108k-110k
 

[CODE]2^108007+1 = 20161650584149961969
2^108007+1 = 78554655680446101913
2^108061+1 = 12873594349810111129
2^108107+1 = 795825355469815511091451
2^108109+1 = 439725587957005366673
2^108127+1 = 22188379941202922393729
2^108131+1 = 15276647725770199673
2^108139+1 = 2582745590063465106349529
2^108139+1 = 5880230261013165697
2^108187+1 = 73834967403236759627
2^108193+1 = 8108249463408458441081
2^108203+1 = 5243445508156841441
2^108211+1 = 3828026832559225291
2^108247+1 = 706008571844699919428441
2^108271+1 = 132351398413842566729
2^108287+1 = 276547846837892081
2^108301+1 = 77794456320986287995163
2^108359+1 = 2321863511288971451
2^108421+1 = 389528342943562676514601
2^108439+1 = 16645832636432230064582569
2^108457+1 = 213000604936177335493967017
2^108497+1 = 22176817467150675209011
2^108499+1 = 167767922698194462940753
2^108499+1 = 2210900571991762993
2^108499+1 = 28718448814483699418150033
2^108533+1 = 670431165743914974521
2^108541+1 = 75106846053782872112552955169
2^108557+1 = 431012264001552592756318619
2^108649+1 = 72851702844603797194153
2^108751+1 = 82171099094885569
2^108769+1 = 205164869773612811
2^108769+1 = 52431431859034698257
2^108803+1 = 103464599754667104757945763
2^108863+1 = 72846067235810690977
2^108881+1 = 40935401561223537859723
2^108893+1 = 2626281013519919587163
2^108907+1 = 26137559760811714331
2^108907+1 = 597560978586734411
2^108967+1 = 217548277489346988689
2^109073+1 = 1858350610137700102721963
2^109103+1 = 108282670444980457
2^109159+1 = 45567038236224260162777
2^109159+1 = 5025984704147602251163
2^109159+1 = 900460656306737968523129
2^109169+1 = 908161286108682336942161
2^109199+1 = 738940767863002777951601
2^109297+1 = 290736326447392513
2^109357+1 = 266179990494217070809
2^109367+1 = 27375331870011563371
2^109391+1 = 42551120467296138617
2^109453+1 = 32272430192962832503445761
2^109469+1 = 371820300609980371
2^109481+1 = 692863390436865079171
2^109517+1 = 17566759943397747083
2^109537+1 = 21486498333611001898651
2^109567+1 = 4211062626325953667
2^109579+1 = 34026820129942162979
2^109589+1 = 1155305061559714845882904729
2^109639+1 = 21058023086293012601
2^109639+1 = 2499302862809748696739
2^109663+1 = 4951583686483024267
2^109663+1 = 5926673484517064963491
2^109841+1 = 5820117122207879398318451
2^109843+1 = 2480220549512587932097
2^109883+1 = 147043337556706027750129
2^109897+1 = 37304198443836366559817
2^109903+1 = 260450070667464187
2^109919+1 = 765680460264949211
2^109937+1 = 792462902650816057
2^109961+1 = 2034372804488913601[/CODE]

110k-112k
 

[CODE]2^110051+1 = 65228366464044326779
2^110161+1 = 29188102365665319058167259
2^110291+1 = 3867434383076500819841
2^110321+1 = 75922143799451987
2^110339+1 = 22777693856762463842081
2^110441+1 = 12058958783275929164659
2^110543+1 = 2245836194166106499
2^110557+1 = 7312248712686045017
2^110569+1 = 162942677419243265472672011
2^110569+1 = 294586778266791446627
2^110597+1 = 12955085535495184121
2^110597+1 = 135361252094163577
2^110641+1 = 618633569908451378627
2^110681+1 = 145331465490016961
2^110681+1 = 1939403983673219889971
2^110711+1 = 1023237052000159259
2^110711+1 = 146844872984198039570991481
2^110729+1 = 491781115198744036507
2^110819+1 = 1935823380424571697631280881
2^110899+1 = 509075540962889466017
2^110909+1 = 770432194150109347
2^110917+1 = 727651461392280043
2^110923+1 = 65476933834210720003425538913
2^110947+1 = 50771322887957337344353
2^111029+1 = 7182586703247506009
2^111103+1 = 663975330197147201531
2^111109+1 = 1729484624185407101618153
2^111121+1 = 74991590832739697
2^111143+1 = 66722490593050649190529
2^111211+1 = 72192650932622514067
2^111229+1 = 157517200252763339
2^111269+1 = 76602908006822468977
2^111301+1 = 21221563560086898313
2^111341+1 = 516844719540913647631468519961
2^111509+1 = 3725609409631134713
2^111509+1 = 85233935575689347
2^111577+1 = 692020081728450407321
2^111599+1 = 245393663959188883
2^111599+1 = 724025586915157911066899
2^111623+1 = 115937493150701947
2^111623+1 = 203103300969769354009
2^111641+1 = 24823417013975832649
2^111697+1 = 185828394324071417
2^111697+1 = 2683079450165557869398613187
2^111721+1 = 20123824899063272490598753
2^111781+1 = 28189374052921757085915257
2^111791+1 = 9751189493994636003971
2^111821+1 = 10416389967281467681
2^111821+1 = 26666212077327574650330739
2^111833+1 = 106303413937867067
2^111833+1 = 18714757354829626633
2^111893+1 = 6844003901836848067
2^111919+1 = 14039282793911716435841
2^111949+1 = 103606711690134381560233673
2^111949+1 = 16586205647299856179
2^111949+1 = 79999745460163651
2^111959+1 = 2682564874505934521
2^111977+1 = 9432834465383409131[/CODE]

