素因数分解結果（追加：Cullen）
ftp://sable.ox.ac.uk//pub/math/
Subject:
Date: 4 Dec 1997 08:37:52 -0000
From: yamasaki@kusm.kyoto-u.ac.jp
To: kc2h-msm@asahi-net.or.jp
Factorization of Cullen numbers, C_n = n.2^n + 1, for n <= 1000.
In the table below, the notation Cxxx indicates a number of xxx decimal
digits known to be composite but with unknown factors. Pxxx means a prime
of xxx digits. Only the final (largest) factor is given in this format;
its value may be easily calculated from the other factors given.
The table will be updated at irregular intervals as new factors are
discovered. If you find new factors, please email them to Wilfrid Keller
(rz2a010@rrz.uni-hamburg.de) and/or Paul Leyland (pcl@oucs.ox.ac.uk). It
would be wise to contact one or both of these before embarking on lengthy
computations, as there may be other factorization attempts in progress.
Last update: 1997 November 17.
n C_n
1 3
2 3.3
3 5.5
4 5.13
5 7.23
6 5.7.11
7 3.13.23
8 3.683
9 11.419
10 7.7.11.19
11 13.1733
12 13.19.199
13 3.3.11833
14 3.157.487
15 17.29.997
16 17.61681
17 5.5.19.4691
18 11.19.107.211
19 3.17.37.5279
20 3.3.103.7541
21 23.1914791
22 13.23.43.7177
23 5.151.421.607
24 5.11.1399.5233
25 3.17.2459.6689
26 3.5.7.7.2373919
27 7.29.53.336823
28 29.29.8937209
29 31.83.6051013
30 17.17.31.59.149.409
31 3.3.7.61.1483.11681
32 3.1777.25781083
33 47.6031230671
34 19.23.67.1061.18803
35 37.32502455213
36 37.37.1933.934861
37 3.5.339016085231
38 3.3.20879.55586743
39 41.3433.152326961
40 41.131611.8150491
41 13.43.1291.124932557
42 23.43.83.2250270487
43 3.5.163.2633.58752797
44 3.5.28909.1785040843
45 11.47.2437.1256655529
46 5.31.47.139297.3189821
47 7.11.43.3593.556021079
48 7.379.997.5107973329
49 3.3.3.3.340549971822769
50 3.163.211.563.857.1130809
51 53.101.21453725107033
52 7.11.17.53.1433.2355599273
53 5591.16747.5098461301
54 29.107.7187.110503.394739
55 3.109.2185637.2772596459
56 3.3.1021.439136496476653
57 5.13.59.10740337.199434979
58 31.59.101.7002713.12923089
59 37.43.61.350446511482643
60 61.2267.1529093.327141571
61 3.19.37.41.21557.110359.683759
62 3.5104570123.18671146721
63 5.313993.370118084366117
64 5.5.29.41.113.7416361.47392381
65 67.149.2357.367019.277685929
66 5.5.5.13.67.107.131.8353.382030403
67 3.3.413009.7451263.356987159
68 3.7.4841894819.197384920991
69 7.71.193.135979.3122721481331
70 37.47.71.139.4815318361753391
71 11.11.73.173.5113.21456452254477
72 41.73.6011.40163.470557385537
73 3.7.89.277.1331752354101535409
74 3.3.3.130860199.395621657653429
75 149.367.298013.663557.262026467
76 47.47.79939.27729643.1172720609
77 5.17.79.1732823680385823649523
78 41.79.78094529.93197166057943
79 3.59.157.3533.36930529.13170269561
80 3.67.1960787.245393561523640963
81 83.13633.984666689.175774509403
82 43.83.163.681615322182320440507
83 5.23.15373.2205616169.205864436623
84 5.2971.22637.4831782703823228467
85 3.3.15607.24763.132157.144163.49620299
86 3.5.3989.6687383.69261971.240088711
87 19.89.173.22853.2013705447963047603
88 89.2137.13607459.10523270337143867
89 7.79867.372067.264833583219205703
90 7.47.179.1891878275724375961367971
91 3.181.9157.74609.607332797678367491
92 3.3.94957781.533057872502798481877
93 71.79.887.127703.1449647415604834793
94 7.62869.4230706069276050048396059
95 29.97.769973.1737512608551063059489
96 97.57735121.1358122681230804234961
97 3.5.13.283583.1806689.153844901960056309
98 3.929.260171.42832142214886804432769
99 13.101.197.35461.6841051101464703338953
101 103.2486072050933032418469262596951
102 53.103.22619.4188641917664387362988929
103 3.3.3.5.5.11.1951.2333.57413.538329365932625711
104 3.5.140624706585318248272700942249711
105 107.39806598287540661579709558598723
106 5.17.17.71.71.107.211.4157.12579245807344233937
107 23.109.9967.4408546339.157608309709749967
