[gdbbyfaq] factoring binary log(2)

see previous post for explanatory details.

the number is log(2) ~= 0.693 (decimal) ~= 0.1011000101110010000101111111011111010001110011110111100110101011101 (binary).

1 floor matrix(0,2)
2 ceil Mat([3, 1])
3 floor Mat([5, 1])
4 floor Mat([11, 1])
5 ceil Mat([23, 1])
6 ceil [3, 2; 5, 1]
7 ceil Mat([89, 1])
8 floor [3, 1; 59, 1]
9 ceil [5, 1; 71, 1]
10 floor Mat([709, 1])
11 floor [3, 1; 11, 1; 43, 1]
12 floor [17, 1; 167, 1]
13 ceil [3, 2; 631, 1]
14 ceil [41, 1; 277, 1]
15 floor [3, 1; 67, 1; 113, 1]
16 ceil Mat([45427, 1])
17 ceil [7, 1; 12979, 1]
18 ceil [5, 1; 36341, 1]
19 ceil [17, 1; 21377, 1]
20 floor [7, 3; 13, 1; 163, 1]
21 ceil [3, 2; 5, 1; 32303, 1]
22 floor [23, 1; 41, 1; 3083, 1]
23 floor [229, 1; 25391, 1]
24 floor [7, 1; 11, 1; 151027, 1]
25 floor [17, 1; 1368127, 1]
26 floor [29, 1; 569, 1; 2819, 1]
27 floor [7, 1; 1733, 1; 7669, 1]
28 floor Mat([186065279, 1])
29 ceil [4999, 1; 74441, 1]
30 floor [3, 1; 23, 1; 10786393, 1]
31 floor [5, 1; 15991, 1; 18617, 1]
32 floor [3, 2; 17, 1; 19457807, 1]
33 floor [11, 1; 541280813, 1]
34 floor [3, 1; 3969392629, 1]
35 ceil [5, 2; 521, 1; 709, 1; 2579, 1]
36 floor [281, 1; 169511429, 1]
37 ceil [3, 2; 7, 1; 11, 1; 107, 2; 12007, 1]
38 ceil Mat([190530846197, 1])
39 ceil [3, 1; 19, 1; 6685292849, 1]
40 floor [5, 1; 7, 2; 25171, 1; 123583, 1]
41 floor [23, 1; 66271598677, 1]
42 floor [13, 1; 29, 1; 83, 1; 97423973, 1]
43 ceil [7, 1; 720397, 1; 1209053, 1]
44 ceil [3, 2; 11, 1; 439, 1; 280572793, 1]
45 floor [5, 1; 59, 1; 103, 1; 233, 1; 397, 1; 8677, 1]
46 floor [573479, 1; 85052629, 1]
47 floor [61129, 1; 1595834927, 1]
48 floor [227, 1; 859487165221, 1]
49 ceil [5, 1; 17, 1; 43, 1; 95219, 1; 1121203, 1]
50 floor [3, 1; 260138115340223, 1]
51 floor [7, 1; 59, 1; 187409, 1; 20165767, 1]
52 floor [3, 2; 13, 1; 587, 1; 7589, 1; 5989309, 1]
53 floor [421, 1; 14829726290179, 1]
54 ceil [3, 1; 7, 2; 11, 1; 114757, 1; 67290851, 1]
55 ceil [201337, 1; 124037107301, 1]
56 floor [3, 2; 5549613127258097, 1]
57 floor [325769, 1; 306637636763, 1]
58 ceil [3, 1; 5, 1; 13, 1; 1024543961955341, 1]
59 floor [17, 1; 37, 1; 67, 1; 9481340795923, 1]
60 ceil [27766027, 1; 28781369777, 1]
61 floor [3, 1; 23, 1; 23163602618120753, 1]
62 ceil [5, 1; 29, 1; 22045359733108027, 1]
63 floor [397, 1; 16103663281111657, 1]
64 floor [3, 4; 4373, 1; 1821377, 1; 19818959, 1]
65 floor [1838203, 1; 13911748207573, 1]
66 floor [3, 1; 2473, 1; 23059, 1; 298964302159, 1]
67 ceil [14551, 1; 205463, 1; 34214382383, 1]
68 ceil [15141821, 1; 13510986447617, 1]
69 floor [81569, 1; 10198897, 1; 491832041, 1]
70 ceil [3, 1; 7, 1; 4365199, 1; 8926923555113, 1]
71 ceil [13, 1; 125895962045072301881, 1]
72 floor [3, 1; 5, 1; 103, 1; 239, 1; 4219, 1; 812699, 1; 2585351, 1]
73 floor [11, 1; 17, 1; 21089, 1; 22433, 1; 73999740169, 1]
74 floor [3, 1; 71, 1; 101, 1; 578658103, 1; 1051773257, 1]
75 floor [3079, 1; 44041, 1; 193111561420273, 1]
76 ceil [3, 2; 5, 1; 3169, 1; 816521, 1; 449782982339, 1]
77 ceil [2216752883, 1; 47251744307983, 1]
78 ceil [3, 1; 51413, 1; 1358222504314734343, 1]
79 floor [31, 1; 151, 1; 89506892049989451113, 1]
80 floor [11, 1; 941, 1; 1021, 1; 5693, 1; 3049421, 1; 4567289, 1]
81 floor [5, 1; 71, 1; 28627, 1; 215589811, 1; 764931749, 1]
82 ceil [47, 1; 1259, 1; 1289, 1; 43944912097474123, 1]
83 floor [3, 2; 149, 1; 4999036679325883617121, 1]
84 floor [7, 1; 11, 1; 174122290570805452741799, 1]
85 ceil [3, 1; 43, 1; 1361, 1; 869153, 1; 5498729, 1; 31957199, 1]
86 ceil [3203, 1; 55901, 1; 79553197, 1; 3765051623, 1]
87 floor [3, 4; 5, 1; 31, 1; 9203, 1; 41863, 1; 576727, 1; 38449289, 1]
88 floor [38861, 1; 513937, 1; 76593331, 1; 140233013, 1]
89 floor [3, 1; 7, 2; 353, 1; 8268048871027049691773, 1]
90 ceil [13, 1; 2797, 1; 27827, 1; 28868071, 1; 29376841451, 1]
91 ceil [61, 1; 73, 1; 5233, 1; 73646419362356390377, 1]
92 floor [5, 1; 37, 1; 103, 1; 293, 1; 614764086308757223243, 1]
93 floor [3, 1; 115873, 1; 198313, 1; 2251201, 1; 44232969353, 1]
94 ceil [7, 1; 11, 1; 1562269, 1; 194335201, 1; 587282472191, 1]
95 ceil [5, 1; 367, 1; 619, 1; 519247, 1; 786673, 1; 59180699051, 1]
96 ceil [13, 1; 35507, 1; 774894839, 1; 153534134079721, 1]
97 ceil [7, 2; 59, 1; 44238169, 1; 858795589526947883, 1]
98 ceil [163, 1; 9439, 1; 41522423821, 1; 3438497782729, 1]
99 ceil [5, 2; 22549, 1; 779341380534231738541189, 1]
100 ceil [7, 1; 137, 1; 557, 1; 3457, 1; 33886681, 1; 14041800912019, 1]
101 ceil [11712570409153, 1; 150038532753949249, 1]
102 ceil [73, 1; 101, 1; 1839422239, 1; 259154856589424219, 1]
