What factors are known of the Fermat numbers F_n = 2^(2^n) + 1?

I include here a list of all the known factors of Fermat numbers.
For F_n, n >= 15 I put the factors in the form k*2^n + 1.

The designation Cxx indicates a composite cofactor of xx digits.
A '?' indicates that the character of the cofactor is unknown.

The factorization of F9 is currently the 'MOST WANTED' factorization
among those of us who do factoring research.

N   Factors

0   3
1   5
2   17
3   257
4   65537
5   641.6700417
6   274177.67280421310721
7   59649589127497217.5704689200685129054721
8   1238936361552897.
    934616397153579777691635581996068965840512375416381885802803217
9   2424833.C148
10  45592577.6487031809.C291
11  319489.974849.C
12  114689.26017793.63766529.190274191361.C
13  2710954639361.C
14  C
15  (579*2^17+1).(17753925353.2^17+1).C
16  (1575.2^19+1).C
17  (59251857.2^19+1).C
18  (13.2^20+1).C
19  (33629.2^21+1).(308385.2^21+1).C
20  C
21  (534689.2^23+1).?
22  ?
23  (5.2^25+1).?
24  ?
25  (48413.2^29 + 1).(1522849979.2^27 + 1).(16168301139.2^27+1).?
26  (143165.2^29 + 1).?
27  (141015.2^30 + 1).(430816215.2^29+1).?
28  ?
29  (1120049.2^31 + 1).?
30  (149041.2^32 + 1).(127589.2^33 + 1).?
32  (1479.2^34 + 1).?
36  (5.2^39 + 1).(3759613.2^38 + 1).?
38  (3.2^41 + 1).(2653.2^40 + 1).?
39  (21.2^41 + 1).?
42  (43485.2^45 + 1).?
52  (4119.2^54 + 1).(21626655.2^54 + 1).?
54  (21626655.2^54 + 1).?
55  (29.2^57 + 1).?
58  (95.2^61 + 1).?
62  (697.2^64 + 1).?
63  (9.2^67 + 1).?
66  (7551.2^69 + 1).?
71  (683.2^73 + 1).?
72  (76432329.2^74+1).?
73  (5.2^75 + 1).?
75  (3447431.2^77 + 1).?
77  (425.2^79 + 1).?
81  (271.2^84 + 1).?
91  (1421.2^93 + 1).?
93  (92341.2^96 + 1).?
99  (16233.2^104 + 1).?
117 (7.2^120 + 1).?
125 (5.2^127 + 1).?
144 (17.2^147 + 1).?
147 (3125.2^149 + 1).?
146 (37092477.2^148+1).?
150 (1575.2^157 + 1).(5439.2^154 + 1).?
201 (4845.2^204 + 1).?
205 (232905.2^207 + 1).?
207 (3.2^209 + 1).?
215 (32111.2^217 + 1).?
226 (15.2^229 + 1).?
228 (29.2^231 + 1).?
250 (403.2^253 + 1).?
255 (629.2^257 + 1).?
267 (177.2^271 + 1).?
268 (21.2^276 + 1).?
275 (22347.2^279 + 1).?
284 (7.2^290 + 1).?
287 (5915.2^289 + 1).?
298 (247.2^302 + 1).?
316 (7.2^320 + 1).?
329 (1211.2^333 + 1).?
341 (27609.2^334 + 1).?
375 (733251.2^377+1).?
376 (810373.2^378+1).?
398 (120845.2^401 + 1).?
416 (8619.2^418 + 1).?
452 (27.2^455 + 1).?
544 (225.2^547 + 1).?
547 (77377.2^550+1).?
556 (127.2^558 + 1).?
637 (11969.2^643 + 1).?
692 (717.2^695 + 1).?
744 (17.2^747 + 1).?
851 (497531.2^859 + 1).?
931 (1985.2^933 + 1).?
1123 (25835.2^1125+1).?
1229 (29139.2^1233+1).?
1451 (13143.2^1454+1).?
1551 (292.2^1553 + 1).?
1945 (5.2^1947 + 1).?
2023 (29.2^2027 + 1).?
2089 (431.2^2099 + 1).?
2456 (85.2^2458 + 1).?
3310 (5.2^3313 + 1).?
3506 (501.2^3508+1).?
4724 (29.2^4747 + 1).?
6537 (17.2^6539 + 1).?
6835 (19.2^6838 + 1).?
9428 (9.2^9431 + 1).?
9448 (19.2^9450 + 1).?
23471 (5.2^23473 + 1).?

-- Bob Silverman

[ Editor: the table is as posted.  Every factor of F_n has the form
k.2^(n+2) + 1, so two lines look like transcription errors: the F54
line repeats the second F52 factor (2^54 < 2^56), and the F341 factor
has 2^334 < 2^343. ]