108 109.20481577.6861664297.2287936306776469
109 3.73.61428359.3417532243.1538758185211703
110 3.3.7.3137736253.722329286054138829730219
111 7.7.7.113.647.659.303139.19064027.3017406215899
112 53.107.113.51861119.17498368696508185445369
113 241.17409703.279678800660274393861538439
114 59.227.5663103129009631.31217061335588719
115 3.7.229.1361.10909.6040974323677.11074968709153
116 3.11.19.191.2377.8448443.160686473.24937413111887
117 5.5.881.8669.17382493.5857312177073603180401
118 61.79.13143468889817839.619091110207218773
119 11.19.3463.11329.9645529884884711309041677511
120 11.983.11789.6974348643991.179412997157803583
121 3.3.19763.50971.42224697299.840291105598486051
122 3.719186379059.300646805348642669176742057
123 5.229.821.11465422699.121354493981577075459727
124 5.29931493.17621495483952458314332353602249
125 23.127.3023.602129308434452999628119625733847
126 5.127.251.1627.41334719904037881929719526509387
127 3.433.16634280446096683933736941933731548443
128 3.3.3.3.11.19.331.811.15121.87211.18837001.385838642647891
129 131.683636977.980307465963544964235926264027
130 67.131.93056049341.216646700655115035509110253
131 7.50945131504734787101373798369784726515127
132 7.8002401833.50192924009.255606837555877927687
133 3.29.89.187038842001228735696774161078342439359
134 3.11.5801.27997.544497530859630004327093119223757
135 23.137.269.1817394275513949491.3817098299210162089
136 7.137.642183982348149971.19237128345740005500773
137 5.29.139.1662697.712252623262432009988578545236219
138 71.139.405497.12015938408495337370950308286687661
139 3.3.19.277.1979.32583013.54516515237.581759112652171901
140 3.13.12251.411469.992554038209956534589200110262601
141 393050634124102232869567034555427371542904833
142 73.283.523.2621.9385153.2978710979175931428632455909
143 5.9623.4143608069.7997721137066284693537861828927
144 5.53.1373.349801.1368841.5345933.27481361353.125467039561
145 3.97.277.499.2393.150091.1431929.135527932327.2306728188553
146 3.3.5.13.26008076089.25947144401291.32989714783078582883
147 31.149.293.19378096520361448752959104728159082592551
148 149.3747769501363.23985387089791.3942713326764029617
149 19.151.42805751.154592140751.1917354724069.2921010204449
150 151.16091.199447.1375019.321287936319825512210658057577
151 3.17.17.47.1259.639827737.1635226069.5835105553.1376176144571
152 3.7.17.67.109.21818809.15254654350908713255649818064549187
153 7.19.1307.132607.730690897.453636682637.228636322485603229
154 47.79.103.307.701.22483.51711640222901.36751825179839702143
155 11.17.157.20063.36299.1034221.149314093.12251789447.174998995597
156 47.157.934606378369.2066225280962497247971207030159067
157 3.3.3.5.7.7.11.13924209627379.28308436597679339307780799112663
158 3.19243104891523555089681850297431059758803111815851
159 317.3517.416610794935849540739.250152176243212998440083
160 13.6397.8430041.19945852483019.16723119620808523976972819
161 17.163.2907271.2615944642573.3734639664419.5979376236465419
162 11.83.113.163.78524336642930939.717188323835077905681698353
163 3.5.13.139.211.52392423893769317.6360284458069554945037633183
164 3.3.5.5.73.5821.1050326180531.38188796193422216538562680498623
165 167.46207955958725553342008718064323199663373196568343
166 5.5.17.167.269.331.1229.14703383.7514212799.18094602641275224172877
167 13.59.101.227.2741.6623272651.97859159910234357874961360006183
168 13.41.263.1193.5351046957296294967143.70240305210365674723429
169 3.113.2371.11771611.41616310457.1222065831793.262803195206866931
170 3.97.163.95289941.110210593399.113552555055259.4497801462419497
171 173.135623.2359451.9245596938440612091244258381346491358921
172 173.48967020459312671529866683.121545229802005060749749407
173 7.7.7.67.113.8553162919139.93252662907342914987443753054690751
174 7.43.89.347.379.1182614792051019187653215427710083905181807381
