Factoring (generalized) Fermat numbers
Fermat factors found
143918649*24654+1 divides 224652 + 1 (9.10.2012)
1784180997819127957596374417642156545110881094717*216+1 divides 2214+1 (3.2.2010, ECM)
Generalized Fermat factors found
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 n | To n | From k | To k | Status | Factors |
---|---|---|---|---|---|
24 | 24 | 1,099,511,627,776 | 2,000,000,000,000 | Completed (gfn) | 1 (gfn) |
25 | 50 | 1,000,000,000,000 | 2,000,000,000,000 | Completed (gfn) | 7 (gfn) |
29 | 31 | 1,000,000,000,000,000 | 2,000,000,000,000,000 | Completed | 0 |
30 | 30 | 200,000,000,000,000 | 400,000,000,000,000 | Completed | 0 |
33 | 34 | 1,000,000,000,000,000 | 2,000,000,000,000,000 | Completed | 0 |
35 | 35 | 71,000,000,000,000,000 | 80,000,000,000,000,000 | Completed | 0 |
37 | 37 | 450,000,000,000,000 | 1,200,000,000,000,000 | Completed | 0 |
37 | 37 | 4,500,000,000,000,000 | 5,000,000,000,000,000 | Completed | 0 |
37 | 37 | 13,000,000,000,000,000 | 16,000,000,000,000,000 | Completed | 0 |
37 | 37 | 18,000,000,000,000,000 | 24,000,000,000,000,000 | Completed | 0 |
37 | 37 | 36,000,000,000,000,000 | 50,000,000,000,000,000 | Completed | 0 |
37 | 37 | 61,000,000,000,000,000 | 72,057,594,037,927,936 | Completed | 0 |
38 | 38 | 500,000,000,000,000 | 1,400,000,000,000,000 | Completed | 0 |
38 | 38 | 6,000,000,000,000,000 | 12,000,000,000,000,000 | Completed | 0 |
38 | 38 | 18,000,000,000,000,000 | 25,000,000,000,000,000 | Completed | 0 |
38 | 38 | 120,000,000,000,000,000 | 160,000,000,000,000,000 | Completed | 0 |
39 | 39 | 200,000,000,000,000 | 300,000,000,000,000 | Completed | 0 |
39 | 39 | 2,250,000,000,000,000 | 10,000,000,000,000,000 | Completed | 0 |
40 | 40 | 1,000,000,000,000,000 | 2,000,000,000,000,000 | Completed | 0 |
40 | 40 | 20,000,000,000,000,000 | 30,000,000,000,000,000 | Completed | 0 |
41 | 41 | 20,000,000,000,000,000 | 30,000,000,000,000,000 | Completed | 0 |
40 | 44 | 2,000,000,000,000,000 | 3,000,000,000,000,000 | Completed | 1 |
42 | 42 | 200,000,000,000,000 | 600,000,000,000,000 | Completed | 0 |
57 | 59 | 50,000,000,000,000 | 100,000,000,000,000 | Completed | 0 |
58 | 63 | 2,500,000,000,000,000 | 3,000,000,000,000,000 | Completed | 0 |
63 | 63 | 1,000,000,000,000,000 | 2,000,000,000,000,000 | Completed | 0 |
70 | 74 | 3,200,000,000,000,000 | 5,000,000,000,000,000 | Completed | 0 |
70 | 73 | 5,000,000,000,000,000 | 10,000,000,000,000,000 | Completed | 0 |
150 | 159 | 1,000,000,000,000 | 1,100,000,000,000 | Completed | 0 |
580 | 589 | 20,000,000,000 | 35,000,000,000 | Completed | 0 |
4,500 | 4,999 | 50,000,000 | 200,000,000 | Completed (gfn) | 1 + 7 (gfn) |
12,000 | 12,999 | 2,000,000 | 5,000,000 | Completed (gfn) | 3 (gfn) |
23,000 | 23,999 | 500,000 | 1,000,000 | Completed (gfn) | 1 (gfn) |
28,000 | 30,000 | 200,000 | 500,000 | Completed (gfn) | 4 (gfn) |
28,000 | 30,000 | 1,000,000 | 1,500,000 | Completed (gfn) | 4 (gfn) |
33,000 | 35,000 | 200,000 | 250,000 | Completed (gfn) | 0 |
33,000 | 36,000 | 250,000 | 300,000 | Completed (gfn) | 3 (gfn) |
40,001 | 45,000 | 100,000 | 300,000 | Completed (gfn) | 9 (gfn) |
50,000 | 60,000 | 100,000 | 125,000 | Completed (gfn) | 3 (gfn) |
61,000 | 100,000 | 50,000 | 60,000 | Completed (gfn) | 9 (gfn) |
150,001 | 160,000 | 10,000 | 20,000 | Completed (gfn) | 2 (gfn) |
ECM curves on Fermat numbers.