103 floor [5, 1; 7, 1; 23, 1; 1254527, 1; 6960478901898629601491, 1]
104 floor [3, 1; 47, 1; 293, 1; 34933408927, 1; 9741308769794621, 1]
105 floor [17, 1; 433, 1; 56569, 1; 158359, 1; 426399744565366553, 1]
106 floor [3, 2; 7, 1; 11, 1; 81146868870032399295193169459, 1]
107 floor [5, 2; 6599, 1; 78007, 1; 10466559557, 1; 834986271307, 1]
108 floor [3, 1; 53, 1; 56081, 1; 25226216539187064313228369, 1]
109 ceil [7, 2; 19, 1; 483220452218538798810473610613, 1]
110 ceil [5, 1; 41, 1; 103, 1; 892321, 1; 37330855409, 1; 1279218828023, 1]
111 floor [9851, 1; 182673125983335548347396581659, 1]
112 ceil [3, 1; 421, 1; 418811, 1; 6803988094622191647046183, 1]
113 floor [13, 1; 89, 1; 130259, 1; 1293613, 1; 36920663834397812423, 1]
114 floor [5, 2; 7, 1; 17, 1; 193, 1; 4973, 1; 4371377, 1; 1153357556985800857, 1]
115 floor [11, 1; 476351, 1; 4826713, 1; 17452549, 1; 65229620802743, 1]
116 floor [61, 1; 181, 1; 148090128383, 1; 35218466239413524401, 1]
117 ceil [7, 1; 57269, 1; 9761233, 1; 767211821, 1; 38361656193353, 1]
118 floor [3, 1; 19, 1; 269, 1; 449, 1; 541, 1; 1579, 1; 296308349, 1; 132180743061299, 1]
119 floor [11, 1; 78707878610503, 1; 532088720667916887719, 1]
120 ceil [3, 1; 5, 1; 277, 1; 15140341, 1; 67948753, 1; 215544410368891057, 1]
121 floor [1259, 1; 1463622935027261803377830512585351, 1]
122 ceil [2521, 1; 52181, 1; 28015584560066991826107866119, 1]
123 floor [3, 2; 13, 1; 29, 1; 47, 1; 9575394401, 1; 4826991554563829690747, 1]
124 ceil [5, 2; 7, 3; 11, 1; 37, 1; 83, 1; 347, 1; 3673, 1; 662531, 1; 60267293166658297, 1]
125 floor [82781, 1; 95032564620949, 1; 3747760253448692021, 1]
126 floor [3, 1; 19, 1; 61, 1; 67, 1; 919, 1; 2621, 1; 2922631, 1; 35955795566606945369, 1]
127 floor [2517803597, 1; 46839587390086903219628719667, 1]
128 floor [3, 1; 78621921075171098045981380921384828133, 1]
129 ceil [17, 1; 1245888905215806427, 1; 22272381754488856061, 1]
130 floor [139, 1; 69514019, 1; 97642232104471082026605782717, 1]
131 ceil [3, 1; 5, 1; 2903, 1; 43332784609119447769056220969416371, 1]
132 ceil [11, 1; 101, 1; 3436547, 1; 988435971082165582450926221617, 1]
133 ceil [3, 1; 941, 1; 2633, 1; 87119, 1; 11655751115454634875504625337, 1]
134 ceil [19, 1; 473503, 1; 51329263753, 1; 32689141057922569480493, 1]
135 ceil [3, 2; 5, 1; 22739, 1; 218143, 1; 19739557, 1; 6851920523707177854821, 1]
136 ceil [523, 1; 1741, 1; 11712090510045587, 1; 5662001648096736949, 1]
137 floor [3, 1; 23, 1; 1750192330021200095632281175293436174093, 1]
138 floor [5, 1; 2017, 1; 2392382158111447, 1; 10010560743529451298833, 1]
139 floor [3, 2; 11, 1; 13, 1; 277, 1; 23827, 1; 29629, 1; 1919332351117747165630603163, 1]
140 floor [613, 1; 15551, 1; 838807, 1; 7813652753, 1; 15462862898361453691, 1]
141 ceil [3, 1; 79, 1; 617, 1; 4831, 1; 20820329, 1; 65936641, 1; 1992369547324472917, 1]
142 ceil [1854598540042953977, 1; 2083698752721603384232549, 1]
143 floor [3, 2; 5, 1; 5275880417, 1; 526477825413151, 1; 61833994069945283, 1]
144 floor [7, 1; 23, 1; 96010550675448690960399424473239927264531, 1]
145 ceil [3, 1; 13, 1; 211, 1; 3756883864077588830872355654439574259227, 1]
146 floor [5, 1; 11, 1; 139, 1; 21407, 1; 69110843, 1; 5466701224528999579986002717, 1]
147 ceil [43, 1; 769, 1; 284858957, 1; 13128350061548492922429987036949, 1]
148 ceil [3, 1; 241, 1; 255679, 1; 60544699, 1; 42854407391, 1; 515655726030547637, 1]
149 ceil [103, 1; 14077759, 1; 341133259655164000267549916952099473, 1]
150 ceil [3, 2; 31, 1; 173, 1; 16091, 1; 74099, 1; 8997973, 1; 146905921, 1; 13004544241641959, 1]
151 floor [857, 1; 17117, 1; 134879619994673669377247860104312520349, 1]
152 floor [47951537, 1; 5113450051, 1; 16138688964704780529400922449, 1]
153 ceil [17, 1; 73, 1; 163, 1; 541, 1; 234431, 1; 308491432014340130431494679966439, 1]
154 ceil [3, 1; 41, 1; 31123, 1; 2753991662408143, 1; 1501397222149475570010499, 1]
155 floor [5, 1; 71, 1; 37691, 1; 164309, 1; 9505543171, 1; 1514852976880689951862199, 1]
156 ceil [29, 1; 231540199638148781, 1; 9429320191211454054256180139, 1]
157 ceil [3, 2; 7, 1; 311, 1; 26817892727, 1; 533823542419, 1; 451451883888836341769, 1]
158 floor [149, 1; 1087, 1; 15540277396079, 1; 100621363184478345509160542933, 1]
159 floor [61949, 1; 310284747614663804569, 1; 26351178536592801925543, 1]
160 ceil [31, 1; 53, 1; 16239143, 1; 29769220211, 1; 1275430032221993601832058353, 1]
161 ceil [3, 1; 239489, 1; 724751, 1; 3850245319, 1; 1010580032177315923466854871, 1]
162 floor [5, 1; 7, 1; 79, 1; 750391729, 1; 169249853237, 1; 11539135780539052516831097, 1]
163 floor [41, 1; 83, 1; 55863289, 1; 1626408929, 1; 7349005537, 1; 3566711475606896641, 1]
