Mersenneplustwo Factorizations (wiki)

Last updated 2023-03-09. Please contact bearnol@gmail.com (James Wanless) for support, or search http://groups.google.com/group/Mersenneplustwo.

Mersenneplustwo numbers are those integers that are two more than a Mersenne prime. Mersenne primes are of the form 2^p-1 (http://www.mersenne.org/). This makes Mersenneplustwo numbers of the form 2^p+1. This project aims to find the factors (ie integer divisors) of Mersenneplustwo numbers.

1) For Twokp binaries click here.

2) For ECM binaries click here. (Java ECM implementation courtesy Dario Alpern). For ECMNet binaries click here. [ECMNet courtesy Mark Rodenkirch/Tim Charron]. GMP-ECM.

ECMNet v2.7.2 server running at bearnol.is-a-geek.com, port 8194 (http://www.loria.fr/~zimmerma/records/ecm/implementations.html). Status.

3) For WE binaries click here. [WE algorithm © James Wanless 2000]

WEP-Boinc server running at http://bearnol.is-a-geek.com/wanless2 [ALPHA software – use at your own risk!]

For estimated running times, please see the stats page.

E(f(M+2)) = ln(ln((M+2)/2p))+1

Index

p

E(f(M+2))

f(M+2)

f

1

2

-0.5

1

5

2

3

0.1

2

3*3

3

5

1.2

2

3*11

4

7

1.8

2

3*43

5

13

2.7

2

3*2731

6

17

3.1

2

3*43691

7

19

3.3

2

3*174763

8

31

3.9

2

3*715827883

9

61

4.6

2

3*768614336404564651

10

89

5

4

3*179*62020897*18584774046020617

11

107

5.2

3

3*643*84115747449047881488635567801

12

127

5.4

2

3*56713727820156410577229101238628035243

13

521

6.9

5

3*501203*443418473521*90268296000189649868678102552775904610963*114062739354387553292910924965889823099187127149057482935407583490192322022502109238664809064671779

14

607

7

7

3*115331*202769117249*16780869326776069043*1622949422129340362249*1956783675173062584155810896697*142061366373466838976870126736192084529788567581972935261638677786736545303496932385392586871843

15

1279

7.8

7

3*706009*3107971*18970768920015252259*115217370846302143114697*728012485667587623793883*993606175009756847472391899814986540430475219741214523758037853444326702794519221253698310818011397675216288870561456112583584428088532799849918530108210299393382273915481171832640932460649156171149976820183188772235159422178758127844554927754096501538179015384479228533295586732233666016869867824298350313

16

2203

8.3

>7

3*13219[AB]*208613913329[AB][wep,rb=6e6]*282324958084937237369[AB]*743372438374143806443[AB]*848425589476255002200418022118728331[TF] [ecm,d>60] [wep,rb>240e10]

17

2281

8.4

>4

3*22811[AB]*95803[AB] [ecm,d>60]

18

3217

8.7

>3

3*7489177[AB] [ecm,d>55]

19

4253

9

>7

3*118071787[AB][wep,rb=1e4]*37876820097827[AB][wep,rb=240e6]*73544505579481[AB]*6992931471271979[AB]*2911147666084217753[AB] [ecm,d>50] [wep,rb>400e6]

20

4423

9

>4

3*2827782322058633[AB]*891652724140019407160713[AB] [ecm,d>50]

21

9689

9.8

>5

3*19379[AB]*835223600534258267[AB]*1467554643492452667875087107[AB] [ecm,d>50]

22

9941

9.8

>5

3*11120148512909357034073[AB]*2937581555281521885883181942758904369[JW,2005-6-05]*53490436327391844747326672641668581779[CG,2005-9-20] [ecm,d>50]

23

11213

10

>3

3*181122707148161338644285289935461939[DT,2005-1-18] [ecm,d>50]

24

19937

10.5

>2

3 [ecm,d>50]

25

21701

10.6

>4

3*43403[DT]*660057617[DT] [ecm,d>50]

26

23209

10.7

>5

3*4688219[DT]*27665129[DT]*128201605404515119370139202836664201936768339[yC,2010-12-05] [ecm,d>50]