[M]M268,435,459[/M] (exponent = 2[SUP]28[/SUP]+3) has been found to be composite by PRP-3 test.

The Wagstaff number with this same exponent has a small factor (414099276471761).

The "[URL="http://mprime.s3-website.us-west-1.amazonaws.com/new_mersenne_conjecture.html"]new Mersenne conjecture[/URL]", which is overwhelmingly likely to be trivially true, thus remains unrefuted.

[QUOTE=axn;500380]You can take 3k onwards to t40 (using P95 + GMP-ECM - just P95 alone would not be most efficient).[/QUOTE]

[QUOTE=GP2;500406]OK, let's do that.[/QUOTE]

I have ECM'd to t=40 the Wagstaff range from 3k to 5k.

There were 40 new factors of 35 different exponents. Only two exponents out of the 35 were previously unfactored. No new PRP cofactors resulted.

I'm continuing past 5k now. Only two cores are being used for this, so it's going slowly.

I'm also doing the 2k to 3k range to t=45. I've almost reached 2.3k, only p=2297 is still pending. There were 2 new factors of 2 different exponents. One of the 2 exponents was previously unfactored. No new PRP cofactors have resulted.

112k-114k
 

[CODE]2^112031+1 = 1910979345058022183326667
2^112103+1 = 83515512541366176140803
2^112139+1 = 5815743905218852233163
2^112199+1 = 2010215840685274597801
2^112199+1 = 786323718506582866249
2^112213+1 = 106497029548103220408449
2^112213+1 = 251422755955621961
2^112289+1 = 12512701387828660438033
2^112303+1 = 8311350638547158641
2^112397+1 = 2399240796804037893721132931
2^112459+1 = 375831592044995414089
2^112459+1 = 776445049666235026096699
2^112559+1 = 2794720627981248137
2^112571+1 = 49526001393468280031081
2^112573+1 = 636825460050432035150256611
2^112577+1 = 27551115531353237897
2^112621+1 = 1013589232168271434781929
2^112741+1 = 11668085678799635206529
2^112757+1 = 1261271778646931314310881
2^112799+1 = 20363535440517925993
2^112831+1 = 553025594888740113336467
2^112843+1 = 14887446047818700003
2^112843+1 = 1816520364952020859051
2^112859+1 = 2214390484782040843
2^112927+1 = 363455995504734793
2^112927+1 = 54000116293238248297
2^112951+1 = 12695680452667613129
2^112967+1 = 4018332491352410771
2^112979+1 = 188348147492137236527331553
2^112997+1 = 1824913074235208731
2^113011+1 = 2625547572826243961057
2^113023+1 = 21847818142372348880449
2^113023+1 = 86839986899358725835245929
2^113039+1 = 2015829528724557883
2^113039+1 = 2995800831811614859
2^113123+1 = 1643110379745335948319577
2^113143+1 = 69598053853807666387
2^113147+1 = 31318095488042954868313843
2^113147+1 = 6083084761062748733339
2^113149+1 = 1152833489823258508548560267
2^113149+1 = 8726751543730916009
2^113153+1 = 184455589859040989932097
2^113159+1 = 311118349570646689
2^113173+1 = 3268839850336231086269176698080107729
2^113173+1 = 918683847655298504676157788707
2^113189+1 = 487068254046171073
2^113213+1 = 59118312964102575769
2^113233+1 = 2720674525064101486628603
2^113287+1 = 2186655841902836641
2^113341+1 = 4489383701941289278750459
2^113341+1 = 5403379610851755529
2^113381+1 = 4635091610159983523765131
2^113383+1 = 167889695306414171
2^113417+1 = 29393519805369961673039899
2^113453+1 = 654252952523696921
2^113467+1 = 246374506417924394208427
2^113489+1 = 471672108093873191419
2^113501+1 = 76734603980709449891
2^113513+1 = 109626760389090963997819
2^113513+1 = 540575926005891362729
2^113537+1 = 143374729891998821507
2^113537+1 = 35290787662497113737
2^113539+1 = 543484110245446406177
2^113647+1 = 7270305779257350739841
2^113657+1 = 2375398635154102731999803
2^113683+1 = 4274281119942093092033
2^113719+1 = 154895530205772046800441427
2^113723+1 = 3034004502637956329
2^113837+1 = 147487993204082546009
2^113837+1 = 1493008605813853238113
2^113891+1 = 63942026456511010985131
2^113933+1 = 246570918531443273
2^113933+1 = 2546221246474770217
2^113933+1 = 563775020565030528315851
2^113947+1 = 2732539978758883817
2^113947+1 = 3297119904032099079089
2^113947+1 = 748152928956257484458707
2^113983+1 = 9013319653109434657[/CODE]

I am doing the 1300 to 2000 range with ECM up to t=50, using mprime for Stage 1 and GMP-ECM for stage 2.