a | b | m | digits | 11e3 | 5e4 | 25e4 | 1e6 | 3e6 | 11e6 | 43e6 | 11e7 | 26e7 | 8e8 | 2e9 | comments |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 1 | 12 | 1133 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2870 | 619(1) | 3 | |
2 | 1 | 13 | 2391 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 257 | 1087(2) | 0 | 0 | |
2 | 1 | 14 | 4880 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 834 | 6 | 0 | 0 | Factor found! |
2 | 1 | 15 | 9808 | 0 | 0 | 0 | 0 | 0 | 0 | 132 | 18 | 0 | 0 | 0 | |
2 | 1 | 16 | 16964 | 0 | 0 | 0 | 0 | 0 | 0 | 69 | 3 | 0 | 0 | 0 | |
2 | 1 | 17 | 39395 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
2 | 1 | 18 | 78884 | 0 | 0 | 0 | 0 | 0 | 9 | 0 | 0 | 0 | 0 | 0 | |
2 | 1 | 19 | 157770 | 0 | 0 | 0 | 0 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | |
2 | 1 | 20 | 315653 | 0 | 0 | 0 | 0 | 352 | 30 | 0 | 0 | 0 | 0 | 0 | (no factor known) |
2 | 1 | 21 | 631294 | 0 | 0 | 0 | 18 | 4 | 6 | 0 | 0 | 0 | 0 | 0 | |
2 | 1 | 22 | 1262577 | 0 | 0 | 0 | 51 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | |
2 | 1 | 23 | 2525215 | 0 | 0 | 0 | 57 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | |
2 | 1 | 24 | 5050446 | 0 | 0 | 13 | 32 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | (no factor known) |
2 | 1 | 25 | 10100842 | 0 | 0 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2 | 1 | 26 | 20201768 | 0 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
(1) 430 with B2=8e10, 189 with B2=15892582605916
(2) 21 with B2=26e9, rest with B2=3178559884516
ECM curves on generalized Fermat numbers.
a | b | m | digits | 11e3 | 5e4 | 25e4 | 1e6 | 3e6 | 11e6 | 43e6 | 11e7 | 26e7 | comments |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8 | 5 | 8 | 149 | 0 | 0 | 0 | 0 | 60 | 732 | 300 | 0 | 0 | GNFS-factored |
11 | 3 | 8 | 143 | 0 | 0 | 0 | 0 | 0 | 200 | 200 | 0 | 0 | GNFS-factored |
11 | 5 | 8 | 228 | 0 | 0 | 0 | 0 | 60 | 540 | 1024 | 129 | 0 | ECM-factored |
9 | 5 | 8 | 215 | 0 | 0 | 0 | 0 | 60 | 29 | 10 | 512 | 0 | |
9 | 7 | 8 | 180 | 0 | 0 | 0 | 0 | 60 | 55 | 90 | 512 | 0 | |
10 | 3 | 8 | 190 | 0 | 0 | 0 | 10 | 70 | 550 | 1095 | 512 | 0 | |
10 | 9 | 8 | 257 | 0 | 0 | 0 | 0 | 60 | 540 | 1024 | 512 | 0 | |
11 | 4 | 8 | 267 | 0 | 0 | 0 | 0 | 60 | 539 | 1024 | 512 | 0 | |
11 | 7 | 8 | 241 | 0 | 0 | 0 | 0 | 60 | 539 | 1024 | 512 | 0 | |
11 | 8 | 8 | 267 | 0 | 0 | 0 | 0 | 60 | 539 | 1024 | 512 | 0 | |
11 | 10 | 8 | 217 | 0 | 0 | 0 | 0 | 60 | 549 | 1024 | 512 | 0 | |
12 | 7 | 8 | 197 | 0 | 0 | 0 | 0 | 60 | 541 | 1164 | 512 | 0 | |
5 | 3 | 9 | 319 | 0 | 0 | 0 | 0 | 310 | 40 | 0 | 0 | 0 | |
5 | 1 | 9 | 329 | 0 | 0 | 0 | 4 | 1 | 1000 | 1000 | 1000 | 1000 | |
10 | 1 | 9 | 473 | 0 | 0 | 0 | 500 | 0 | 0 | 51 | 0 | 0 | |
