Factors of Tangent Numbers,
from T(2) to T(422). 

Computed by Simon Plouffe in May 2002.

Here _cnnnn_k indicates a composite number of
unknown factors of length nnnn, k being the rank whitin
this table.

2, 1
4, (2)
6, (2)^4
8, (2)^4*(17)
10, (2)^8*(31)
12, (2)^9*(691)
14, (2)^12*(43)*(127)
16, (2)^11*(257)*(3617)
18, (2)^16*(73)*(43867)
20, (2)^17*(31)*(41)*(283)*(617)
22, (2)^20*(89)*(131)*(593)*(683)
24, (2)^20*(17)*(103)*(241)*(2294797)
26, (2)^24*(657931)*(8191)*(2731)
28, (2)^25*(43)*(113)*(127)*(362903)*(9349)
30, (2)^28*(151)*(331)*(1001259881)*(1721)
32, (2)^26*(37)*(257)*(683)*(65537)*(305065927)
34, (2)^32*(151628697551)*(131071)*(43691)
36, (2)^33*(73)*(109)*(26315271553053477373)
38, (2)^36*(154210205991661)*(174763)*(524287)
40, (2)^36*(17)*(31)*_c21_1*(61681)
42, (2)^40*(127)*(337)*(1520097643918070802691)*(5419)
44, (2)^41*(59)*(89)*(397)*(683)*(1798482437)*(8089)*(2947939)*(2113)
46, (2)^44*_c23_1*(2796203)*(178481)
48, (2)^43*(97)*(241)*(257)*(653)*(673)*(153289748932447906241)*(56039)
50, (2)^48*(31)*(251)*(601)*_c26_1*(4051)*(1801)
52, (2)^49*(157)*(577)*(1613)*_c22_1*(58741)*(8191)*(2731)
54, (2)^52*(73)*_c27_1*(39409)*(87211)*(262657)
56, (2)^52*(17)*(43)*(113)*(127)*(19088082706840550550313)*(163979)*(15790321)*(113161)
58, (2)^56*(67)*(233)*(1103)*_c33_1*(186707)*(2089)
60, (2)^57*(41)*(151)*(331)*(1321)*_c39_1*(2003)
62, (2)^60*(157)*_c28_1*(266689)*(715827883)*(2147483647)
64, (2)^57*(257)*(641)*_c48_1*(65537)
66, (2)^64*(89)*(683)*(839)*(159562251828620181390358590156239282938769)*(599479)*(20857)
68, (2)^65*(37)*(101)*(137)*(953)*_c40_1*(131071)*(43691)*(26317)
70, (2)^68*(31)*(43)*(127)*(281)*_c41_1*(86171)*(688531)*(122921)
72, (2)^68*(17)*(109)*(241)*(433)*_c55_1*(38737)
74, (2)^72*(223)*_c56_1*(616318177)*(1777)
76, (2)^73*(229)*(457)*_c53_1*(58231)*(174763)*(524287)
78, (2)^76*_c63_1*(121369)*(8191)*(2731)
80, (2)^75*(31)*(257)*(631)*_c64_1*(10589)*(61681)
82, (2)^80*_c69_1*(38189)*(13367)*(4003)
84, (2)^81*(113)*(127)*(233)*(271)*(337)*(1429)*_c57_1*(68767)*(5419)*(14449)
86, (2)^84*(431)*(541)*_c73_1*(21563)*(9719)
88, (2)^84*(17)*(307)*(353)*(397)*(683)*_c76_1*(2113)
90, (2)^88*(73)*(151)*(331)*(587)*(631)*_c69_2*(23311)*(18837001)
92, (2)^89*(277)*(587)*(1013)*(1657)*_c68_1*(2796203)*(178481)*(30269)
94, (2)^92*(283)*(467)*(1499)*_c76_2*(13264529)*(2351)*(4513)
96, (2)^90*(193)*(241)*(257)*(673)*_c88_1*(65537)
98, (2)^96*(43)*(127)*_c88_2*(1671211)*(3221)*(2857)
