[QUOTE=paulunderwood;496736]Factors of Mersennes are 8*n+-1 and factors of Wagstaff are 8*m+-3.[/QUOTE]
That is incorrect. Wagstaff factors are 8n + {1,3}. So 1 (mod 8) is a common class for both of them.

[QUOTE=GP2;496734]It appears that the set of all factors of all Mersenne numbers with prime exponent and the set of all factors of all Wagstaff numbers with prime exponent are disjoint. Is there an elementary proof of this?
[/QUOTE]
Yes, znorder( Mod(2, f) ) = p for f | 2^p-1 and znorder( Mod(2, g) ) = 2p where g | (2^p+1)/3. Therefore they are disjoint sets.

[QUOTE=axn;496778]That is incorrect. Wagstaff factors are 8n + {1,3}. So 1 (mod 8) is a common class for both of them.
[/QUOTE]

Thanks for the correction! :blush:

[QUOTE=axn;496778]
Yes, znorder( Mod(2, f) ) = p for f | 2^p-1 and znorder( Mod(2, g) ) = 2p where g | (2^p+1)/3. Therefore they are disjoint sets.[/QUOTE]

Wrong proof. Nobody (except me) recognise that p=3 is a common factor?

[QUOTE=R. Gerbicz;496792]Wrong proof. Nobody (except me) recognise that p=3 is a common factor?[/QUOTE]

Except for the trivial exception of 3, are there any other case where the proof fails?

2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime!


[URL="http://factordb.com/index.php?query=2%5E19379%2B1"]http://factordb.com/index.php?query=2%5E19379%2B1[/URL]


P5804 [URL]http://factordb.com/index.php?id=1100000001172464482[/URL]

[QUOTE=pinhodecarlos;497063]2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime!


[URL="http://factordb.com/index.php?query=2%5E19379%2B1"]http://factordb.com/index.php?query=2%5E19379%2B1[/URL]


P5804 [URL]http://factordb.com/index.php?id=1100000001172464482[/URL][/QUOTE]

This had me fooled at first, but:

[CODE]factor 1767177497789872389034125489321
1767177497789872389034125489321: 3 11627401 50661292745468868151307
[/CODE]

and:
[CODE]
time ./pfgw64 -k -f0 -od -q"(2^19379+1)/3/50661292745468868151307/11627401" | ../../coding/gwnum/s2 - 1 2 19379 1

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

real 0m0.212s
user 0m0.304s
sys 0m0.000s
[/CODE]

[QUOTE=pinhodecarlos;497063]2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime![/QUOTE]

:w00t: Congratulations!

17500-18000
[CODE]2^17551+1 has a factor: 25735713653693529449 (ECM curve 8, B1=250000, B2=25000000)
2^17569+1 has a factor: 179227535070013504018942273739 (ECM curve 98, B1=250000, B2=25000000)
2^17569+1 has a factor: 2206370228865414510833059 (ECM curve 7, B1=250000, B2=25000000)
2^17581+1 has a factor: 105547448860925250997366606819 (ECM curve 483, B1=250000, B2=25000000)
2^17581+1 has a factor: 40091191606504248827275161779123 (ECM curve 98, B1=250000, B2=25000000)
2^17623+1 has a factor: 698517626064061766822912882747 (ECM curve 25, B1=250000, B2=25000000)
2^17627+1 has a factor: 19897288830906370321 (ECM curve 44, B1=250000, B2=25000000)
2^17681+1 has a factor: 1640778478824054691934851 (ECM curve 139, B1=250000, B2=25000000)
2^17707+1 has a factor: 145380863162377258174769 (ECM curve 64, B1=250000, B2=25000000)
2^17713+1 has a factor: 621845319559233013940510249 (ECM curve 196, B1=250000, B2=25000000)
2^17737+1 has a factor: 1176542531701657484481082913 (ECM curve 212, B1=250000, B2=25000000)
2^17783+1 has a factor: 12488572654928988532921782764588801 (ECM curve 298, B1=250000, B2=25000000)
2^17807+1 has a factor: 553279164410641071695422843 (ECM curve 151, B1=250000, B2=25000000)
2^17807+1 has a factor: 63431661672479249 (ECM curve 1, B1=250000, B2=25000000)
2^17827+1 has a factor: 6486130363802766148587218449 (ECM curve 357, B1=250000, B2=25000000)
2^17851+1 has a factor: 8989993295392804145476248169 (ECM curve 225, B1=250000, B2=25000000)
2^17863+1 has a factor: 74167942985744072715878249 (ECM curve 11, B1=250000, B2=25000000)
2^17881+1 has a factor: 2806154593843559467 (ECM curve 10, B1=250000, B2=25000000)
2^17957+1 has a factor: 40852609716914003537511405329 (ECM curve 348, B1=250000, B2=25000000)
2^17959+1 has a factor: 461118648758359233113203 (ECM curve 31, B1=250000, B2=25000000)[/CODE]

