Primality testing Phi(11971,89) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 25.64% and helper 0.32% (77.25% proof) Phi(11971,89) is Fermat and Lucas PRP! (394.8081s+0.0009s)

GP/PARI CALCULATOR Version 2.3.4 (released) amd64 running linux (x86-64/GMP-4.3.0 kernel) 64-bit version compiled: Apr 17 2009, gcc-4.1.2 (Gentoo 4.1.2 p1.0.2) (readline v5.2 enabled, extended help not available) Copyright (C) 2000-2006 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 8000000, primelimit = 500000 Testing a PRP called "89_11971.in". Pol[1, 1] with [h, u]=[5, 1] has ratio=1.6276345495500688194 E-1380 at X, ratio=3.580073548520162205 E-1380 at Y, witness=2. Pol[2, 1] with [h, u]=[5, 1] has ratio=0.08660704902544096269 at X, ratio=3.3936549920888186994 E-658 at Y, witness=3. Pol[3, 1] with [h, u]=[5, 1] has ratio=0.007060644288023561680 at X, ratio=1.3527880275180646789 E-329 at Y, witness=3. Pol[4, 1] with [h, u]=[4, 1] has ratio=7.694101170290470078 E-112 at X, ratio=1.0465645168878783589 E-275 at Y, witness=3. Pol[5, 1] with [h, u]=[4, 1] has ratio=1.0407484864493000166 E-193 at X, ratio=1.1030445043210059088 E-275 at Y, witness=5. Pol[6, 1] with [h, u]=[4, 1] has ratio=4.511090965074270439 E-235 at X, ratio=1.0791938965290461405 E-275 at Y, witness=2. Pol[7, 1] with [h, u]=[4, 1] has ratio=3.110122511856801657 E-256 at X, ratio=3.3832484827740377300 E-276 at Y, witness=7. Pol[8, 1] with [h, u]=[4, 1] has ratio=8.872749154206530550 E-266 at X, ratio=5.580498414015664906 E-276 at Y, witness=5. Pol[9, 1] with [h, u]=[7, 2] has ratio=1.1262493967659725278 E-158 at X, ratio=1.8186119493212746442 E-647 at Y, witness=3. Pol[10, 1] with [h, u]=[7, 2] has ratio=1.2971375494992113004 E-333 at X, ratio=7.730393532825986227 E-496 at Y, witness=2. Pol[11, 1] with [h, u]=[7, 2] has ratio=3.475208283184315273 E-224 at X, ratio=1.6776840328877040217 E-332 at Y, witness=3. Pol[12, 1] with [h, u]=[8, 2] has ratio=0.17191352918397914197 at X, ratio=1.3501666378789559442 E-297 at Y, witness=7. Pol[13, 1] with [h, u]=[8, 2] has ratio=0.08685480477240545768 at X, ratio=1.1604250092500893465 E-170 at Y, witness=2. Pol[14, 1] with [h, u]=[8, 2] has ratio=0.09090047494910361583 at X, ratio=5.103062575433676584 E-98 at Y, witness=3. Pol[15, 1] with [h, u]=[9, 3] has ratio=0.10401045455876733599 at X, ratio=6.498699574866059618 E-331 at Y, witness=19. Pol[16, 1] with [h, u]=[10, 3] has ratio=0.008117400135258075392 at X, ratio=5.082494391432160645 E-495 at Y, witness=5. Pol[17, 1] with [h, u]=[10, 3] has ratio=0.08635824519284576177 at X, ratio=2.0267658172977691788 E-330 at Y, witness=3. Pol[18, 1] with [h, u]=[10, 3] has ratio=0.012674748137336487208 at X, ratio=7.608149990471885206 E-221 at Y, witness=5. Pol[19, 1] with [h, u]=[10, 3] has ratio=0.05172879542200615169 at X, ratio=1.0562498093053093778 E-147 at Y, witness=11. Pol[20, 1] with [h, u]=[12, 4] has