100, (2)^97*(31)*(41)*(251)*(263)*(379)*(601)*_c78_1*(268501)*(8101)*(4051)*(1801)
102, (2)^100*(59)*(307)*(827)*_c79_1*(131071)*(43691)*(11119)*(2143)*(2857)*(6529)
104, (2)^100*(17)*(37)*(157)*(1613)*_c93_1*(8191)*(2731)*(858001)
106, (2)^104*_c93_2*(37217)*(3967)*(69431)*(20394401)*(6361)
108, (2)^105*(73)*_c97_1*(87211)*(279073)*(262657)*(246241)
110, (2)^108*(31)*(89)*(157)*(683)*(881)*_c94_1*(76493)*(3191)*(201961)*(2971)
112, (2)^107*(43)*(127)*(257)*_c103_1*(8065483)*(15790321)*(5153)
114, (2)^112*(571)*_c111_1*(174763)*(524287)*(32377)
116, (2)^113*(233)*(1103)*_c120_1*(7559)*(2089)
118, (2)^116*_c122_1*(179951)*(37171)*(2833)
120, (2)^116*(17)*(151)*(241)*(331)*(1321)*_c113_1*(4562284561)*(61681)
122, (2)^120*_c105_1*(2305843009213693951)*(768614336404564651)
124, (2)^121*(67)*_c95_1*(14066893)*(715827883)*(2147483647)*(74747)*(384773)*(49477)*(8681)*(5581)
126, (2)^124*(73)*(103)*(337)*(409)*_c125_1*(649657)*(5419)*(92737)
128, (2)^120*(257)*(641)*_c133_1*(65537)*(35089)*(274177)
130, (2)^128*(31)*(149)*(463)*_c122_2*(409891)*(2264267)*(7623851)*(8191)*(2731)
132, (2)^129*(89)*(397)*(683)*_c119_1*(804889)*(4327489)*(599479)*(312709)*(20857)*(2113)
134, (2)^132*_c149_1*(42859)*(7327657)
136, (2)^132*(17)^2*(953)*_c140_1*(131071)*(43691)*(354689)*(26317)
138, (2)^136*_c148_1*(9733)*(2957)*(2796203)*(178481)
140, (2)^137*(31)*(37)*(41)*(43)*(113)*(127)*(281)*_c123_1*(47392381)*(86171)*(6251263)*(122921)*(7416361)*(17681)
142, (2)^140*_c165_1*(228479)*(4003)
144, (2)^139*(97)*(109)*(241)*(257)*(433)*(577)*(673)*_c157_1*(38737)
146, (2)^144*(439)*_c168_1*(2298041)*(1753)
148, (2)^145*(223)*(593)*_c146_1*(616318177)*(172331)*(231769777)*(30817)*(1979)*(1777)
150, (2)^148*(251)*(331)*(601)*_c156_1*(153427)*(10567201)*(100801)*(4051)*(1801)
152, (2)^148*(17)*(131)*(229)*(457)*(1217)*_c151_1*(9743)*(230165249)*(174763)*(524287)*(148961)
154, (2)^152*(43)*(89)*(127)*(617)*(683)*_c153_1*(35532364099)*(1569473)*(78233)*(2213)*(125929)
156, (2)^153*(293)*(313)*(953)*(1249)*(1613)*_c163_1*(121369)*(8191)*(2731)*(3121)*(21841)
158, (2)^156*_c180_1*(10463)*(50929)*(5309)*(42487)*(2687)
160, (2)^154*(31)*(59)*(257)*_c190_1*(65537)*(61681)
162, (2)^160*(73)*(881)*_c173_1*(1356077)*(71119)*(87211)*(135433)*(262657)*(2593)
164, (2)^161*(257)*_c193_1*(43249589)*(13367)*(10169)
166, (2)^164*(499)*(971)*(1163)*_c197_1*(155377)*(2657)
168, (2)^164*(17)*(101)*(113)*(127)*(241)*(337)*(1429)*_c180_2*(15790321)*(5419)*(14449)*(28211)*(3361)
170, (2)^168*(31)*_c210_1*(131071)*(43691)