164 floor [11, 1; 11251, 1; 38447241841, 1; 3406400835414089176602515113697863, 1]
165 ceil [7, 1; 239, 1; 490180179679671127, 1; 39529658091384852037865286337, 1]
166 ceil [3, 2; 19, 1; 82301, 1; 166447933, 1; 3012155007068017, 1; 9188567187495298063, 1]
167 floor [5, 1; 13, 1; 109607526419, 1; 18200402958947908308697025163291283523, 1]
168 ceil [2069, 1; 2141, 1; 562699, 1; 1342727, 1; 7982611281107401, 1; 9706859148478183, 1]
169 floor [3, 1; 89959, 1; 20780093, 1; 92487143766699632552633936746386539461, 1]
170 ceil [7, 1; 11, 1; 71, 1; 189747319744439526036757887760585644196929538129, 1]
171 ceil [5, 1; 255803, 1; 1691658893503, 1; 958884471295635459788549308205533, 1]
172 floor [31, 1; 5323, 1; 90462286788253, 1; 277970682372904095497317031442121, 1]
173 floor [3, 2; 23, 1; 40090767035472498119534507145396008379695218742077, 1]
174 ceil [13, 1; 79, 1; 1335053, 1; 9018733, 1; 10160362573, 1; 132105536798541469252555001, 1]
175 ceil [61, 1; 223, 1; 99538610968892071133, 1; 24515933134871783735257874843, 1]
176 ceil [29, 1; 53, 1; 39133817, 1; 29743270013407, 1; 37109910496630846035536278271, 1]
177 floor [5, 2; 761, 1; 1157293, 1; 6030685795035668237582575134951279475220357, 1]
178 ceil [3, 1; 13, 1; 541, 1; 12586437311861691432949266568610036471259354895849, 1]
179 floor [7, 1; 1637, 1; 1889, 1; 13818401, 1; 1775653476988306074647731285971905784151, 1]
180 floor [13009, 1; 719959, 1; 1744044463387, 1; 65030253801296611003653703156199, 1]
181 ceil [23, 1; 31, 1; 2979649266120278569916371111709432364736057547798239, 1]
182 floor [3, 3; 227, 1; 71636922037, 1; 1241282363345287, 1; 7796282152444471915853263, 1]
183 floor [59, 1; 84603007, 1; 1702459764491092042971685433939858462979874079, 1]
184 ceil [3, 1; 5, 1; 103, 1; 241, 1; 827, 1; 20246297, 1; 2726139176654129660095205826898104306341, 1]
185 ceil [1229, 1; 47237, 1; 85939351, 1; 1958401833389, 1; 42346127545331, 1; 82154790040637, 1]
186 ceil [3, 2; 13, 1; 211, 1; 87256703, 1; 944118292087952011, 1; 33428056405332589554437627, 1]
187 floor [200401, 1; 1289111, 1; 526313429420135079839935906153705213615826503, 1]
188 ceil [19, 1; 37, 1; 89757817, 1; 102104426896848589, 1; 42207775829169192208312496153, 1]
189 floor [3, 1; 79, 1; 97, 1; 317, 1; 1429609, 1; 216208921, 1; 1709082758938459, 1; 141273701092574939191, 1]
190 floor [83, 1; 38933, 1; 720623437, 1; 33276411226126576063, 1; 14037307374981034714663, 1]
191 ceil [3, 2; 5, 1; 112559, 1; 401411, 1; 1223170373, 1; 874753462708016351617504252779017299, 1]
192 floor [7, 1; 11, 1; 131, 1; 22512509, 1; 19160141331465036679883957621197390323075018343, 1]
193 floor [5651, 1; 806017, 1; 201994847, 1; 65046777157, 1; 145404899642929079085677074523, 1]
194 ceil [17, 1; 43, 1; 67, 1; 355346825650506781099500834287505904025509516440462727, 1]
195 ceil [3, 1; 19, 1; 2237, 1; 272981851945899828528343134381089596208226550074183673, 1]
196 ceil [144967, 1; 5288659, 1; 42031668218063, 1; 2160296025721780837364960196925867, 1]
197 floor [3, 1; 5, 2; 23, 1; 281, 1; 25943, 1; 1017504269633963, 1; 20013774855000587, 1; 543693000234754547, 1]
198 ceil [7, 1; 31, 1; 2939, 1; 181421, 1; 2370037, 1; 1015459483892622560287054649776348352629201, 1]
199 floor [7243, 1; 441636931514131949887, 1; 174104793834552015382908391163538961, 1]
200 ceil [3, 2; 37, 1; 191763823, 1; 1623355180654387907271397, 1; 10744844378104133583573061, 1]
201 ceil [5, 1; 13, 1; 312799483231, 1; 109565848403524878308436052006071953366287973707, 1]
202 ceil [3, 1; 7, 1; 43, 1; 83, 1; 2753, 1; 4363, 1; 12583, 1; 234977, 1; 1673854740975925678209847669377022530409, 1]
203 ceil [5810138053, 1; 19356902927, 1; 79230474535386655583517837346103527999507, 1]
204 ceil [3, 1; 31, 1; 191629174144108682932689230296352224745509211793391957116181, 1]
205 floor [5, 1; 7, 2; 19, 1; 59, 1; 67003, 1; 1936906367642364464189750223192944994313192033987559, 1]
206 floor [2903, 1; 24555994757701836049245743599808139030426946878106031018677, 1]
207 ceil [1087, 1; 1447, 1; 8663, 1; 6584228713633, 1; 1589144047580435657978356406331456867673, 1]
208 floor [3, 2; 5, 2; 479, 1; 251761, 1; 438769, 1; 176829577, 1; 135446325781590116459648666942449607291, 1]
209 ceil [1373, 1; 510481, 1; 833700388111, 1; 975965423007383903065451154273696539145257, 1]
210 ceil [7, 1; 1907, 1; 45038504285810536651, 1; 1897107138058014257652909204718219036499, 1]
211 ceil [659, 1; 6047, 1; 13691, 1; 23444237, 1; 1300918211, 1; 1513948311347, 1; 905517500847288901410283, 1]
212 floor [193, 1; 539584131529, 1; 174403160063243, 1; 26287129790279843, 1; 9555876855099217417, 1]