ratio=0.019235200054676021500 at X, ratio=2.0816038266543071378 E-554 at Y, witness=3. Pol[21, 1] with [h, u]=[12, 4] has ratio=0.07774206369888864278 at X, ratio=1.0657878408348948562 E-403 at Y, witness=7. Pol[22, 1] with [h, u]=[12, 4] has ratio=0.03437644411117730445 at X, ratio=5.701514329638646543 E-294 at Y, witness=5. Pol[23, 1] with [h, u]=[12, 4] has ratio=0.007574084119533420700 at X, ratio=2.204123948583350118 E-214 at Y, witness=3. Pol[24, 1] with [h, u]=[12, 4] has ratio=0.021448809055287624244 at X, ratio=3.210665225648335482 E-156 at Y, witness=7. Pol[25, 1] with [h, u]=[12, 4] has ratio=0.005545263614259560663 at X, ratio=4.661708018943123030 E-114 at Y, witness=3. Pol[26, 1] with [h, u]=[14, 5] has ratio=0.04013590208351762291 at X, ratio=6.798598290223572616 E-475 at Y, witness=5. Pol[27, 1] with [h, u]=[14, 5] has ratio=0.05205791299013295463 at X, ratio=1.0932528898866788670 E-365 at Y, witness=5. Pol[28, 1] with [h, u]=[14, 5] has ratio=0.03684700897030245628 at X, ratio=8.469295359499301626 E-282 at Y, witness=3. Pol[29, 1] with [h, u]=[14, 5] has ratio=0.03211802344930026146 at X, ratio=4.169519063187898225 E-217 at Y, witness=3. Pol[30, 1] with [h, u]=[14, 5] has ratio=0.0007829063801177717266 at X, ratio=1.9660298739276459676 E-167 at Y, witness=13. Pol[31, 1] with [h, u]=[14, 5] has ratio=0.04102403050727998453 at X, ratio=4.120768035721435585 E-129 at Y, witness=5. Pol[32, 1] with [h, u]=[16, 6] has ratio=0.023264787203660780686 at X, ratio=1.8498731517983751678 E-450 at Y, witness=19. Pol[33, 1] with [h, u]=[16, 6] has ratio=0.007429526928510799737 at X, ratio=1.0177015446773477022 E-360 at Y, witness=5. Pol[34, 1] with [h, u]=[16, 6] has ratio=0.009595965114034005882 at X, ratio=6.055686060340420475 E-289 at Y, witness=7. Pol[35, 1] with [h, u]=[16, 6] has ratio=0.03190182764590156245 at X, ratio=1.5113376503765830509 E-231 at Y, witness=47. Pol[36, 1] with [h, u]=[16, 6] has ratio=0.04802602954892544437 at X, ratio=1.3934160344400962711 E-185 at Y, witness=11. Pol[37, 1] with [h, u]=[18, 7] has ratio=0.025307651942113461604 at X, ratio=4.835552820002924950 E-472 at Y, witness=3. Pol[38, 1] with [h, u]=[16, 6] has ratio=0.005901196380147038511 at X, ratio=3.087130380024557399 E-68 at Y, witness=11. Pol[39, 1] with [h, u]=[18, 7] has ratio=0.006885237989511493483 at X, ratio=1.9434038354803348134 E-375 at Y, witness=19. Pol[40, 1] with [h, u]=[18, 7] has ratio=0.003432980526624849114 at X, ratio=1.6905937002582526076 E-309 at Y, witness=11. Pol[41, 1] with [h, u]=[18, 7] has ratio=0.004825496687717025156 at X, ratio=2.886113119406868059 E-255 at Y, witness=7. Pol[42, 1] with [h, u]=[18, 7] has ratio=0.005157919956925831649 at X, ratio=1.7027458713703474762 E-210 at Y, witness=2. Pol[43, 1] with [h, u]=[18, 7] has ratio=0.010884061269051163250 at X, ratio=9.988863015495347215 E-174 at Y, witness=2. Pol[44, 