172, (2)^169*(431)*(1613)*_c205_1*(500177)*(101653)*(9719)
174, (2)^172*(233)*(379)*(617)*(1103)*_c207_1*(8419)*(2089)*(4177)
176, (2)^171*(37)*(257)*(353)*(397)*(683)*(1301)*_c201_1*(119782433)*(229153)*(2113)
178, (2)^176*_c224_1*(9433)*(62020897)
180, (2)^177*(41)*(73)*(109)*(151)*(331)*(631)*(1321)*_c194_1*(29247661)*(403783)*(23311)*(18837001)*(54001)
182, (2)^180*(43)*(127)*(911)*_c199_1*(23140471537)*(1210483)*(112901153)*(8191)*(2731)*(224771)
184, (2)^180*(17)*(277)*(1013)*(1657)*_c215_1*(2796203)*(178481)*(30269)*(389621)
186, (2)^184*(353)*_c210_2*(2903110321)*(1301919607)*(715827883)*(2147483647)
188, (2)^185*(283)*_c228_1*(13264529)*(53377)*(2351)*(3761)*(4513)
190, (2)^188*(31)*(67)*_c235_1*(174763)*(524287)*(2281)*(5101)
192, (2)^185*(241)*(257)*(641)*(673)*_c246_1*(65537)
194, (2)^192*(467)*(971)*(1553)*_c246_2*(11447)*(31817)
196, (2)^193*(43)*(113)*(127)*(461)*_c259_1
198, (2)^196*(73)*(89)*(683)*_c238_1*(34470847)*(599479)*(153649)*(20857)*(5347)
200, (2)^196*(17)*(31)*(251)*(389)*(401)*(601)*(691)*_c226_1*(61681)*(268501)*(2787601)*(340801)*(8101)*(4051)*(1801)
202, (2)^200*(1297)*_c270_1*(145121)
204, (2)^201*(137)*(307)*(409)*(953)*_c235_2*(131071)*(43691)*(11119)*(13669)*(26317)*(2143)*(2857)*(6529)*(3061)
206, (2)^204*(1291)*_c270_2*(22643)*(46654213)
208, (2)^203*(157)*(257)*(1613)*_c269_1*(8191)*(2731)*(858001)
210, (2)^208*(127)*(151)*(281)*(331)*(337)*_c240_1*(86171)*(122921)*(152041)*(29191)*(106681)*(664441)*(5419)*(1564921)
212, (2)^209*(37)*_c264_1*(1801439824104653)*(69431)*(20394401)*(6361)
214, (2)^212*(643)*_c294_1*(4339)
216, (2)^212*(17)*(241)*(433)*_c253_1*(29567)*(38737)*(33975937)*(4663)*(87211)*(279073)*(262657)*(3851)*(246241)
218, (2)^216*(59)*(157)*_c287_1*(104124649)*(6379)*(13721)
220, (2)^217*(31)*(41)*(89)*(397)*(683)*(797)*(881)*(1297)*_c271_1*(171253)*(3191)*(201961)*(2971)*(2113)
222, (2)^220*(557)*_c279_1*(616318177)*(26295457)*(17539)*(321679)*(3331)*(1777)
224, (2)^218*(43)*(127)*(257)*(449)*(659)*(1483)*_c273_1*(65537)*(13259)*(183076097)*(15790321)*(5153)*(2689)
226, (2)^224*(631)*_c279_2*(636190001)*(23279)*(65993)*(1868569)*(3391)*(48817)*(40194577)
228, (2)^225*(103)^2*(457)*(571)*_c291_1*(160969)*(174763)*(524287)*(32377)*(131101)
230, (2)^228*(31)*(691)*_c289_1*(4036961)*(2796203)*(178481)*(1884103651)*(44371)*(14951)
232, (2)^228*(17)*(1103)*_c322_1*(59393)*(2089)
234, (2)^232*(73)*(937)*(1367)*_c308_1*(121369)*(86113)*(8191)*(6553)*(2731)
236, (2)^233*(647)*(1181)*_c297_1*(5521693)*(157649)*(6521)*(179951)*(174877)*(37171)*(3541)*(2833)