213 ceil [3, 1; 17, 1; 31, 1; 73, 1; 46653071, 1; 4557582024019, 1; 371830556740071937620720577359925196419, 1]
214 floor [5, 1; 258827, 1; 14101488262114661988931495384625417801824642141282248652643, 1]
215 floor [7, 1; 1867, 1; 2281, 1; 1817933020485679251641, 1; 673486674757055059882325673927838039, 1]
216 floor [1637, 1; 7489, 1; 41579, 1; 867343, 1; 165107612175682200351350169194956981088552258063, 1]
217 ceil [23, 1; 474709, 1; 105528509, 1; 239969551, 1; 53932341349, 1; 4499645946997, 1; 2175833505399672623, 1]
218 floor [3, 1; 313, 1; 391083865605068260522361, 1; 795113311425890205712730012244023562767, 1]
219 ceil [281, 1; 929027926695569, 1; 2236966201805445235975407793623374067733424054083, 1]
220 floor [7, 1; 823457, 1; 110611547, 1; 10526272697, 1; 10806413448937, 1; 16103818931257708171136282969, 1]
221 floor [3, 2; 173, 1; 6154171, 1; 1660374269821, 1; 134981849791542109, 1; 1087714606972152664568344709, 1]
222 ceil [5, 1; 11, 1; 151, 1; 916525337903429, 1; 613762550478695357715198954351907019036761760411, 1]
223 floor [71, 1; 647, 1; 18593, 1; 25733577323459, 1; 15989056014042379537, 1; 26587616636334631525025263, 1]
224 floor [3, 1; 19, 1; 33365053, 1; 6757156990109, 1; 1454165396716017865988747420887363015468830011, 1]
225 floor [37, 1; 137, 1; 521, 1; 14151890869821386393511545613559510788410891127158080014972091, 1]
226 ceil [3, 1; 59, 1; 73, 1; 909451, 1; 1461450191980657, 1; 14146127113983762613, 1; 307685815095358445105329, 1]
227 ceil [63815918978999482572073, 1; 2342639431585280821680047926471101780236382869, 1]
228 ceil [3, 1; 99665125442037121532154461004225003885714545363672011353228076678291, 1]
229 floor [5, 1; 68539096267, 1; 11246229330685599361302731051, 1; 155159779870937165302633531397, 1]
230 ceil [2161, 1; 28547287, 1; 270361499, 1; 25759812957270797, 1; 2783667151931656649092106683288571, 1]
231 floor [3, 1; 7, 1; 89, 1; 8573, 1; 9788138399261, 1; 4746435702971491, 1; 16374349024906427, 1; 196236860631689569, 1]
232 floor [127, 1; 3467, 1; 127081, 1; 641143, 1; 3512701820538074810021, 1; 37962086816238164609330457785149, 1]
233 floor [3, 1; 17, 1; 49827058568969668867, 1; 106777569952331016421301, 1; 35261354540323961302021331, 1]
234 ceil [5, 1; 7, 1; 23, 1; 977, 1; 24330666299892721837255200687630661418917325454172712994932885843, 1]
235 floor [6091, 1; 326590863130549, 1; 14778798930684161, 1; 1301795217052356246557072670917245691, 1]
236 ceil [3, 1; 359, 1; 71070395858388588056355270242567133690091709228690905031828377798447, 1]
237 floor [467, 1; 74905601200649, 1; 4376261437127457970625448473683078723929754023116046239, 1]
238 ceil [5, 2; 263, 1; 47639423763250354429847333, 1; 977467153023766995611053493717461687920353, 1]
239 floor [3, 2; 1952062699, 1; 34854443457828028999160123141217608324704634039831162761132039, 1]
240 ceil [7, 1; 26856582519720269200740071, 1; 6514418156051631403439391603693197169253118267, 1]
241 floor [13, 1; 17, 1; 1723, 1; 7951, 1; 809012275629989323240973119711405192611266576692091704473629909, 1]
242 floor [3, 1; 5, 1; 101221, 1; 655847, 1; 15858945968240251, 1; 310202771250011501696210891291845739250802069, 1]
243 floor [11, 1; 139, 1; 1297, 1; 8273, 1; 619309, 1; 7447187213, 1; 129480467444107896929387976531674757430265721527, 1]
244 floor [3, 1; 220041670391997660457, 1; 29683712404715883952363289704444480240400998573902173, 1]
245 floor [47, 1; 4093, 1; 20543285209, 1; 9916648060491676297534422451875252730343149652589125638253, 1]
246 ceil [3, 3; 5, 1; 404779717, 1; 25187254007030783, 1; 56947027717235451507583479442330837096711802251, 1]
247 floor [23, 1; 113, 1; 74905109, 1; 149690618295349, 1; 5379254452170756238552893743408384984024999549491, 1]
248 ceil [31223, 1; 10041295702736077578807327556797832143721008402708683628420313589118493, 1]
249 ceil [3, 1; 29, 1; 13649, 1; 7281707, 1; 8650627, 1; 23211466519, 1; 361152751800141552401622038429552187719318869, 1]
250 ceil [31, 1; 383, 1; 1109, 1; 530279, 1; 127461824857, 1; 1991383925879, 1; 41145275370340109, 1; 17197797543913946166913, 1]
251 floor [3, 1; 5, 1; 11, 1; 42899, 1; 66353712594989, 1; 5340206271850220801352019809628117516618508015140428427, 1]
252 ceil [17, 1; 172974209, 1; 1705902060273742824076710974019314945581217944232698625262437830387, 1]
253 floor [291951046139, 1; 34364048890827782175352015362927758379402672312096363834860053439, 1]
254 ceil [3, 2; 389, 1; 5731288216651764414612532434040993325763401000541984190668585226036843543, 1]
255 floor [5, 1; 64434949, 1; 400291102559, 1; 2706199385783, 1; 114986573829222501372376406003474080485871189, 1]