175 3.3.349.610636526570407.4369548603444690816798576426688164523
176 3.453233666209.12397910251258996071136535829806600652739531
177 5.29.37.179.229.58601.2630990210462819023277622922299442696731403
178 7.13.23.179.104009.7181770244100625578659.243688224134989561205669
179 181.70019.34313123150277995235473.315404239836621269661961199
180 181.45307.33637820086813508688423918112864104768776725071943
181 3.11.67.4698961.1452194066821.36769908479361891441651743290026143
182 3.3.3.79.353.16607.3351244652513.26623657540544754777906191202869731
183 5.168710373676753.2659674592537291694589130233037496019078461
184 5.19.31.84633443.18101297956950597394135162472909116787571143627
185 29.31.31.3623.1196519931107497.81054482601806621.926476123489354759
186 5.3691.11454196829.58289035793179932431.1480561919718931673161469
187 3.373.1601.701791.75585331.1908359156468173.202266495831450688643431
188 3.17.53.61.79.49547.114281701649546000039332035757076516534215319551
189 191.39937.7318601.850076641.6393623158493.488752498681295030883539
190 97.127.191.379.334352630758026753052127780858903849247119855257171
191 193.3106027024504808357234807719773741672216450491949820186433
192 193.11383.994666835144756887.551529457980348023610894749089746961
193 3.3.3578059.95891935319.784647113438392662261760342143380984191213
194 3.7.239.1579.3440291.258428384479.691331222132562469456138153231784173
195 7.197.389.144271.577503957059.219096728033538551241509971530768156779
196 197.1306853.76461401853778034066768844022748638369403043419360777
197 5.13.41.97.199.12377333.22037693.2820071657532197816708510413355632510367
198 101.199.3957581630470173572781089784113018002131899507052502380587
199 3.7.19.397.1009389565877979157064103761847601869604484750171321800171
200 3.3.89.39559890596883894046336801.10142418591118067444952844786737601
201 31.181648470879949.152234888317472507.753559506051402250594270231841
202 103.3368839219.3741906956914804121263869968093512255563484539202637
203 5.5.5.73.89.331.9708100959919126819787692624900260511576321906985675711
204 5.249249502567489762624541249.4208671008313152579142859138434137997
205 3.97.137.114013.102402353.22647752313807400005917418020769922702665910847
206 3.5.7583.17987.55794643146654907249416619.185593504807036534455657377521
207 43.709.51871.670077917.269814080263139609.148919037720472758528349210837
208 67.67.4660549.418344753855451.9776455370458015781829130967923440106559
209 211.64109.1555593851281.17795774525367388104409.459198868810706139014479
210 107.211.419.701.14096035847.365134180927300543727.10124430995685040682150303
211 3.3.3.3.421.521.86499277.62044429938066576799.7282683333123000735471098243863
212 3.19.26479201931116897.67454333484203031308029.13705829947029499713115933
213 11.13.17.31.687787.7177381.190198081.39627432310915016379803870358483286377511
214 109.233.6958891882439729.24352829561682522854453.1309064085711725204919193
215 7.589967429.1163966779.22544929787.104465281680787733678608685761751329859
216 7.937.7873.212209.228443.89111069.4369882862911.23335216218720582447682525567
217 3.5.5.5.5.1399.146056139.119297128568689961707642244398477420825893265620330647
218 3.3.277.347.733.839.119643181199.1442746095312477234937165153483866937996573091
219 587.129517.7811923380407761.310663558546160778660332508944737162149276767
220 7.199.1810358633773.52985156679853.2774289447889131977885172730745823233513
221 223.313553.30828930277.345499192337242646670577414083916186836335594022211
222 13.113.223.443.344171.29957623136932610989003744979202166525658042985384148499
223 3.5.171428753575820291.1169012000878749466715954227972307209438830230891429
224 3.5.131.5250967.186338701.1948401751.363555433037.4434176636929744615926922744141