1] with [h, u]=[20, 8] has ratio=0.002000921912743121300 at X, ratio=2.503009890787826333 E-445 at Y, witness=7. Pol[45, 1] with [h, u]=[20, 8] has ratio=0.00003338263496929236844 at X, ratio=2.5039445216267157700 E-375 at Y, witness=5. Pol[46, 1] with [h, u]=[20, 8] has ratio=0.012950616094528861736 at X, ratio=2.2979276231726596000 E-316 at Y, witness=7. Pol[47, 1] with [h, u]=[20, 8] has ratio=0.014983565001885331023 at X, ratio=9.086248814015717698 E-267 at Y, witness=5. Pol[48, 1] with [h, u]=[20, 8] has ratio=0.002869955519565375994 at X, ratio=5.457590251717533512 E-225 at Y, witness=7. Pol[49, 1] with [h, u]=[20, 8] has ratio=0.0017577071234049536226 at X, ratio=8.294742153627984320 E-190 at Y, witness=3. Pol[50, 1] with [h, u]=[20, 8] has ratio=0.011777831171316476521 at X, ratio=3.707089653771678045 E-160 at Y, witness=5. Pol[51, 1] with [h, u]=[20, 8] has ratio=0.007277373214562809450 at X, ratio=3.377144517245425541 E-135 at Y, witness=2. Pol[52, 1] with [h, u]=[21, 9] has ratio=0.010633997254611386123 at X, ratio=2.1931960197392222864 E-274 at Y, witness=3. Pol[53, 1] with [h, u]=[21, 9] has ratio=0.004428920219803951330 at X, ratio=4.128480859888360236 E-247 at Y, witness=2. Pol[54, 1] with [h, u]=[22, 9] has ratio=0.002818988029597297585 at X, ratio=3.539477340343346077 E-326 at Y, witness=11. Pol[55, 1] with [h, u]=[22, 9] has ratio=0.0004912077514066266543 at X, ratio=7.081795190279813147 E-280 at Y, witness=2. Pol[56, 1] with [h, u]=[22, 9] has ratio=0.010611671817143623172 at X, ratio=3.472728168072166020 E-240 at Y, witness=3. Pol[57, 1] with [h, u]=[22, 9] has ratio=0.0008040264706712018540 at X, ratio=3.258416001069933594 E-206 at Y, witness=7. Pol[58, 1] with [h, u]=[22, 9] has ratio=0.013223525788128237961 at X, ratio=4.867682533951676213 E-177 at Y, witness=3. Pol[59, 1] with [h, u]=[23, 10] has ratio=0.0005347855881484648913 at X, ratio=1.6889875708337374280 E-339 at Y, witness=19. Pol[60, 1] with [h, u]=[23, 10] has ratio=0.003674233742184270100 at X, ratio=1.0366688395432904620 E-308 at Y, witness=7. Pol[61, 1] with [h, u]=[23, 10] has ratio=0.002444672206245324286 at X, ratio=5.537525022646524968 E-281 at Y, witness=19. Pol[62, 1] with [h, u]=[23, 10] has ratio=0.000000016707758966911152969 at X, ratio=6.891974076249926785 E-261 at Y, witness=7. Pol[63, 1] with [h, u]=[23, 10] has ratio=8.246841472787701256 E-36 at X, ratio=1.4662405334570236994 E-241 at Y, witness=13. Pol[64, 1] with [h, u]=[23, 10] has ratio=0.006348679351796856524 at X, ratio=1.3296521143600452526 E-211 at Y, witness=5. Pol[65, 1] with [h, u]=[23, 10] has ratio=0.00004002614647898101914 at X, ratio=1.3633237411147619888 E-192 at Y, witness=2. Pol[66, 1] with [h, u]=[23, 10] has ratio=0.0013340556701777180632 at X, ratio=3.036919221985604575 E-175 at Y, witness=5. Pol[67, 1] with [h, u]=[23, 10] has ratio=0.010797511837541458393 at