256 floor [11, 1; 131, 1; 4567, 1; 1807249837, 1; 443614007927089, 1; 183102781586846530217, 1; 83078944661219418441816553, 1]
257 floor [1861, 1; 20427569650080823, 1; 129600620250225589183, 1; 32580983775662030917737863600219265107, 1]
258 floor [17, 1; 1811, 1; 114423285463260307093109393, 1; 91134445826692213847521462066879709363195235157, 1]
259 floor [5, 5; 207611879821, 1; 9335990759341, 1; 106006306355565272475067277090414404243118005992619, 1]
260 ceil [70799234670079, 1; 18138266168554728796031300993808817054622827679757515411448232769, 1]
261 ceil [3, 1; 7, 1; 1686945015723983, 1; 342465011926239397272358607, 1; 211698557587700577370902483136772201, 1]
262 floor [41, 1; 5701, 1; 75133, 1; 709739, 1; 412116522758638852710306001815394441470859126696380249159092003, 1]
263 floor [31, 3; 10709, 1; 32201812772182725555553252631542965400422349265054070251167414246833337, 1]
264 floor [11, 1; 2053, 1; 50263, 1; 17728157, 1; 1173631150600178987599130609, 1; 869999610587407376887552416992626291, 1]
265 floor [5, 1; 151051604614762919, 1; 54410029896777800686395639640856539386338238090096988065628037, 1]
266 ceil [13, 2; 661, 1; 83311, 1; 57142769, 1; 154544130239806731271108658416450948012541237654534079728457301, 1]
267 floor [3, 1; 19, 1; 859939, 1; 3353449743077659762808044051074839079336836830889376030391621875160342807, 1]
268 floor [11, 1; 43, 1; 71, 1; 389, 1; 25164899957555982893758913217817011935913052971322360147075213741788666929, 1]
269 floor [3, 1; 25583, 1; 31123, 1; 13721590774433, 1; 26104486168452431695615494761, 1; 768458651272903618876532136697, 1]
270 ceil [5, 1; 59, 1; 1592367503, 1; 2799361390518476257309307668596851104676569546702886699723891737373687, 1]
271 ceil [7, 1; 375713020482080458399668653290338341608258028042368481484204874631085878599314427, 1]
272 ceil [23, 1; 65287, 1; 361187992119222241, 1; 42580735862944300961, 1; 227763048398015512654625834329093191577, 1]
273 ceil [79, 1; 454385195851, 1; 184537062321509, 1; 1588637609500471798993, 1; 999665191346500016895824667263561, 1]
274 floor [5, 1; 7, 1; 11, 1; 29, 1; 169235070133, 1; 7860040483884626348822057, 1; 1416675544539237289992558972585430525435897, 1]
275 floor [3, 2; 2921534897, 1; 1600371029367056684776417418174458172305830282454255563953950909900070107, 1]
276 floor [107, 1; 113, 1; 11665879, 1; 6524354215039465449059, 1; 91450702128969097849495017057721819261668479875073, 1]
277 ceil [3, 1; 7, 1; 853, 1; 2881315875841834682708639854208555647901, 1; 3261182190086599652226012815731098983219, 1]
278 floor [239, 1; 1408530821556251425632230599783025749292883653246703595857102793596037436087806387, 1]
279 floor [23, 2; 38299, 1; 16023111959, 1; 2073978631402413975531378517819269605992068019892467686876247300183, 1]
280 ceil [5, 2; 11, 1; 67, 1; 2624203, 1; 34251764663321, 1; 42295977287809227075779885039, 1; 19223714466412076982651709140571, 1]
281 ceil [3, 2; 299234547868394747312091656309460581405332616111966363919864504595069286422209534661, 1]
282 ceil [7, 1; 937, 1; 4435661, 1; 61767707, 1; 2997276307217541246308964452619426027192375551550382629824281986329, 1]
283 floor [3, 1; 37, 1; 43, 1; 79, 1; 877, 1; 45472239227, 1; 716390427101097718239501316686547588165152334972881093575191903501, 1]
284 ceil [47, 1; 811, 1; 297500653981, 1; 59196129639980874511, 1; 2999534062136243669718157, 1; 10700165180630987314381553, 1]
285 ceil [6607, 1; 5967433, 1; 20972989, 1; 36908977596037655969290267, 1; 1411854760997454876912833106528598071854941, 1]
286 ceil [5, 1; 7, 1; 11, 1; 31, 1; 211, 1; 9341828591492857, 1; 93162229220023126990973, 1; 39321273597776411271648330597763605669497, 1]
287 ceil [19, 1; 53, 1; 678178561, 1; 450936039894293, 1; 2948243979594004723, 1; 41707358395930876801, 1; 4551658166257218252913, 1]
288 ceil [17, 1; 4591, 1; 102461, 1; 533696222943601021, 1; 80770966321919108254078897902453700044789377595060197867911, 1]
289 ceil [7, 1; 254489, 1; 80331235183, 1; 6685352618034234283, 1; 8092442108793354217219, 1; 89050997322633344295192097121, 1]
290 floor [5, 1; 859, 1; 13323917, 1; 24095121290261905475209101822800832415121018929671739058539474499762982862867, 1]
291 floor [3, 4; 1301, 1; 26169286618604169548858301824313573777355931240810791412925207336694077145472932231, 1]
292 ceil [283397, 1; 1663465855944371621, 1; 11699708876368363842520449901130286870601742551562080362450562879, 1]
293 floor [5, 1; 947, 1; 1307, 1; 4179022637011, 1; 426524415039064170939876198161815885977159546291337444567844735404211, 1]
