 = 37891440257273
2^36913+1 = 196321550950142097643
2^36931+1 = 752337650641
2^36931+1 = 964926802350402223417
2^36943+1 = 44208867677630448846065611
2^36943+1 = 613936728299
2^36979+1 = 80640886583732873
2^36997+1 = 105202897796309030699[/CODE]

Factors that I've found added in FDB (from about last week), most likely from GP2's t40:

[URL="http://factordb.com/index.php?id=1100000000017315340"]2^3089+1[/URL]: P35+C879
[URL="http://factordb.com/index.php?id=1100000000017315425"]2^3109+1[/URL]: P35+P36+P44+C807 (nice!)
[URL="http://factordb.com/index.php?id=1100000000017315642"]2^3167+1[/URL]: P35+C890

Looks like t40 is going fairly well!

[QUOTE=DukeBG;502644]Factors that I've found added in FDB (from about last week), most likely from GP2's t40:[/QUOTE]

Yes, that was me. However, I will probably pause the t40 ECM soon because spot prices in the cloud are starting to rise, as they usually do at this time of year. Presumably for online holiday shopping, and maybe also corporations and accounting firms doing some quarter-end and year-end financial crunching.

(2^1430131+1)/(3*356468732537*36519993971459) is a 430487-digit PRP

Some background:

The factoring efforts from 2013 stopped when a first factor was found, because they were mainly interested in just eliminating potential Wagstaff primes. So there are a lot of second-and-higher factors still waiting to be found, some of them actually quite small.

I redid the range from 1M to 2M and found more than 16,000 new factors. One of them resulted in the above PRP. I'm going on work on ranges below 1M next.

So the Gerbicz cofactor-compositeness test was really useful once again, because I did the original PRP test on (2^1430131+1)/3 (with no divisors) several months ago. The new cofactors were checked very quickly, in an afternoon on a single core, whereas redoing all the PRP tests would have taken very much longer.

[QUOTE=GP2;502686](2^1430131+1)/(3*356468732537*36519993971459) is a 430487-digit PRP

Some background:

The factoring efforts from 2013 stopped when a first factor was found, because they were mainly interested in just eliminating potential Wagstaff primes. So there are a lot of second-and-higher factors still waiting to be found, some of them actually quite small.

I redid the range from 1M to 2M and found more than 16,000 new factors. One of them resulted in the above PRP. I'm going on work on ranges below 1M next.

So the Gerbicz cofactor-compositeness test was really useful once again, because I did the original PRP test on (2^1430131+1)/3 (with no divisors) several months ago. The new cofactors were checked very quickly, in an afternoon on a single core, whereas redoing all the PRP tests would have taken very much longer.[/QUOTE]

Congrats to you for the find and to Robert for his method in action,

[CODE]time ./pfgw64 -k -f0 -od -q"(2^1430131+1)/(3*356468732537*36519993971459)" | ../../coding/gwnum/hybrid - 1 2 1430131 1

Testing (x + 1)^(n + 1) == 2 + 5 (mod n, x^2 - 5*x + 1)...
Likely prime!

real 20m31.553s
user 43m12.772s
sys 4m21.160s
[/CODE]