X, ratio=1.3739753020432144047 E-159 at Y, witness=5. Pol[68, 1] with [h, u]=[25, 11] has ratio=0.002128908579847056864 at X, ratio=8.599530773021368685 E-381 at Y, witness=2. Pol[69, 1] with [h, u]=[25, 11] has ratio=0.011191012683457016786 at X, ratio=3.140237578183987821 E-349 at Y, witness=2. Pol[70, 1] with [h, u]=[25, 11] has ratio=0.0005368598477042684036 at X, ratio=2.495590292440575163 E-320 at Y, witness=2. Pol[71, 1] with [h, u]=[25, 11] has ratio=0.0011776063530132000897 at X, ratio=7.681719546194277147 E-294 at Y, witness=5. Pol[72, 1] with [h, u]=[25, 11] has ratio=0.003733037701423788068 at X, ratio=1.6655008162302403898 E-269 at Y, witness=7. Pol[73, 1] with [h, u]=[25, 11] has ratio=0.0004716144036731915163 at X, ratio=3.136490935730841646 E-247 at Y, witness=7. Pol[74, 1] with [h, u]=[25, 11] has ratio=0.006654280787176095130 at X, ratio=6.933035192446414584 E-227 at Y, witness=11. Pol[75, 1] with [h, u]=[25, 11] has ratio=0.002628071824628631658 at X, ratio=3.926919189753072506 E-208 at Y, witness=2. Pol[76, 1] with [h, u]=[27, 12] has ratio=0.002140989207660000089 at X, ratio=4.494284462617937037 E-424 at Y, witness=3. Pol[77, 1] with [h, u]=[25, 11] has ratio=0.004535446123679673568 at X, ratio=8.835352388838363855 E-159 at Y, witness=7. Pol[78, 1] with [h, u]=[27, 12] has ratio=0.002085062630903842715 at X, ratio=1.3773141862296258476 E-378 at Y, witness=11. Pol[79, 1] with [h, u]=[27, 12] has ratio=0.002107514042204827413 at X, ratio=1.2382927131375664639 E-349 at Y, witness=3. Pol[80, 1] with [h, u]=[27, 12] has ratio=0.0015134564878487343238 at X, ratio=6.309792873086469274 E-323 at Y, witness=5. Pol[81, 1] with [h, u]=[27, 12] has ratio=0.0007308393252279501130 at X, ratio=2.994514532690816401 E-298 at Y, witness=7. Pol[82, 1] with [h, u]=[27, 12] has ratio=0.0012054242470060426216 at X, ratio=1.6774688300833391471 E-275 at Y, witness=7. Pol[83, 1] with [h, u]=[27, 12] has ratio=0.002583268771034132285 at X, ratio=1.3890359790167784195 E-254 at Y, witness=3. Pol[84, 1] with [h, u]=[27, 12] has ratio=0.002861581573217274174 at X, ratio=3.891277992305916962 E-235 at Y, witness=17. Pol[85, 1] with [h, u]=[27, 12] has ratio=0.006274197837916598271 at X, ratio=3.5020106014877371408 E-217 at Y, witness=3. Pol[86, 1] with [h, u]=[28, 13] has ratio=0.0019258270711376581060 at X, ratio=3.376822899863925413 E-374 at Y, witness=3. Pol[87, 1] with [h, u]=[28, 13] has ratio=0.002695578795170324074 at X, ratio=1.985155782148016194 E-360 at Y, witness=7. Pol[88, 1] with [h, u]=[28, 13] has ratio=0.0014469443905976850799 at X, ratio=3.584772088176161542 E-347 at Y, witness=17. Pol[89, 1] with [h, u]=[28, 13] has ratio=0.002998539410261169340 at X, ratio=2.0748801050215478842 E-334 at Y, witness=7. Pol[90, 1] with [h, u]=[28, 13] has ratio=0.0017255385572497470788 at X, ratio=4.437743009778393459 E-322 at Y, witness=11. Pol[91, 