Mersenneplustwo Factorizations (wiki)
Last updated 2023-07-10. 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>250e10] |
17 |
2281 |
8.4 |
>4 |
3*22811[AB]*95803[AB] [ecm,d>60] [wep,rb>10e6] |
18 |
3217 |
8.7 |
>3 |
3*7489177[AB] [ecm,d>55] [wep,rb>10e6] |
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] [wep,rb>1e6] |
21 |
9689 |
9.8 |
>5 |
3*19379[AB]*835223600534258267[AB]*1467554643492452667875087107[AB] [ecm,d>50] [wep,rb>1e6] |
22 |
9941 |
9.8 |
>5 |
3*11120148512909357034073[AB]*2937581555281521885883181942758904369[JW,2005-6-05]*53490436327391844747326672641668581779[CG,2005-9-20] [ecm,d>50] [wep,rb>1e6] |
23 |
11213 |
10 |
>3 |
3*181122707148161338644285289935461939[DT,2005-1-18] [ecm,d>50] [wep,rb>1e6] |
24 |
19937 |
10.5 |
>2 |
3 [ecm,d>50] [wep,rb>1e6] |
25 |
21701 |
10.6 |
>4 |
3*43403[DT]*660057617[DT] [ecm,d>50] [wep,rb>1e6] |
26 |
23209 |
10.7 |
>5 |
3*4688219[DT]*27665129[DT]*128201605404515119370139202836664201936768339[yC,2010-12-05] [ecm,d>50] [wep,rb>1e6] |
27 |
44497 |
11.3 |
>3 |
3*2135857[DT] [ecm,d>40] [wep,rb>1e6] |
28 |
86243 |
12 |
>4 |
3*1627710365249[DT][wep,rb=206e3]*72063880646676880537[DT,2005-2-02] [ecm,d>40] [wep,rb>1e6] |
29 |
110503 |
12.2 |
>3 |
3*48832113344350037579071829046935480686609[JW,2017-11-25] [ecm,d>40] [wep,rb>1e6] |
30 |
132049 |
12.4 |
>3 |
3*618913299601153[DT,2005-2-02][wep,rb=29e3] [ecm,d>40] [wep,rb>1e6] |
31 |
216091 |
12.9 |
>3 |
3*10704103333093885136919332089553661899[ys,2011-11-21] [ecm,d>40] [wep,rb>1e6] |
32 |
756839 |
14.2 |
>3 |
3*1640826953[DT][wep,rb=120] [ecm,d>35] [wep,rb>1e3] |
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>1e3] |
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] [wep,rb>1e3] |
36 |
2976221 |
15.5 |
>5 |
3*434313978089[DT]*4230621174520057[CG,2006-1-25]*22968413704492177[JW,2005-8-02] [ecm,d>35] [wep,rb>200] |
37 |
3021377 |
15.6 |
>4 |
3*95264016811[DT]*510207862179110491801[JW,2008-04-08] [ecm,d>35] [wep,rb>500] |
38 |
6972593 |
16.4 |
>4 |
3*142921867730820791335455211[JW,2016-07-26]*2194866270224408542085820822929656883[JW,2016-07-28] [ecm,d>35] |
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>30] |
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 |
88.7 |
>2 |
3*886407410000361345663448535540258622490179142922169401[FM,2020-7-05] [2kp,k>1e12] |
JB=J. Berg
AB=Arjen Bot
TF=Tony Forbes
CG=?CG to advise?
AK=Alex Kruppa
FM=Fan Ming
DT=?DT to advise?
Thank you to these, and all the other people who have contributed computer-time!