238, (2)^236*(43)*(127)*_c323_1*(131071)*(43691)*(14767)*(20231)
240, (2)^235*(97)*(151)*(257)*(331)*(421)*(673)*(1321)*_c309_1*(249107671)*(4562284561)*(61681)
242, (2)^240*(89)*(647)*(683)*(727)*_c320_1*(2159191)*(117371)*(2371)*(1889)*(2927)
244, (2)^241*(733)*_c307_1*(2305843009213693951)*(768614336404564651)*(3456749)*(1709)
246, (2)^244*(739)*_c337_1*(3887047)*(13367)*(19553)*(165313)
248, (2)^244*(17)*(37)*_c314_1*(715827883)*(2147483647)*(290657)*(564097)*(384773)*(49477)*(8681)*(5581)
250, (2)^248*(31)*(601)*_c356_1*(4051)*(1801)
252, (2)^249*(73)*(109)*(113)*(337)*(1429)*_c337_2*(649657)*(4783)*(5419)*(14449)*(92737)
254, (2)^252*_c375_1
256, (2)^247*(67)*(641)*_c366_1*(65537)*(274177)
258, (2)^256*(431)*(1033)*_c364_1*(1591582393)*(9719)
260, (2)^257*(31)*(41)*(157)*(521)*(761)*(1613)*_c340_1*(34110701)*(409891)*(7623851)*(51481)*(8191)*(2731)
262, (2)^260*(1049)*(1193)*_c377_1*(4744297)
264, (2)^260*(17)*(241)*(353)*(397)*(683)*_c338_1*(4327489)*(98618273953)*(599479)*(312709)*(20857)*(74201)*(7393)*(2113)
266, (2)^264*(43)*(127)*(157)*(1381)*_c362_1*(53717)*(174763)*(524287)*(80349811)*(4523)
268, (2)^265*(101)*_c378_1*(42875177)*(15152453)*(7327657)
270, (2)^268*(73)*(151)*(331)*(547)*(631)*(811)*(1663)*_c356_2*(348031)*(23311)*(18837001)*(87211)*(262657)*(15121)
272, (2)^267*(257)*(953)*_c380_1*(131071)*(43691)*(354689)*(383521)*(26317)
274, (2)^272*(1097)*_c406_1*(15619)
276, (2)^273*(59)*(1013)*(1657)*_c389_1*(2796203)*(38971)*(178481)*(30269)
278, (2)^276*(149)*_c388_1*(450479)*(707633)*(5625767248687)*(4506937)
280, (2)^276*(17)*(31)*(43)*(113)*(127)*(347)*_c378_2*(47392381)*(86171)*(122921)*(15790321)*(61681)*(7416361)
282, (2)^280*(131)*_c391_1*(62189)*(1681003)*(35273039401)*(13264529)*(2351)*(4513)
284, (2)^281*(37)^2*(569)*_c402_1*(228479)*(148587949)*(472287102421)
286, (2)^284*(89)*(683)*_c389_2*(16865476527940273)*(6156182033)*(724153)*(2003)*(8191)*(2731)
288, (2)^282*(109)*(193)*(241)*(257)*(433)*(577)*(673)*(1153)*_c386_1*(65537)*(278452876033)*(38737)*(38941695937)*(6337)
290, (2)^288*(31)*(233)*(751)*(1103)*_c405_1*(7109)*(967289)*(1778099)*(2423)*(7553921)*(2089)
292, (2)^289*(311)*(439)*(491)*_c427_1*(2298041)*(9929)*(1753)
294, (2)^292*(127)*(337)*_c438_1*(748819)*(5419)
296, (2)^292*(17)*(223)*(593)*_c430_1*(616318177)*(231769777)*(1777)
298, (2)^296*(1193)*_c439_1*(38369587)*(650833)*(26113)
300, (2)^297*(41)*(251)*(331)*(353)*(601)*(1201)*(1321)*_c407_1*(268501)*(2967583)*(63901)*(10567201)*(100801)*(8101)*(4051)*(1801)