1] with [h, u]=[28, 13] has ratio=0.0016225297701974585832 at X, ratio=3.0831289973661454892 E-310 at Y, witness=7. Pol[1, 2] with [h, u]=[5, 1] has ratio=2.697031699238860107 E-1380 at X, ratio=2.721327373652221996 E-1380 at Y, witness=5. Pol[2, 2] with [h, u]=[5, 1] has ratio=0.10705508251270807009 at X, ratio=5.206878373572677967 E-658 at Y, witness=5. Pol[3, 2] with [h, u]=[5, 1] has ratio=0.3333985427166455234 at X, ratio=1.7950098562725369696 E-329 at Y, witness=3. Pol[4, 2] with [h, u]=[4, 1] has ratio=6.964841614849832521 E-137 at X, ratio=7.883524555351360668 E-301 at Y, witness=2. Pol[5, 2] with [h, u]=[4, 1] has ratio=3.606724515701922816 E-219 at X, ratio=1.1760902963875158209 E-300 at Y, witness=5. Pol[6, 2] with [h, u]=[4, 1] has ratio=2.6175421991267143176 E-260 at X, ratio=7.403088177711536565 E-301 at Y, witness=2. Pol[7, 2] with [h, u]=[4, 1] has ratio=1.0469190416062769626 E-280 at X, ratio=5.441394066784074375 E-301 at Y, witness=2. Pol[8, 2] with [h, u]=[4, 1] has ratio=9.053314793206067075 E-291 at X, ratio=9.537437480241060494 E-301 at Y, witness=3. Pol[9, 2] with [h, u]=[7, 2] has ratio=1.4393487668771091203 E-157 at X, ratio=1.3651537649682312076 E-647 at Y, witness=7. Pol[10, 2] with [h, u]=[7, 2] has ratio=1.1171169349033105514 E-332 at X, ratio=1.0399239762164730378 E-495 at Y, witness=5. Pol[11, 2] with [h, u]=[7, 2] has ratio=7.307316491849909943 E-224 at X, ratio=2.4788539342068100114 E-332 at Y, witness=3. Pol[12, 2] with [h, u]=[8, 2] has ratio=0.03210638610606863384 at X, ratio=6.608764615149762445 E-298 at Y, witness=3. Pol[13, 2] with [h, u]=[8, 2] has ratio=0.06396284508963929494 at X, ratio=1.2287648813926929973 E-170 at Y, witness=13. Pol[14, 2] with [h, u]=[8, 2] has ratio=0.18867961204082568362 at X, ratio=4.317794622524219145 E-98 at Y, witness=5. Pol[15, 2] with [h, u]=[9, 3] has ratio=0.03522475081585598996 at X, ratio=6.957849491323385601 E-331 at Y, witness=17. Pol[16, 2] with [h, u]=[10, 3] has ratio=0.03796485492054546388 at X, ratio=5.482299549367765805 E-495 at Y, witness=7. Pol[17, 2] with [h, u]=[10, 3] has ratio=0.015523145461949960007 at X, ratio=1.7170153940167003362 E-330 at Y, witness=2. Pol[18, 2] with [h, u]=[10, 3] has ratio=0.03758488086959789016 at X, ratio=9.143633655548932911 E-221 at Y, witness=5. Pol[19, 2] with [h, u]=[10, 3] has ratio=0.03631649094835362057 at X, ratio=1.2483296965092361103 E-147 at Y, witness=7. Pol[20, 2] with [h, u]=[12, 4] has ratio=0.015995873332353288222 at X, ratio=2.1150463838826216342 E-554 at Y, witness=17. Pol[21, 2] with [h, u]=[12, 4] has ratio=0.09997554883319061183 at X, ratio=1.4754253841572911990 E-403 at Y, witness=3. Pol[22, 2] with [h, u]=[12, 4] has ratio=0.014120167697435035747 at X, ratio=6.046461389212203122 E-294 at Y, witness=11. Pol[23, 2] with [h, u]=[12, 4] has ratio=0.05883981114328891747 at X, ratio=3.062201215562837759 