12 | 1 | 9 | 553 | 0 | 0 | 0 | 0 | 0 | 5000 | 1500 | 100 | 0 | |
6 | 1 | 10 | 777 | 0 | 0 | 0 | 2 | 1 | 1000 | 1000 | 1000 | 0 | |
6 | 1 | 11 | 1543 | 0 | 0 | 3 | 4 | 5 | 1000 | 0 | 0 | 0 | |
6 | 1 | 12 | 3126 | 0 | 0 | 0 | 0 | 500 | 0 | 0 | 0 | 0 | |
6 | 1 | 13 | 6375 | 5 | 1 | 1 | 100 | 100 | 105 | 11 | 0 | 0 | Factor found! |
6 | 1 | 14 | 12730 | 0 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | |
6 | 1 | 15 | 25494 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | |
6 | 1 | 16 | 50980 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | |
6 | 1 | 17 | 101970 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | |
6 | 1 | 18 | 203973 | 0 | 0 | 400 | 0 | 0 | 0 | 0 | 0 | 0 | |
6 | 1 | 19 | 407969 | 0 | 50 | 21 | 5 | 0 | 0 | 0 | 0 | 0 | |
6 | 1 | 20 | 815908 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 10 | 449 | 0 | 0 | 100 | 200 | 520 | 2 | 0 | 0 | 0 | |
3 | 2 | 11 | 969 | 0 | 0 | 200 | 200 | 0 | 0 | 0 | 0 | 0 | |
4 | 3 | 11 | 1182 | 0 | 0 | 200 | 15 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 12 | 1943 | 0 | 50 | 75 | 40 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 13 | 3876 | 0 | 20 | 66 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 14 | 7752 | 0 | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 15 | 15610 | 33 | 101 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 16 | 31251 | 40 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 17 | 62527 | 69 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 2 | 18 | 125075 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
3 | 1 | 19 | 250125 | 0 | 10 | 100 | 12 | 0 | 0 | 0 | 0 | 0 |
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.
k | m | Status | Known search limit | My search |
---|---|---|---|---|
0 | 1 | 5 is a prime | - | - |
1 | 3 | 257 is a prime | - | - |
2 | 6 | composite with known factors | - | - |
3 | 11 | composite with known factors | - | - |
4 | 20 | composite with no known factor | - | - |
5 | 37 | 1275438465*239+1 divides | 6,000,000,000,000,000 | - |
6 | 70 | unknown | 1,000,000,000,000,000 | - |
7 | 135 | unknown | 100,000,000,000,000 | - |
8 | 264 | unknown | 200,000,000,000 | - |
9 | 521 | unknown | 40,000,000,000 | - |
10 | 1034 | unknown | 4,100,000,000 | 6,040,000,000 |
11 | 2059 | 591909*22063+1 divides | 1,500,000,000 | - |
12 | 4108 | unknown | 200,000,000 | 1,000,000,000 |
13 | 8205 | unknown | 30,000,000 | 100,000,000 |
14 | 16398 | unknown | 5,000,000 | 50,000,000 |
15 | 32783 | unknown | 300,000 | 22,000,000 |
16 | 65552 | unknown | 50,000 | 1,500,000 |
17 | 131089 | unknown | 20,000 | 278,000 |
18 | 262162 | unknown | 10,000 | 100,000 |
19 | 524307 | unknown | 10,000 | 97,800 |
20 | 1048596 | unknown | 1,200 | 135,500 |
21 | 2097173 | unknown | 1,200 | 22,260 |
- last update 29.2.2016 -