225 227.761.4241.1072961.113814671468528690819.135603397399560926442698695439019857
226 5.11.151.191.227.9917196447643013.73284847859761399627.93129118285917703947087139
227 47.229.6209419.62128127.11791316735969054283607404655004239311478415164229303
228 73.229.4789.4986353.246369906404931694515150716644093907285813170600449519521
229 3.3.11.11.301622720557.601468042011727828798175118399606521407976771404850227813
230 3.11.12025770149710830841742377638816029197452689875751431118843792208135137
231 131.233.461.534923.105906243682847231529032716522706094337896612242917198909981
232 61.233.1619.10867044065993.6403286680858672500278743016763657043150626907580263
233 17389.2928794234257417.269609587388273533.234231937394770864916994779747201153
234 467.13833050493781515428348889693985644161657897211887541361096622427143771
235 3.4099.1556886580277184344040121.677736218372881262725293897897133069953750913
236 3.3.3.7.29.17299.321599692831.251697875255953361345641.3395588110484196695386292342453
237 5.7.239.604957.1724555797.21728147227.89540042563.526901242589.5850869369504648329721
238 11.239.367.11146451.9775132739540874354718871345092992601891565837981197747905361
239 149.241.431.2783631563.1696193174414482124371.2889343792379245231620838873568570899
240 137.241.17380141.738957218516252080684598573500764773335500464682492379380336653
241 3.7.109.251.677.2189464030257870753445989668989298767725536124698370882465915236711
242 3.17.523.4730766374357138123.13554108269985058358487232861679484449015640448451411
243 5.59.58907.588173.1837799976254802979327009873.182853371472745707629899247710097017
244 5.11.4517.14234771.103522546497268413031966177.18841286651106599908117994762880526169
245 25935383.520121395131517.1026875133968298790290301311434366816754670072046572531
246 5.491.47353.10030753.310516454471.76823995509149163135689436209093988797254033153481
247 3.3.85601.16906867.4288657838987505489083265995422139071696310223720461494745297539
248 3.5851.294793.456037.47535931194198795805054783832555059137863892056681930873819893
249 241.251.4013.91081.856411.246522216963224591.7776427048612116457.6205290956587022060099
250 127.167.251.499.425237.400417841207696712567676935386528856087546972294730009761050053
251 307653395464509967970123309.2952166994886852822203661125488300039959347527434661
252 18424659817.144533935823133455939.684841612087118520440290253291601020761365983411
253 3.13.29453.16247207.129471682943.1515520351663525174124856168201726604067335822054026731
254 3.3.53.113.8680459887401.15714951977153850676064404775841388607720588553787678580347837
255 13.41.61.257.509.32911.35393.34053463247.87510745593982551680978494233590596051965655060469
256 97.257.673.229153.119782433.43872038849.16875081675650881.86945388997210442828259494992321
257 5.7.53.10429.668929.2416591963.1903145868505016520662461808277015601211380010611929552497
258 7.7.23.97.131.167.337.2297.559667.230313647.364364467.1374354864151970369444666742571056483339013
259 3.43.71.83.85381.3696419499732125646706963461461021671039074633001871227584244477847849
260 3.23.1690253.5083453.29861808013.13221664979960397979.2057834075534750295653953912741327883
261 229.263.337666820937693285382073012867537183.47554295895258130750249795244285213964853
262 7.263.523.1906481897.947398496715727410177818323379917.1116450058618544811875311313785607
263 5.2278693640955397246797207757.342128035294000424548423630263238151657973481442952193
264 5.5.5.5021.592119738209.21057800617666298008854305549489669777978005563191687444712436793
265 3.3.3.11.17367004185637.3045884049468885854869458741512451211892441394706905389061898125029
266 3.5.5.349.461.25981.34429.3873678985788394758989958001.754343180093642323226325905652223147859
267 11.37.269.1780361920474953713.324836720804831150887201065617965599666539818439699414938163