E-214 at Y, witness=5. Pol[24, 2] with [h, u]=[12, 4] has ratio=0.016328964711131802362 at X, ratio=2.966481389077048647 E-156 at Y, witness=2. Pol[25, 2] with [h, u]=[12, 4] has ratio=0.04855705752101181923 at X, ratio=4.675358260192131547 E-114 at Y, witness=11. Pol[26, 2] with [h, u]=[14, 5] has ratio=0.018076934976142081032 at X, ratio=5.610344511951583432 E-475 at Y, witness=2. Pol[27, 2] with [h, u]=[14, 5] has ratio=0.0006609903108622118298 at X, ratio=7.634979847286988220 E-366 at Y, witness=5. Pol[28, 2] with [h, u]=[14, 5] has ratio=0.028437050422738190064 at X, ratio=1.0541052121745242853 E-281 at Y, witness=2. Pol[29, 2] with [h, u]=[14, 5] has ratio=0.04470158826602348428 at X, ratio=4.012503755697252436 E-217 at Y, witness=3. Pol[30, 2] with [h, u]=[14, 5] has ratio=0.0004131272546560228339 at X, ratio=2.2498582625868938484 E-167 at Y, witness=2. Pol[31, 2] with [h, u]=[14, 5] has ratio=0.04588777333387185553 at X, ratio=3.790561614785791424 E-129 at Y, witness=2. Pol[32, 2] with [h, u]=[16, 6] has ratio=0.004882646431975632741 at X, ratio=1.8215329800416762258 E-450 at Y, witness=11. Pol[33, 2] with [h, u]=[16, 6] has ratio=0.014875293411644849198 at X, ratio=8.463120392992621585 E-361 at Y, witness=5. Pol[34, 2] with [h, u]=[16, 6] has ratio=0.024059458271665445274 at X, ratio=6.115849407490656748 E-289 at Y, witness=2. Pol[35, 2] with [h, u]=[16, 6] has ratio=0.007267010114379166157 at X, ratio=1.6538968639097066515 E-231 at Y, witness=7. Pol[36, 2] with [h, u]=[16, 6] has ratio=0.003117787036594418798 at X, ratio=1.4413235532614177300 E-185 at Y, witness=3. Pol[37, 2] with [h, u]=[18, 7] has ratio=0.019787829462183970350 at X, ratio=5.379118032510874648 E-472 at Y, witness=5. Pol[38, 2] with [h, u]=[16, 6] has ratio=0.016624020568024547203 at X, ratio=3.213661242229349314 E-68 at Y, witness=3. Pol[39, 2] with [h, u]=[18, 7] has ratio=0.0016037053762497140487 at X, ratio=2.2982354320309409650 E-375 at Y, witness=17. Pol[40, 2] with [h, u]=[18, 7] has ratio=0.0016526757568233879183 at X, ratio=1.8271142587485652267 E-309 at Y, witness=11. Pol[41, 2] with [h, u]=[18, 7] has ratio=0.008828484873134986003 at X, ratio=3.079480441800319633 E-255 at Y, witness=11. Pol[42, 2] with [h, u]=[18, 7] has ratio=0.007116719469440952554 at X, ratio=1.7271967197390732131 E-210 at Y, witness=2. Pol[43, 2] with [h, u]=[18, 7] has ratio=0.00012908567117953554950 at X, ratio=9.304691754601338030 E-174 at Y, witness=2. Pol[44, 2] with [h, u]=[20, 8] has ratio=0.006958040387039118401 at X, ratio=2.2329911427725664572 E-445 at Y, witness=5. Pol[45, 2] with [h, u]=[20, 8] has ratio=0.0008344038514504084139 at X, ratio=2.4261485170209140644 E-375 at Y, witness=5. Pol[46, 2] with [h, u]=[20, 8] has ratio=0.013129176324140056248 at X, ratio=2.1842985158473835198 E-316 at Y, witness=11. Pol[47, 2] with [h, u]=[20, 8] has ratio=0.002660044212762904803 