302, (2)^300*(283)*_c432_1*(18717738334417)*(2332951)*(165799)*(55871)*(18121)
304, (2)^299*(229)*(257)*(457)*(1217)*(1319)*_c439_2*(174763)*(524287)*(148961)*(27361)
306, (2)^304*(73)*(919)*_c426_1*(27983)*(54787)*(11359393)*(131071)*(43691)*(11119)*(2143)*(2857)*(123931)*(6529)
308, (2)^305*(43)*(89)*(113)*(127)*(397)*(617)*(683)*_c434_1*(35532364099)*(12613)*(78233)*(5227)*(8317)*(2113)
310, (2)^308*(31)^2*_c450_1*(715827883)*(2147483647)*(73471)*(11471)*(11161)
312, (2)^308*(17)*(241)*(1249)*(1613)*_c453_1*(121369)*(8191)*(2731)*(3121)*(21841)*(858001)
314, (2)^312*_c482_1*(2350291)*(15073)
316, (2)^313*(233)*_c486_1*(27617)*(2687)
318, (2)^316*_c469_1*(13960201)*(69431)*(20394401)*(6043)*(6679)*(6361)
320, (2)^313*(31)*(37)*(257)*(641)*_c469_2*(65537)*(120430291)*(3602561)*(23131)*(61681)
322, (2)^320*(43)*(67)*(127)*(1289)*_c488_1*(2796203)*(178481)
324, (2)^321*(73)*_c466_1*(71119)*(3618757)*(7309)*(87211)*(279073)*(135433)*(262657)*(246241)*(2593)
326, (2)^324*_c505_1*(150287)*(704161)
328, (2)^324*(17)*_c500_1*(43249589)*(13367)*(10169)*(13121)
330, (2)^328*(89)*(103)*(151)*(683)*(809)*(881)*_c480_1*(9138229)*(599479)*(20857)*(3191)*(201961)*(2971)
332, (2)^329*(499)*(997)*(1163)*_c501_1*(13063537)*(2939)*(155377)*(2657)
334, (2)^332*(59)*_c524_1*(2349023)
336, (2)^331*(97)*(127)*(241)*(257)*(491)*(673)*(1429)*_c494_1*(15790321)*(5419)*(14449)*(5153)*(3361)*(2017)
338, (2)^336*(491)*(617)*_c524_2*(4057)*(8191)*(2731)
340, (2)^337*(31)*(41)*(137)*(953)*(1021)*_c499_1*(23650061)*(11489)*(131071)*(43691)*(26317)*(4421)*(550801)
342, (2)^340*(73)*(571)*_c517_1*(5939)*(93507247)*(174763)*(524287)*(32377)
344, (2)^340*(17)*(431)*_c531_1*(500177)*(3559)*(101653)*(9719)
346, (2)^344*_c537_1*(1505447)*(730753)*(4153)*(6491)
348, (2)^345*(233)*(1103)*(1129)*_c534_1*(5689)*(7321)*(29581)*(2089)*(4177)
350, (2)^348*(31)*(43)*(127)*(251)*(281)*(601)*(1051)*_c510_1*(32009)*(86171)*(122921)*(60816001)*(39551)*(110251)*(4051)*(1801)
352, (2)^346*(257)*(397)*(683)*_c531_2*(65537)*(119782433)*(5304641)*(229153)*(2861)*(2113)
354, (2)^352*(271)*_c548_1*(179951)*(13099)*(184081)*(37171)*(2833)
356, (2)^353*(37)*(1069)*_c565_1*(62020897)
358, (2)^356*(1409)*(1433)*_c564_1*(58745093521)
360, (2)^356*(17)*(109)*(151)*(241)*(331)*(433)*(631)*(1321)*_c510_2*(168692292721)*(29247661)*(3593)*(38737)*(4562284561)*(61681)*(23311)*(18837001)*(54001)
362, (2)^360*(263)*_c566_1*(7648337)*(1164193)*(43441)*(1811)
