Factoring (generalized) Fermat numbers

Fermat factors found

2864929972774011*241+1 divides 2239 + 1 (7.12.2012)
143918649*24654+1 divides 224652 + 1 (9.10.2012)
1784180997819127957596374417642156545110881094717*216+1 divides 2214+1 (3.2.2010, ECM)

Generalized Fermat factors found

299539*242762+1 divides 11242760 + 8242760 (13.4.2015)
296347*240802+1 divides 12240801 + 7240801 (10.4.2015)
284601*243484+1 divides 6243480 + 1 (5.4.2015)
5307525893895917242366340332957337689*214+1 divides 6213 + 1 (28.1.2015, ECM)
1358193*229412+1 divides 11229410 + 4229410 (27.12.2014)
1074965*229829+1 divides 12229828 + 7229828 (19.12.2014)
1038791*228729+1 divides 11228728 + 5228728 (3.12.2014)
1037277*228598+1 divides 3228594 + 1 (2.12.2014)
57737*262247+1 divides 8262246 + 5262246 (10.10.2014)
57019*263970+1 divides 9263969 + 5263969 (18.7.2014)
51949*280234+1 divides 12280233 + 1 (2.5.2014)
52743*284180+1 divides 9284178 + 2284178 (10.4.2014)
52527*274942+1 divides 11274940 + 10274940 (20.3.2014)
51525*286490+1 divides 9286488 + 2286488 (20.3.2014)
53463*264061+1 divides 11286752 + 6286752 (14.3.2014)
52395*286753+1 divides 11286752 + 3286752 (7.2.2014)
52017*298472+1 divides 10298471 + 9298471 (2.1.2014)
107957*258343+1 divides 10258341 + 7258341 (25.12.2013)
106737*252618+1 divides 9252617 + 7252617 (24.12.2013)
105087*250118+1 divides 11250117 + 6250117 (17.12.2013)
3075606176684927981313930069826611108475792452445*210+1 divides 1128 + 528 (22.9.2013, ECM)
51651074664519*249+1 divides 10246 + 1 (5.9.2013)
12093892381215*266+1 divides 3264 + 1 (29.8.2013)
18657*2152163+1 divides 52152162 + 22152162 (13.6.2013)
16683*2158432+1 divides 112158431 + 82158431 (5.6.2013)
266019*234543+1 divides 7234541 + 6234541 (3.2.2013)
271119*234433+1 divides 8234431 + 5234431 (26.1.2013)
284699*235083+1 divides 7235081 + 5235081 (24.1.2013)
52608577*24696+1 divides 924693 + 724693 (6.12.2012)
65517225*24666+1 divides 924664 + 524664 (2.11.2012)
191630505*24664+1 divides 1124662 + 824662 (1.11.2012)
57724945*24858+1 divides 1124854 + 624854 (30.10.2012)
195975843*24740+1 divides 524738 + 324738 (29.9.2012)
87064885*24912+1 divides 524909 + 424909 (27.9.2012)
139978813*24550+1 divides 1124548 + 324548 (22.9.2012)
420231*228531+1 divides 11228530 + 9228530 (25.4.2012)
236043*229292+1 divides 8229290 + 1 (9.4.2012)
454245*229581+1 divides 11229576 + 8229576 (6.4.2012)
223875*229830+1 divides 5229827 + 2229827 (4.4.2012)
2996017*212888+1 divides 12212887 + 1 (21.3.2012)
2931621*212804+1 divides 8212803 + 5212803 (16.3.2012)
3931131*212891+1 divides 11212980 + 5212980 (15.3.2012)
531561*223907+1 divides 11223906 + 1 (2.11.2011)
132997*243936+1 divides 8243935 + 3243935 (30.10.2011)
180837*241858+1 divides 10241855 + 9241855 (21.10.2011)
120491*243659+1 divides 9243656 + 2243656 (16.10.2011)
124425*243586+1 divides 11243583 + 3243583 (15.10.2011)
407304603106063483079172393194013665752688271*29 + 1 divides 828+528(28.4.2011, GNFS)
130979*240315+1 divides 10240314+9240313 (23.1.2011)
142539*240054+1 divides 12240046+1 (25.11.2010)
1542198568081*244+1 divides 11243+3243 (17.11.2010)
1776222707793*238+1 divides 12237+11237 (15.11.2010)
1126076307213*248+1 divides 10246+9246 (4.11.2010)
1743008953897*236+1 divides 12234+11234 (2.11.2010)
1080162533745*240+1 divides 5238+4238 (29.10.2010)
1017106336065*239+1 divides 8236+7236 (28.10.2010)
4939288522896862862274058441750761001846486945939098334865201*29 + 1 divides 1128+328(17.10.2010, GNFS)
1310333370909*227+1 divides 5226+1 (21.9.2010)
1757605718005*224+1 divides 9222+2222 (19.9.2010)