I found a 48-digit factor today:

2^1301+1 has a factor: 158538524646017900250810607995506380920082613411

This is [I]just[/I] beyond the Cunningham range for 2+ odd. Obviously the factor would have been found long ago if the exponent was the least bit smaller.

It's been [URL="http://factordb.com/index.php?query=2%5E1301%2B1"]added to FactorDB[/URL]. Sigma was 117554418598932.

The 276-digit cofactor is composite.

Nice find! Congrats!

[QUOTE=GP2;519714]I am doing the 1300 to 2000 range with ECM up to t=50, using mprime for Stage 1 and GMP-ECM for stage 2.

I found a 48-digit factor today:

2^1301+1 has a factor: 158538524646017900250810607995506380920082613411

This is [I]just[/I] beyond the Cunningham range for 2+ odd. Obviously the factor would have been found long ago if the exponent was the least bit smaller.

It's been [URL="http://factordb.com/index.php?query=2%5E1301%2B1"]added to FactorDB[/URL]. Sigma was 117554418598932.

The 276-digit cofactor is composite.[/QUOTE]

You found a factor of Phi_n(2) for n=2602.

Who can give a list (or a text file) of factorization of Phi_n(2) for n<=2^16 like a text file [URL="https://oeis.org/A250197/a250197_1.txt"]factor of Phi_n(2) for n<=1280[/URL]?

(Same as [URL="https://stdkmd.net/nrr/repunit/phin10.htm"]https://stdkmd.net/nrr/repunit/phin10.htm[/URL], but is for Phi_n(2) instead of Phi_n(10))

Also the "First composite factors" (I know the n's are 1207, 1213, ...), "Smallest composite factors", "First blank Φn(2)", "Smallest blank Φn(2)", "Smallest blank Mersenne numbers" (I know this is n=1277), "Smallest blank Wagstaff numbers" (I know this is n=2246=1123*2), and "[URL="https://stdkmd.net/nrr/repunit/prpfactors.htm"]PRP factors list[/URL]", but all are for Phi_n(2) instead of Phi_n(10).

By the way, for the n's such that Phi_n(2) is (probable) prime, see [URL="https://oeis.org/A072226"]OEIS A072226[/URL].

[QUOTE=sweety439;519807]You found a factor of Phi_n(2) for n=2602.

Who can give a list (or a text file) of factorization of Phi_n(2) for n<=2^16 like a text file [URL="https://oeis.org/A250197/a250197_1.txt"]factor of Phi_n(2) for n<=1280[/URL]?

(Same as [URL="https://stdkmd.net/nrr/repunit/phin10.htm"]https://stdkmd.net/nrr/repunit/phin10.htm[/URL], but is for Phi_n(2) instead of Phi_n(10))

Also the "First composite factors" (I know the n's are 1207, 1213, ...), "Smallest composite factors", "First blank Φn(2)", "Smallest blank Φn(2)", "Smallest blank Mersenne numbers" (I know this is n=1277), "Smallest blank Wagstaff numbers" (I know this is n=2246=1123*2), and "[URL="https://stdkmd.net/nrr/repunit/prpfactors.htm"]PRP factors list[/URL]", but all are for Phi_n(2) instead of Phi_n(10).

By the way, for the n's such that Phi_n(2) is (probable) prime, see [URL="https://oeis.org/A072226"]OEIS A072226[/URL].[/QUOTE]

Also... (for Phi_n(2) for n<=2^16)

??? of 65536 Φn(2) factorization were finished.
??? of 65536 Φn(2) factorization were cracked.
12 of 16 Fermat factorization were finished.
16 of 16 Fermat factorization were cracked.
??? of 6542 Mersenne factorization were finished.
??? of 6542 Mersenne factorization were cracked.
??? of 3512 Wagstaff factorization were finished.
??? of 3512 Wagstaff factorization were cracked.
??? (probable) prime factors were discovered.
??? composite factors are remaining.
??? factors are unidentified.

I want to know how many..? (like [URL="https://stdkmd.net/nrr/repunit/"]https://stdkmd.net/nrr/repunit/[/URL], but for Phi_n(2) instead of Phi_n(10))

[QUOTE=sweety439;519807]Who can give a list (or a text file) of factorization of Phi_n(2) for n<=2^16 like a text file?[/QUOTE]I'm almost tempted to do so. Won't happen today though.

[QUOTE=xilman;519810]I'm almost tempted to do so. Won't happen today though.[/QUOTE]

Thanks!!!