20000-22000
[CODE]2^20023+1 has a factor: 37510552791647458771
2^20051+1 has a factor: 257425412435536649
2^20051+1 has a factor: 3869488172299271890904297
2^20063+1 has a factor: 4659288072900311334648711315841
2^20107+1 has a factor: 2743589598602187505747
2^20117+1 has a factor: 4890446030623424048707
2^20129+1 has a factor: 46208108810799404871122419
2^20143+1 has a factor: 964033675819142651
2^20161+1 has a factor: 134469591069683
2^20173+1 has a factor: 743601397045097627453299
2^20219+1 has a factor: 182985666224987960298637765803059
2^20233+1 has a factor: 4189494144638412163
2^20249+1 has a factor: 6271693669868573161299252319777
2^20261+1 has a factor: 3103962310297339
2^20297+1 has a factor: 13133704985817620272140420384689
2^20333+1 has a factor: 47794427621302424593025083
2^20359+1 has a factor: 857182102209462004718363615779
2^20389+1 has a factor: 4106216082433866721
2^20407+1 has a factor: 1991711889529714740363107681
2^20477+1 has a factor: 4408421234877896603
2^20479+1 has a factor: 2403526884029539686014236094659
2^20479+1 has a factor: 3422976667427
2^20483+1 has a factor: 11413480849819
2^20483+1 has a factor: 1924821469502924137
2^20521+1 has a factor: 3109639586095160002494173679115321
2^20533+1 has a factor: 20557323121358214361
2^20543+1 has a factor: 2308491964735217383129886833
2^20563+1 has a factor: 2522018807708129
2^20593+1 has a factor: 8157158140843971595528897248457
2^20611+1 has a factor: 4167333623203120606265560076873
2^20627+1 has a factor: 16001463124310535561113
2^20641+1 has a factor: 1680552399763578899
2^20641+1 has a factor: 44709189903899
2^20693+1 has a factor: 11039167817257937443157587
2^20693+1 has a factor: 32372699951864750067423360211
2^20719+1 has a factor: 283203828833237869481
2^20749+1 has a factor: 20391614891030525371
2^20753+1 has a factor: 48003675801500392248161
2^20789+1 has a factor: 1364080160622986883250321266667
2^20789+1 has a factor: 214237277547136797379
2^20807+1 has a factor: 5750818063280593
2^20849+1 has a factor: 156575928020521902700628923
2^20849+1 has a factor: 711635844333463783790443043
2^20857+1 has a factor: 71042575998539
2^20873+1 has a factor: 532684992928685427252905009
2^20903+1 has a factor: 18661968104583443235718665731
2^20921+1 has a factor: 2027720050341472185904615803073
2^20921+1 has a factor: 335520589852300390243
2^20939+1 has a factor: 20933804099550553
2^20947+1 has a factor: 3088382574101887558709344614683
2^20963+1 has a factor: 4355362012024784470653011
2^20981+1 has a factor: 51942572296376948317505038164957371
2^21013+1 has a factor: 3668929788863717138772900457
2^21017+1 has a factor: 16593735922243244859134070491
2^21023+1 has a factor: 2660003581454497729459
2^21031+1 has a factor: 15498026210331776641
2^21059+1 has a factor: 10892326048051503533266007123
2^21067+1 has a factor: 19933173060194242778264017
2^21101+1 has a factor: 20275268810217203
2^21121+1 has a factor: 150766158290940179027587
2^21121+1 has a factor: 764232573191224161100819
2^21121+1 has a factor: 86463076942819
2^21149+1 has a factor: 3230258365665452655137
2^21163+1 has a factor: 95559678958037312400273961
2^21211+1 has a factor: 3832944410199417231337
2^21211+1 has a factor: 683495906696251150826234104545947
2^21247+1 has a factor: 48095430631346489
2^21313+1 has a factor: 568787927050811249
2^21317+1 has a factor: 11298468738572894718067
2^21317+1 has a factor: 4389851798588466214795562339
2^21341+1 has a factor: 449867031167363
2^21341+1 has a factor: 49591774383454134099132643
2^21379+1 has a factor: 1299003843005694933567331
2^21379+1 has a factor: 54798678469523996671365241
2^21383+1 has a factor: 3438568416814276987709579
2^21391+1 has a factor: 134477468200008576403553689313
2^21391+1 has a factor: 43007001846266587
2^21397+1 has a factor: 167380355069488915217
2^21467+1 has a factor: 806646395384184216569
2^21487+1 has a factor: 5758749036874074697366069067
2^21493+1 has a factor: 25553144664907
2^21503+1 has a factor: 16916741153700802937
2^21523+1 has a factor: 77381746151979035203
2^21529+1 has a factor: 1702941136495035897886291
2^21529+1 has a factor: 465086981569239321244339
2^21557+1 has a factor: 4694330692397593661473
2^21569+1 has a factor: 361772772464521091
2^21569+1 has a factor: 425895424990514993
2^21587+1 has a factor: 579269658222000497
2^21649+1 has a factor: 1413110454707564001068513
2^21649+1 has a factor: 50269535917652870459
2^21649+1 has a factor: 6922502237649947040849362251
2^21661+1 has a factor: 475888569773731407813690353
2^21727+1 has a factor: 49809185155493429630858507
2^21737+1 has a factor: 177903299744917729
2^21751+1 has a factor: 542538499273227893441
2^21757+1 has a factor: 22624105778237266001406089
2^21773+1 has a factor: 2487149567869465481
2^21773+1 has a factor: 308672408980908803
2^21787+1 has a factor: 50290917986637486315257
2^21803+1 has a factor: 144985052235826097
2^21821+1 has a factor: 30696428098561013756621570419963
2^21863+1 has a factor: 13204242361797596073473843
2^21881+1 has a factor: 156579746660319571
2^21881+1 has a factor: 24286354927538843123
2^21893+1 has a factor: 1031342237529259
2^21893+1 has a factor: 23100546344437470254058168365009
2^21893+1 has a factor: 34722125531238472939
2^21911+1 has a factor: 23235161223671815545480155441
2^21961+1 has a factor: 765091067506747755283
2^21977+1 has a factor: 9552297931135241269073[/CODE]

Almost done with 18000-20000.

[QUOTE=pinhodecarlos;497404]Almost done with 18000-20000.[/QUOTE]

Sure. I'll send you the next range (24500-26500) shortly. Let me know if you want to adjust the range up/down.