294 floor [3, 1; 3735787051, 1; 207377287283197, 1; 134394845159348131325294839, 1; 70631270564641336271106264447022996609, 1]
295 ceil [16540787, 1; 14936690114453, 1; 178592674805768183150646545138188399921529822268772901632376733700153, 1]
296 floor [5, 1; 2173727, 1; 1861596223, 1; 9875476067, 1; 3932476560271323081713853625759, 1; 112310277625515191142743850552221, 1]
297 floor [3, 3; 31, 1; 107, 1; 821, 1; 1167676357, 1; 3580889747, 1; 574074616152497521613273772852578579283337961468989721263984151, 1]
298 floor [101, 1; 1597, 1; 586361, 1; 47304505243, 1; 78898781773886685474231896665824675450445379913338071073560891904173, 1]
299 floor [3, 1; 3024167, 1; 23940967, 1; 29819597828919834262739381, 1; 108999290216015497216485892621261697605120958592001, 1]
300 ceil [5, 1; 7919, 1; 492671959880669, 1; 72381231434217032223582010597724541184424496546728096228434832936781761, 1]
301 floor [17, 1; 181837, 1; 407357014350279477963674431613227, 1; 2242579139200497290342548458788785210469128928042723, 1]
302 ceil [3, 5; 23, 1; 641788733, 1; 1574555428075277478481254215076354553739588570525855620759548565591438216220987, 1]
303 floor [28641973, 1; 394376670544427789945575939961557878358324334632951602617979227189762988564383195969, 1]
304 floor [5, 2; 107, 1; 15787, 1; 33696043, 1; 15876027549245776722577187719728954712423238491167609243458318711163355328881, 1]
305 floor [13, 2; 19, 1; 83, 1; 106275825908693849, 1; 4756562357101014073723842285239, 1; 335372970302662579880136730106913529657, 1]
306 ceil [839, 1; 53712947, 1; 754149681496649, 1; 2658922263947308284417274173067533421615583452457699328614793474859, 1]
307 floor [3, 1; 5, 1; 11, 1; 1095343122381905072491719519207618112957712476877572335756692396579884353441005794967060057, 1]
308 ceil [7, 2; 67, 1; 110101501792881106890730259317244586438027754300822074565856987776838817129312187736561017, 1]
309 floor [37, 1; 71, 1; 280009, 1; 3412499, 1; 511060326544075363885019, 1; 563530409919334101748800050437516823613116320899359087, 1]
310 floor [3, 1; 11468371, 1; 1434799223304730604497039438706237, 1; 29289367644305345725222295721394825836808660096963903, 1]
311 ceil [971, 1; 2339, 1; 638256893, 1; 3371247724469, 1; 1475432527036696607, 1; 5432731160819691583, 1; 73821168062304791452291704599, 1]
312 ceil [5025192169, 1; 31128735881, 1; 44437727490132589772170455053791229, 1; 831990002957398950123907094546197616833, 1]
313 floor [5, 1; 7, 1; 571, 1; 1505328194499491, 1; 1471370171157171538103531, 1; 261310468090819921255184697386103058338669539686697, 1]
314 ceil [3, 2; 1187, 1; 1223, 1; 1770616121264781041996413268577489789615147067065488288962882042496442873618529985758799, 1]
315 ceil [23, 1; 37, 1; 707011, 1; 76898587802903061522580672399150114844685117809517450257390552089606211322404452622221, 1]
316 floor [3, 1; 5272447, 1; 21976814129, 1; 707400364773561880697, 1; 376305528504388670155907125403890796631116803794182499317, 1]
317 floor [47540136233036923996501141, 1; 3892903736128486653179356760919527390180404544257077398033501320269703, 1]
318 ceil [3, 2; 7, 1; 1009639826207, 1; 5819116598978897720196274006719892695879968088196590623087974255588162466286842567, 1]
319 ceil [53, 1; 409, 1; 11370819947, 1; 128208859913, 1; 2729160601403, 1; 8583333481996298511354159970879195512136773315061773735473, 1]
320 ceil [3, 1; 5, 1; 67, 1; 25060993, 1; 58784081476309710147019117095661392923677372239246315721716110437078206100669337211229, 1]
321 ceil [7, 1; 18077, 1; 17687192710351783, 1; 1323033264008475943544819868419464155422703018007760040776906346973640122837, 1]
322 floor [3, 1; 17, 1; 151, 1; 1471, 1; 8513, 1; 70621274970173, 1; 292874166714013, 1; 22109519730077917, 1; 1798739680795078823, 1; 74658178738838734463041, 1]
323 ceil [5, 4; 11, 1; 43, 2; 1697, 1; 40519, 1; 2473104284433458565504557, 1; 5479254288001999441946614395547674911931721044712355906003, 1]
324 floor [107, 1; 98627, 1; 979132442521, 1; 53790716988342403, 1; 42620219450204692554259727938468291866435057782185417287191407, 1]
325 ceil [3, 2; 53, 1; 5879, 1; 11713310207, 1; 1442356339226792566738751443513052793821442129650505396088764678415676153143489679, 1]
326 floor [19, 1; 569, 1; 691, 1; 75011, 1; 75707, 1; 2112793, 1; 4631676353, 1; 228246426391371444193703884355428181207253874494391461967720028909, 1]
327 ceil [5, 1; 7, 2; 13, 1; 59501046823431774377820330387593976803172101254465385486291229281621524209095684538919213326427, 1]
328 floor [3, 1; 11, 1; 491, 1; 45329, 1; 6235087811, 1; 82765605079413568430701948130388740282121943171529775977034732546468689544696677, 1]
329 ?