Searched ranges

From nTo nFrom kTo kStatusFactors
24241,099,511,627,7762,000,000,000,000Completed (gfn)1 (gfn)
25501,000,000,000,0002,000,000,000,000Completed (gfn)7 (gfn)
29311,000,000,000,000,0002,000,000,000,000,000Completed0
3030200,000,000,000,000400,000,000,000,000Completed0
33341,000,000,000,000,0002,000,000,000,000,000Completed0
353571,000,000,000,000,00080,000,000,000,000,000Completed0
3737450,000,000,000,0001,200,000,000,000,000Completed0
37374,500,000,000,000,0005,000,000,000,000,000Completed0
373713,000,000,000,000,00016,000,000,000,000,000Completed0
373718,000,000,000,000,00024,000,000,000,000,000Completed0
373736,000,000,000,000,00050,000,000,000,000,000Completed0
373761,000,000,000,000,00072,057,594,037,927,936Completed0
3838500,000,000,000,0001,400,000,000,000,000Completed0
38386,000,000,000,000,00012,000,000,000,000,000Completed0
383818,000,000,000,000,00025,000,000,000,000,000Completed0
3838120,000,000,000,000,000160,000,000,000,000,000Completed0
3939200,000,000,000,000300,000,000,000,000Completed0
39392,250,000,000,000,00010,000,000,000,000,000Completed0
40401,000,000,000,000,0002,000,000,000,000,000Completed0
404020,000,000,000,000,00030,000,000,000,000,000Completed0
414120,000,000,000,000,00030,000,000,000,000,000Completed0
40442,000,000,000,000,0003,000,000,000,000,000Completed1
4242200,000,000,000,000600,000,000,000,000Completed0
575950,000,000,000,000100,000,000,000,000Completed0
58632,500,000,000,000,0003,000,000,000,000,000Completed0
63631,000,000,000,000,0002,000,000,000,000,000Completed0
70743,200,000,000,000,0005,000,000,000,000,000Completed0
70735,000,000,000,000,00010,000,000,000,000,000Completed0
1501591,000,000,000,0001,100,000,000,000Completed0
58058920,000,000,00035,000,000,000Completed0
4,5004,99950,000,000200,000,000Completed (gfn)1 + 7 (gfn)
12,00012,9992,000,0005,000,000Completed (gfn)3 (gfn)
23,00023,999500,0001,000,000Completed (gfn)1 (gfn)
28,00030,000200,000500,000Completed (gfn)4 (gfn)
28,00030,0001,000,0001,500,000Completed (gfn)4 (gfn)
33,00035,000200,000250,000Completed (gfn)0
33,00036,000250,000300,000Completed (gfn)3 (gfn)
40,00145,000100,000300,000Completed (gfn)9 (gfn)
50,00060,000100,000125,000Completed (gfn)3 (gfn)
61,000100,00050,00060,000Completed (gfn)9 (gfn)
150,001160,00010,00020,000Completed (gfn)2 (gfn)

ECM curves on Fermat numbers.

abmdigits11e35e425e41e63e611e643e611e726e78e82e9comments
21121133000000002870619(1)3
2113239100000002571087(2)00
211448800000000834600Factor found!
2115980800000013218000
211616964000000693000
21173939500000010000
21187888400000900000
2119157770000064000000
212031565300003523000000(no factor known)
2121631294000184600000
21221262577000516000000
21232525215000576000000
212450504460013328000000(no factor known)
212510100842001000000000
212620201768056000000000
By default B2 = 100*B1
(1) 430 with B2=8e10, 189 with B2=15892582605916
(2) 21 with B2=26e9, rest with B2=3178559884516

ECM curves on generalized Fermat numbers.

abmdigits11e35e425e41e63e611e643e611e726e7comments
85814900006073230000GNFS-factored
11381430000020020000GNFS-factored
115822800006054010241290ECM-factored
95821500006029105120
97818000006055905120
1038190000107055010955120
109825700006054010245120
114826700006053910245120
117824100006053910245120
118826700006053910245120
1110821700006054910245120
127819700006054111645120
539319000031040000
519329000411000100010001000
1019473000500005100
121955300000500015001000
6110777000211000100010000
61111543003451000000
6112312600005000000
611363755111001001051100Factor found!
6114127300001001000000
61152549400010000000
6116509800010010000000
61171019700010010000000
611820397300400000000
611940796905021500000
6120815908000000000
3210449001002005202000
32119690020020000000
43111182002001500000
32121943050754000000
3213387602066000000
321477520400000000
321515610331010000000
3216312514020000000
3217625276910000000
3218125075100000000
31192501250101001200000

Sierpinksi numbers of the first kind

Sierpinski proved that possible prime numbers of the form nn + 1 are Fermat numbers with m = k + 2k. So, these numbers form a special subset of the Fermat numbers.

kmStatusKnown search limitMy search
015 is a prime--
13257 is a prime--
26composite with known factors--
311composite with known factors--
420composite with no known factor--
5371275438465*239+1 divides6,000,000,000,000,000-
670unknown1,000,000,000,000,000-
7135unknown100,000,000,000,000-
8264unknown200,000,000,000-
9521unknown40,000,000,000-
101034unknown4,100,000,0006,040,000,000
112059591909*22063+1 divides1,500,000,000-
124108unknown200,000,0001,000,000,000
138205unknown30,000,000100,000,000
1416398unknown5,000,00050,000,000
1532783unknown300,00022,000,000
1665552unknown50,0001,500,000
17131089unknown20,000278,000
18262162unknown10,000100,000
19524307unknown10,00097,800
201048596unknown1,200135,500
212097173unknown1,20022,260
- last update 29.2.2016 -