364, (2)^361*(43)*(113)*(127)*(157)*(911)*(1093)^2*(1613)*_c533_1*(23140471537)*(1210483)*(112901153)*(4733)*(8191)*(2731)*(224771)
366, (2)^364*(433)*_c546_1*(89071)*(2305843009213693951)*(768614336404564651)*(55633)*(2441)
368, (2)^363*(101)*(257)*(277)*(1013)*(1657)*_c570_1*(2796203)*(178481)*(30269)*(7681)
370, (2)^368*(31)*(223)*(1481)*_c580_1*(616318177)*(28136651)*(1777)
372, (2)^369*_c559_1*(2903110321)*(715827883)*(2147483647)*(2675483)*(384773)*(49477)*(8681)*(5581)
374, (2)^372*(89)*(157)*(683)*_c592_1*(707983)*(131071)*(43691)
376, (2)^372*(17)*(283)*_c575_1*(23592342593)*(1198107457)*(13264529)*(2087)*(2351)*(3761)*(4513)
378, (2)^376*(73)*(337)*(727)*_c580_2*(649657)*(431219)*(119827)*(5419)*(92737)*(87211)*(262657)
380, (2)^377*(31)*(41)*(229)*(457)*(761)*_c597_1*(174763)*(524287)*(54721)*(2281)
382, (2)^380*(401)*(1307)*_c615_1*(7068569257)
384, (2)^376*(241)*(257)*(641)*(673)*(769)*_c613_1*(65537)*(274177)
386, (2)^384*_c628_1*(13821503)*(6563)
388, (2)^385*(67)*(971)*(1553)*(1669)*_c598_1*(11447)*(31817)*(3555339061)*(3881)*(5821)*(194569)*(4657)
390, (2)^388*(151)*(331)*_c609_1*(38639)*(409891)*(121369)*(7623851)*(107251)*(8191)*(2731)
392, (2)^388*(17)*(37)*(43)*(59)*(113)*(127)*_c611_1*(375327457)*(15790321)*(1007441)*(273617)*(7057)
394, (2)^392*(307)*_c650_1*(7487)
396, (2)^393*(73)*(89)*(109)*(683)*_c607_1*(4327489)*(599479)*(312709)*(153649)*(20857)*(42373)*(235621)*(5347)*(2113)
398, (2)^396*_c659_1*(664679)
400, (2)^395*(31)*(251)*(257)*(523)*(601)*(1601)*_c614_1*(2909)*(61681)*(268501)*(2787601)*(340801)*(8101)*(4051)*(1801)*(25601)
402, (2)^400*(1609)*_c651_1*(7327657)*(22111)*(2011)*(9649)
404, (2)^401*(809)*_c660_1*(35608471)*(2671)*(3851)
406, (2)^404*(43)*(127)*(233)*(1103)*_c664_1*(136417)*(2089)
408, (2)^404*(17)^2*(241)*(307)*(673)*(953)*_c627_1*(131071)*(43691)*(354689)*(11119)*(13669)*(26317)*(2143)*(2857)*(8161)*(6529)*(3061)
410, (2)^408*(31)*_c678_1*(2940521)*(13367)
412, (2)^409*(131)*_c680_1*(17325013)*(41201)
414, (2)^412*(73)*_c680_2*(2796203)*(79903)*(178481)
416, (2)^410*(157)*(257)*(1613)*_c657_1*(65537)*(23877647873)*(21193)*(928513)*(8191)*(2731)*(858001)
418, (2)^416*(89)*(683)*(887)*_c688_1*(174763)*(524287)
420, (2)^417*(41)*(113)*(127)*(151)*(257)*(281)*(331)*(337)*(1321)*(1429)*_c628_2*(47392381)*(86171)*(122921)*(152041)*(29191)*(106681)*(7416361)*(664441)*(5419)*(14449)*(1564921)
422, (2)^420*(157)*_c667_1*(199061567251)*(5344743097)*(678871)*(9878177)*(15193)*(39443)*(4643)