268 157.269.1486932233537747.2024093281893002169646399088467053249387445166447159770764521459
269 101.271.733.88328239.264727681.33447645469614844621.16261552134150963256912978499933376120277
270 137.271.70831729.567934312924591.512697534125707566113.668937519497448245927220004712218729
271 3.29.541.1300967.208725859.63588827359.322811751482293647881.3919303615375085762677680382154321
272 3.3.11.53.9561577711705862764264581308221.41142161186296083798629261151732988683965520142699
273 19.37.148139.135718328880164683.7168668256270117427.40893072558579066008461166663892553438861
274 23.139.547.6569.1897367.19799729220030924786873035843.19272122899853613240731304575970612524867
275 23.277.2620438046235262784996723553879236478411267269361846493605048327765454198867094731
276 277.14625971419341908904640781.8271483272931793203824472393717770295239506398478479535601
277 3.5.83.359.461.617.31033.48991.348015520606546495198707540784129919687499081381258652843892344369
278 3.7.89.1471.34253.381859.4352019290125240214226680479.862718595692748732130923523546771373848499
279 7.281.557.25261.9791808235385133358162235180872541743870982469665046865033523780751837342967
280 281.61543.31453706835836398961247610394594647844803122345126459100494528792957087022247407
281 283.3564719.236025301.72774196049.24090224171782970193199073.2615450753768236321962498506410297
282 283.563.15937.81457.216607.10552853.47082195578299225313557321.98441673542918995179550353894161179
283 3.3.5.7.4007741.19922095489.23012605391.7599135689022649549878288839033088264904083993165247090529
284 3.5.8207406980508682207.71703421614464637948404131875849518088397138180635120435525537315569
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951 7.11.953.1901.4049.71799983. C270
952 151.953.21893. C281
953 381287.81563651538829.611449058377470811. C253
954 479.1907.6007.41700557. C273
955 3.7. C290
956 3.3.1249. C287
957 5.19.193.753031.3148396446127001.19981278697661177353. C247
958 13.157. C289
959 31.59.277.4603. C283
960 31.3947.24323142361789.63568881091579.2277615256784599. P245
961 3.641.1252523.3194377262779. C271
962 3.310663. C287
963 5. P293
964 5.5.3253.6947. C285
965 967.1637. C288
966 5.5.83.83.967.1931.287827877. C274
967 3.3.3.17.37.43.71.1933.7829. C280
968 3.17.67.462953.251576157433. C274
969 211.971.1129.1187.999337127581766201069. P263
970 487.647.971.64223.7247761. C275
971 7.17.13963.115751.5455951. C278
972 7.362293.15135979.18116175274449247. C266
973 3. C296
974 3.3.2539.13781693.5342575129.45193807016308427. C259
975 977.1949.272927.7387573.69277451. C271
976 7.31.977.202664732464741. C278
977 5.13.17.37.197.6076817.695530897. C275
978 491.1549.8681.202201.147174020183. C272
979 3. C298
980 3.83.1016569.582770247653079901. C272
981 983.159673.40352472619.9774452304734586593. C261
982 17.983.12919. C291
983 5.11.1151.208829641. C286
984 5.1609.32888371067.1159100339029.124087073741814785803. C253
985 3.3.797.7833313.8058927870697513. C273
986 3.5.211.60289.40786761527924869. P275
987 199.1973.62946942748526423. P278
988 31.41.59.49801.6327878899. C282
989 29.991.1381.171091.43320499.181442862405691. C266
990 991.1979.193559.495527.100147281853.1560101669253091. C258
991 3.41801331521.14875148899704889253. C272
992 3.3.3.7.403391.437723955883305643.303719311081127531540813. P253
993 7.7.13.239.1387927.32396963.3671320892806991366172931. C259
994 317.499.1987.3613.65270346607.53876824215887. C266
995 997.27893.1529754028009507. C280
996 11.19.569.997.161336613848309. C281
997 3.5.7.29. C300
998 3.337.373.151609.4662302893. C284
999 11.1997.9133.18749. C292
1000 11.251586613.6650877341515619. C279
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E-mail : kc2h-msm@asahi-net.or.jp三島 久典