at X, ratio=8.336998472527172290 E-267 at Y, witness=5. Pol[48, 2] with [h, u]=[20, 8] has ratio=0.004036742455543674494 at X, ratio=4.555404022392737834 E-225 at Y, witness=11. Pol[49, 2] with [h, u]=[20, 8] has ratio=0.005662099927381009773 at X, ratio=1.0202232878533004217 E-189 at Y, witness=23. Pol[50, 2] with [h, u]=[20, 8] has ratio=0.005192003929348401192 at X, ratio=3.492003093831764079 E-160 at Y, witness=5. Pol[51, 2] with [h, u]=[20, 8] has ratio=0.023703035309880702168 at X, ratio=3.694043093012294643 E-135 at Y, witness=2. Pol[52, 2] with [h, u]=[21, 9] has ratio=0.004840187948601853691 at X, ratio=2.2492350014526484224 E-274 at Y, witness=13. Pol[53, 2] with [h, u]=[21, 9] has ratio=0.0014425549454055985963 at X, ratio=4.010874271667781490 E-247 at Y, witness=3. Pol[54, 2] with [h, u]=[22, 9] has ratio=0.003722455414957501526 at X, ratio=3.886418251977453318 E-326 at Y, witness=2. Pol[55, 2] with [h, u]=[22, 9] has ratio=0.009153693835673468553 at X, ratio=7.245121049883145039 E-280 at Y, witness=11. Pol[56, 2] with [h, u]=[22, 9] has ratio=0.002359372538362088087 at X, ratio=3.178675749642641646 E-240 at Y, witness=5. Pol[57, 2] with [h, u]=[22, 9] has ratio=0.002695376023557842404 at X, ratio=3.200336164110746866 E-206 at Y, witness=13. Pol[58, 2] with [h, u]=[22, 9] has ratio=0.010997305024975105532 at X, ratio=5.109492848835602702 E-177 at Y, witness=2. Pol[59, 2] with [h, u]=[23, 10] has ratio=0.005393935318190739750 at X, ratio=2.484953399330564612 E-339 at Y, witness=13. Pol[60, 2] with [h, u]=[23, 10] has ratio=0.0007889473569082460419 at X, ratio=8.491328920220983746 E-309 at Y, witness=3. Pol[61, 2] with [h, u]=[23, 10] has ratio=0.0018738487047188125120 at X, ratio=7.829132133408909538 E-281 at Y, witness=2. Pol[62, 2] with [h, u]=[23, 10] has ratio=0.00000003954772763435028654 at X, ratio=7.104964084090141535 E-261 at Y, witness=7. Pol[63, 2] with [h, u]=[23, 10] has ratio=4.504222674499113578 E-35 at X, ratio=1.6026741389573257810 E-241 at Y, witness=7. Pol[64, 2] with [h, u]=[23, 10] has ratio=0.010391921175709166460 at X, ratio=1.4844679113273990320 E-211 at Y, witness=2. Pol[65, 2] with [h, u]=[23, 10] has ratio=0.009317534876000226821 at X, ratio=1.1156398985129602949 E-192 at Y, witness=11. Pol[66, 2] with [h, u]=[23, 10] has ratio=0.003789854486214475990 at X, ratio=2.774612975095634850 E-175 at Y, witness=13. Pol[67, 2] with [h, u]=[23, 10] has ratio=0.00011194582193241333855 at X, ratio=1.4218695131680493929 E-159 at Y, witness=7. Pol[68, 2] with [h, u]=[25, 11] has ratio=0.003562508724754614967 at X, ratio=9.001651782077120158 E-381 at Y, witness=2. Pol[69, 2] with [h, u]=[25, 11] has ratio=0.0011194838483371833177 at X, ratio=3.088200529274584466 E-349 at Y, witness=13. Pol[70, 2] with [h, u]=[25, 11] has ratio=0.000008212740856607978446 at X, ratio=2.670897365079623067 E-320 at Y, witness=5. Pol[71, 