330 ceil [3, 2; 623803, 1; 18048764248703, 1; 511848280446313, 1; 17662149724999602178400197991, 1; 1655014407322690021750268673305025133, 1]
331 ceil [9421, 1; 45191, 1; 92269, 1; 1962011144393, 1; 39341216659449599941689524287186906723167927300617734669895803593151823291, 1]
332 floor [3, 1; 7, 1; 11619037, 1; 56127809, 1; 2243483628752651543047942207702613, 1; 197375661190662140463248093371886939890328875030037, 1]
333 ceil [13, 1; 4801967151893, 1; 2119748174280995938421459951, 1; 91657331699569094891480686172045889203676365435826010058413, 1]
334 floor [422657810299, 1; 57392496194063725963858891497167658880984766930027870638360793646902172916526442444740767, 1]
335 ceil [3, 1; 43, 1; 1187, 1; 5737, 1; 215722343, 1; 256008037695083321981844543338207779054952333303740359384894460160429920490132067719, 1]
336 floor [17, 1; 68881, 1; 82862043469604153722403744197928097522384136458428981457539160388398620944951535932222699127029, 1]
337 ceil [59, 1; 195458773, 1; 1244834444251582189009, 1; 13518086571524532839559192071944501705139921292748440958841949920720509, 1]
338 ?
339 ?
340 floor [14930810039051, 1; 15653889811269250837, 1; 62811031321498289053717, 1; 105750497680899938062971819964643676557977778327, 1]
341 ceil [3, 1; 773, 1; 1124183892283, 1; 6151979407163, 1; 749246223820854050303293, 1; 258390438945289847897782703295085772645390593600369, 1]
342 ceil [43, 1; 449, 1; 4969, 1; 113957, 1; 9540059, 1; 106108949, 1; 37435542966165739, 1; 185074538930583334493, 1; 80988860967155931525720813366574254499, 1]
343 floor [3, 2; 5, 1; 577, 1; 1733, 1; 8779, 1; 154957433, 1; 202894195083478620056232180143323823978870709664067209621316104702675564403458359251, 1]
344 ceil [1002545757675128299, 1; 540506380397457412066263916441424756626727, 1; 45839401740064427699948204288178157977759647, 1]
345 floor [233, 1; 4327, 1; 38711, 1; 114203, 1; 75005753219, 1; 235477006040839687, 1; 631068007704828212562863785819810100902967747302928432535979, 1]
346 floor [3, 1; 41, 1; 1504319, 1; 536980986652153349805042643852232495472794468604596511789464767054791253464163302566569836556879, 1]
347 floor [17, 1; 73, 1; 683, 1; 1493, 1; 157029650304261742202875786056822904550373537750857412327395459468290109498810159948162192474393, 1]
348 floor [3, 1; 5, 1; 617, 1; 2262150071, 1; 18983055452727815034316084525739785307462428955102450241010849811036013882806960032188427279, 1]
349 floor [197, 1; 1109, 1; 4925394244637, 1; 738678020821944740595544543637456690637737215030766161862389555415171780498435501858291, 1]
350 ?
351 floor [5, 1; 7, 1; 11, 1; 13007, 1; 36510912370489633, 1; 28234009363067999574731, 1; 615915068437702013598757505179051749512779521444550672533209, 1]
352 floor [71, 1; 107, 1; 729943, 1; 5909904307, 1; 194031576077992537144650240506008960305827677157721043672488369507056087856156700132523, 1]
353 ceil [806363, 1; 810251951, 1; 91280449949280587927, 1; 213248252457801194014192808063497323967673948282159367838682172245799613, 1]
354 floor [3, 1; 5, 2; 32609, 1; 5242544487716275746744152129303, 1; 1983823622750557217579955975078109721973094648444371504797705586038417, 1]
355 ceil [11, 1; 73, 1; 863, 1; 19777, 1; 3711822219852467190638661878983643634123130881592306152278924548705367289581002642148075831992567, 1]
356 ceil [7, 2; 43, 1; 710959, 1; 67919554015700567798414933866640004386531048189959615065615036268622084711942572866410369359188577, 1]
357 floor [13, 1; 211, 1; 22993, 1; 733119545482660723, 1; 857639380860838711284619359373241675807, 1; 5131365539383020852571054499977914131019659, 1]
358 ceil [3, 2; 8117283116177, 1; 38364066065597411, 1; 145206506011909550146186835295403608741003854624846553732799721040691309779961, 1]
359 floor [5, 1; 11, 1; 109, 1; 283, 1; 1894117, 1; 150226020377, 1; 78558949895761809194592017777, 1; 21462022576963058753657969108603719622310963919197851441, 1]
360 ceil [17, 1; 397, 1; 2591971, 1; 411246936359703971342929, 1; 226282859460355120250922238049786751363363291461439888273128844093060236221, 1]
361 ?
362 floor [7, 1; 5261, 1; 1908923, 1; 357165948709, 1; 9983962346287, 1; 25975035922153289241706179189411514693713622563613554973136991887040906601, 1]
363 floor [3, 2; 19, 1; 76158393902907812065156975690286798911852039351848529004825976815569912022816024813250048228998223077672197, 1]
364 ?
365 floor [3, 1; 7, 1; 41, 1; 307, 1; 2699, 1; 140507931829007, 1; 7839425037090857134853, 1; 175077308728699095058928849, 1; 378629590623774615008119121236883846753, 1]
366 ceil [47, 1; 9209, 1; 83371871353, 1; 3188290565699, 1; 230251021625844423478973297, 1; 3932914757232446169711128618414942000852543894589890779, 1]
367 floor [5, 1; 109171, 1; 70537001, 1; 5411773179747698074261757368070733159080858393968729104708244562647743200119955600608403950881931, 1]
368 ceil [3, 2; 659, 1; 76243, 1; 102019, 1; 12904603549, 1; 110766054846287, 1; 6319803106546331592184233473924793723054012632627304517798382008072584611, 1]
369 ?
370 ceil [3, 1; 11, 1; 112187576363, 1; 201346673389734435575830511, 1; 67491980126953243264494684623347, 1; 33133592167755101068388133190602024030487, 1]
371 ceil [13, 1; 19, 1; 97501, 1; 1545007, 1; 89601932758176712160489817659522075116856127340708468329416865948539444626125260303466919330629389, 1]
372 floor [3, 1; 29, 2; 20389, 1; 79341767630031149, 1; 493587076698316172732328822938458907431189, 1; 3309824905713765750671203156589053299233759783, 1]
373 floor [69125513, 1; 2317804066667, 1; 236945171802671, 1; 22245321418615561857061330577343617, 1; 15791093575592596282279664078205888378190159, 1]
374 ceil [3, 1; 280519338749792063738951007019, 1; 31692739296593099569146545249078036123261903173096965735194708862003454772925604871, 1]
375 ?