27

44497

11.3

>3

3*2135857[DT] [ecm,d>40]

28

86243

12

>4

3*1627710365249[DT][wep,rb=206e3]*72063880646676880537[DT,2005-2-02] [ecm,d>40] [wep,rb>412e3]

29

110503

12.2

>3

3*48832113344350037579071829046935480686609[JW,2017-11-25] [ecm,d>40]

30

132049

12.4

>3

3*618913299601153[DT,2005-2-02][wep,rb=29e3] [ecm,d>40] [wep,rb>88e3]

31

216091

12.9

>3

3*10704103333093885136919332089553661899[ys,2011-11-21] [ecm,d>40]

32

756839

14.2

>3

3*1640826953[DT][wep,rb=120] [ecm,d>35] [wep,rb>240]

33

859433

14.3

>6

3*1718867[DT][wep,rb=1]*268143097[DT][wep,rb=30]*229733542465352507[JW,2005-7-29]*4202079252549756513473[CG,2005-12-18] [ecm,d>35] [wep, rb>60]

34

1257787

14.7

>5

3*20124593[AK][wep,rb=1]*276519162416003291[JW,2005-7-30]*900228597258955415819[JW,2007-11-28] [ecm,d>35] [wep,rb>1e3]

35

1398269

14.8

>3

3*23609117451215727502931[JB,2007-7-02] [ecm,d>35]

36

2976221

15.5

>5

3*434313978089[DT]*4230621174520057[CG,2006-1-25]*22968413704492177[JW,2005-8-02] [ecm,d>35] [wep,rb>100]

37

3021377

15.6

>4

3*95264016811[DT]*510207862179110491801[JW,2008-04-08] [ecm,d>35] [wep,rb>358]

38

6972593

16.4

>4

3*142921867730820791335455211[JW,2016-07-26]*2194866270224408542085820822929656883[JW,2016-07-28] [ecm,d>30]

39

13466917

17

>6

3*781081187[DT]*2262442057[DT]*658043023758050881[JW,2006-10-21]*1808838937982978761[JW,2006-10-04] [ecm,d>30]

40

20996011

17.5

>3

3*50965926368055564259063193[JW,2018-01-13] [ecm,d>30]

41

24036583

17.6

>5

3*11681779339[AK]*455181217684410622619[JW,2016-3-25]*228826184600325074341662763[JW,2010-02-28] [ecm,d>30]

42

25964951

17.7

>5

3*155789707[JW,2005-2-27]*812215323627522177851[JW,2010-4-06]*724704549317978699462953[JW,2010-4-06] [ecm,d>30]

43

30402457

17.9

>2

3 [ecm,d>30]

44

32582657

17.9

>3

3*13526662966442476828963[JW,2010-12-06] [ecm,d>30]

45

37156667

18.1

>3

3*297253337[JW,2008-9-16] [ecm,d>30]

46

42643801

18.2

>3

3*405661842777846034141594389769[JW,2019-5-12] [ecm,d>30]

47

43112609

18.2

>6

3*86225219[JW,2008-9-16]*5259738299[JW,2008-9-16]*5949540043[JW,2008-9-16]*12482997260297[JW,2008-9-16] [ecm,d>25]

48

57885161

18.5

>4

3*7061989643[JW,2013-2-05]*100271784664656667[JW,2013-2-05] [ecm,d>30]

49

74207281

18.8

>2

3 [ecm,d>25]

50

77232917

18.8

>3

3*3460697185562027[JW,2018-1-03] [ecm,d>25]

51

82589933

18.9

>3

3*17973642059656480077259129[JW,2020-5-25] [ecm,d>25]

~225

M127

88.7

>2

3*886407410000361345663448535540258622490179142922169401[FM,2020-7-05] [2kp,k>1e12]

JB=J. Berg

AB=Arjen Bot

yC=yoyo@home/[P3D] Crashtest

TF=Tony Forbes

CG=?CG to advise?

AK=Alex Kruppa

FM=Fan Ming

ys=yoyo@home/shauge

DT=?DT to advise?

JW=James Wanless

Thank you to these, and all the other people who have contributed computer-time!