2] with [h, u]=[25, 11] has ratio=0.003007379124514089538 at X, ratio=9.539856223576833253 E-294 at Y, witness=2. Pol[72, 2] with [h, u]=[25, 11] has ratio=0.005272578169155549923 at X, ratio=1.6774639566648019732 E-269 at Y, witness=5. Pol[73, 2] with [h, u]=[25, 11] has ratio=0.008402632226402782931 at X, ratio=2.938036110851068221 E-247 at Y, witness=11. Pol[74, 2] with [h, u]=[25, 11] has ratio=0.0019277241574896004474 at X, ratio=7.069370205923520798 E-227 at Y, witness=3. Pol[75, 2] with [h, u]=[25, 11] has ratio=0.0013403896476976787768 at X, ratio=4.153001981356500745 E-208 at Y, witness=3. Pol[76, 2] with [h, u]=[27, 12] has ratio=0.004095921533260436613 at X, ratio=4.659646719994380944 E-424 at Y, witness=11. Pol[77, 2] with [h, u]=[25, 11] has ratio=0.003206991085056617513 at X, ratio=9.238052409430196440 E-159 at Y, witness=7. Pol[78, 2] with [h, u]=[27, 12] has ratio=0.0009416439947623540681 at X, ratio=1.6009826376976127056 E-378 at Y, witness=3. Pol[79, 2] with [h, u]=[27, 12] has ratio=0.005781757920972739952 at X, ratio=1.2016817692575006528 E-349 at Y, witness=23. Pol[80, 2] with [h, u]=[27, 12] has ratio=0.00010509323230450691724 at X, ratio=6.848542060642634626 E-323 at Y, witness=11. Pol[81, 2] with [h, u]=[27, 12] has ratio=0.002364674468838728044 at X, ratio=3.289204643040281341 E-298 at Y, witness=5. Pol[82, 2] with [h, u]=[27, 12] has ratio=0.002573593414136458872 at X, ratio=1.7074160079434692510 E-275 at Y, witness=5. Pol[83, 2] with [h, u]=[27, 12] has ratio=0.0015489610111122002963 at X, ratio=1.2981774817055430499 E-254 at Y, witness=17. Pol[84, 2] with [h, u]=[27, 12] has ratio=0.003917670529926937422 at X, ratio=3.668869209763165404 E-235 at Y, witness=2. Pol[85, 2] with [h, u]=[27, 12] has ratio=0.004640924800463198913 at X, ratio=3.0050576338230114472 E-217 at Y, witness=11. Pol[86, 2] with [h, u]=[28, 13] has ratio=0.0008403246085377766062 at X, ratio=3.557776796629505378 E-374 at Y, witness=29. Pol[87, 2] with [h, u]=[28, 13] has ratio=0.002582218320535849434 at X, ratio=2.268274656193541833 E-360 at Y, witness=3. Pol[88, 2] with [h, u]=[28, 13] has ratio=0.002599970018356594929 at X, ratio=3.819077500527086208 E-347 at Y, witness=7. Pol[89, 2] with [h, u]=[28, 13] has ratio=0.002306076716086692479 at X, ratio=2.5548637881224193240 E-334 at Y, witness=7. Pol[90, 2] with [h, u]=[28, 13] has ratio=0.0006424165092147135069 at X, ratio=4.294955958886652571 E-322 at Y, witness=13. Pol[91, 2] with [h, u]=[28, 13] has ratio=0.0010421579758292881981 at X, ratio=3.0299266831491240734 E-310 at Y, witness=5. Validated in 250 sec. Goodbye!A copy of the CHG certificate

`89_11971.out`

(153MB) is
included in:
`89_11971.zip`

and can be verified by running the Pari-GP script `verify.gp`

.
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`89_11971.zip`

Tom Wu Last modified: Wed May 27 19:00:00 PDT 2009