376 floor [7, 1; 635839084663, 1; 23969477682805807484316318002663481900471871251275520185750711006811766862548783684329114781804182107, 1]
377 ceil [5, 2; 8534809219823852495268638125614066967463001279146294286631070620360674479899633413695575324857923106427335925967, 1]
378 ceil [3, 1; 17, 1; 19, 1; 3391909, 1; 22900277, 1; 29305396351583294555535431, 1; 193467276336615515103247951255764675267041838986344686858624044095007387, 1]
379 ceil [13, 1; 101, 1; 839, 1; 894198762404878375188252170442983, 1; 1114664468060028089413471542186199, 1; 777300431671029782040860589819198011800063, 1]
380 floor [3, 3; 86297, 1; 1127849, 1; 3818681, 1; 3992575838833, 1; 42603652867175537863285651075730254322990413166908524712392487762925982707423708011, 1]
381 ceil [563077, 1; 216003031, 1; 392096333, 1; 1706625709, 1; 31098376789, 1; 1348830538477898540934837608968253806416281751135772594988782559800610597, 1]
382 ceil [31, 1; 89, 1; 6143, 1; 1228013, 1; 49506157, 1; 6626579455900349582225280987770916697216472571961210459967624528466335663706468303281075943269, 1]
383 ceil [5, 1; 73, 1; 1361, 1; 5370851, 1; 182298290524157, 1; 348304780434469, 1; 204522172238277787, 1; 394127989999591756237018504806951938854271714248789275133, 1]
384 ceil [855467, 1; 42266227, 1; 92108299, 1; 5810134758653, 1; 1411438911611546229538369971986834936773130819006225017164154856756220213512766943, 1]
385 floor [19, 1; 43, 1; 4483230177389, 1; 14912851671019141628823577907775434813772378494362105403378655010181930467814822233757414102508747029, 1]
386 floor [3, 1; 5, 1; 41213241847, 1; 176715950372307389364295463739410335583359569297141241490323026372458927751924242999324508114214296923291, 1]
387 floor [41, 1; 139, 1; 709, 1; 54074049075368089440103473975891178881270792501924875281303009357104756874781588978099176164170744211562070921, 1]
388 ceil [3, 1; 29, 1; 24419, 1; 62477273, 1; 79048566503, 1; 41648617251314616345913447346915758833921672255395231709057889727293120698926298837668164589, 1]
389 ?
390 ?
391 ceil [1301, 1; 1267332043979966838557279, 1; 2875895229316186646710319, 1; 737246963935662654264509778643947327428834518076528134543132115083, 1]
392 floor [3, 1; 5, 1; 7, 1; 59, 1; 137, 1; 65673810180799, 1; 125438158608762501567681885532294678247733238635442319549234705029656936168358676470382737690004249, 1]
393 ceil [124756526693, 1; 112085770551866448539972072216931090828532171147347385691908476354225789794668433275335082290124118962037567, 1]
394 ceil [19, 1; 209431, 1; 12735337, 1; 506004788221893730621, 1; 49818186982405659741433, 1; 21892542363472531077180179480228963579423797169611047584860789, 1]
395 floor [17, 2; 641, 1; 109313, 1; 316037, 1; 93424729517288471629703, 1; 12373287066783458637263941, 1; 7560685864002252436908766986179329170303080578718573383, 1]
396 ceil [3, 1; 53, 1; 3706938008311, 1; 39644050340189, 1; 14583203792519524223183, 1; 1581102277356546759679128361, 1; 207634907305276058673782449268997776048401, 1]
397 floor [5, 1; 7307, 1; 10313, 1; 12894829, 1; 29337031, 1; 63077126797214694341027, 1; 24884903471549108193905287223052970106909157432379403298582139220708906939, 1]
398 floor [594168017593, 1; 753103149908707775174772936123141146963993353608020229748191039202449101067500883991429238078618325869325347, 1]
399 floor [43, 1; 245223758478119774613769, 1; 2236002031852499257881293063, 1; 37956882641640506646449158155179271213895142952907407663235109244283, 1]
400 ?
401 floor [3, 2; 23, 1; 4523, 1; 1246254199, 1; 3067963260278207127603213389076864011421745743133796742520611819164976673913555028253246723957780374387407, 1]
402 ceil [25613423547361019, 1; 252329536387805788421, 1; 186186337617831311639221859, 1; 5949770141444418049069651180793510208137576105281311541967, 1]
403 floor [29, 1; 47, 1; 733, 1; 1271920232881048807535411, 1; 11268186004725386006863586891051230439312822374474629021518434017268834262617721257252310897, 1]
404 ceil [3, 1; 461, 1; 11047, 1; 11655239, 1; 160825900456082271315749596962586084776330413209200953517238284376295223432750104051666031075100278025043533, 1]
405 floor [2218214722553, 1; 7697439913218018411920789, 1; 3354469242018870579366215204089752239309930476836843901196867635338433967111262373769, 1]
406 floor [43, 1; 101, 1; 26376299847990099979785571238178647782931935430534409366129474392640116722074843767421234256396324249214350105366389229, 1]
407 ?
408 ceil [61, 1; 797, 1; 28871, 1; 7129061, 1; 104482271, 1; 188939651433018823817087465969, 1; 3163170359881352774565855131821, 1; 733319243922876598330123282833183391327, 1]
409 ceil [3, 1; 29, 1; 251861, 1; 1359493, 1; 30763556082630535856953661762891360910421801573147537503780170512898154430796142966347638704657636109856639731, 1]
410 ceil [24286179637, 1; 1783501412057, 1; 22004938574481176056662358111, 1; 1922962708380611455311699538979594327488376357905041008705619734830027939, 1]
411 floor [3, 2; 53, 1; 15476639815718937494837923, 1; 6278186574247795029659050883, 1; 79090515564374247751241045582791341765845108400547815771374838488797, 1]