# Primality Proof of phi(4969,9473)

## OpenPFGW

```Primality testing Phi(4969,9473) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 23
Running N-1 test using base 31
Running N+1 test using discriminant 41, base 8+sqrt(41)
Calling N-1 BLS with factored part 25.61% and helper 0.11% (76.93% proof)
Phi(4969,9473) is Fermat and Lucas PRP! (325.8668s+0.0011s)
```

## CHG

```                  GP/PARI CALCULATOR Version 2.3.1 (released)
amd64 running linux (x86-64/GMP-4.2.1 kernel) 64-bit version
compiled: Mar 24 2007, gcc-3.4.4 20050721 (Red Hat 3.4.4-2)
(readline v4.3 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 "9473_4969.in".

Pol[1, 1] with [h, u]=[5, 1] has ratio=8.634809812209786134 E-92 at X, ratio=3.152831453231551835 E-610 at Y, witness=3.
Pol[2, 1] with [h, u]=[5, 1] has ratio=0.24968205591677964722 at X, ratio=1.0980985656838625863 E-305 at Y, witness=5.
Pol[3, 1] with [h, u]=[4, 1] has ratio=4.557773743140520849 E-31 at X, ratio=2.5020575089354201446 E-182 at Y, witness=29.
Pol[4, 1] with [h, u]=[7, 2] has ratio=1.7717033341314084919 E-44 at X, ratio=5.516427221920360170 E-522 at Y, witness=13.
Pol[5, 1] with [h, u]=[7, 2] has ratio=2.2033985606068881252 E-125 at X, ratio=2.1042252665811438708 E-442 at Y, witness=2.
Pol[6, 1] with [h, u]=[8, 2] has ratio=0.08019648836593216074 at X, ratio=2.2311929742643704844 E-395 at Y, witness=5.
Pol[7, 1] with [h, u]=[8, 2] has ratio=0.09223893782860422040 at X, ratio=1.3672522008579897505 E-226 at Y, witness=11.
Pol[8, 1] with [h, u]=[8, 2] has ratio=0.020649271968837137792 at X, ratio=4.505193546919047161 E-130 at Y, witness=2.
Pol[9, 1] with [h, u]=[9, 3] has ratio=0.08015960979020026483 at X, ratio=7.109528625846366500 E-242 at Y, witness=3.
Pol[10, 1] with [h, u]=[10, 3] has ratio=0.05369272163173044857 at X, ratio=3.284875916703772003 E-430 at Y, witness=3.
Pol[11, 1] with [h, u]=[10, 3] has ratio=0.07318640611950921900 at X, ratio=2.1397243736755279964 E-287 at Y, witness=3.
Pol[12, 1] with [h, u]=[10, 3] has ratio=0.03283457852547504102 at X, ratio=4.351447690310665178 E-192 at Y, witness=2.
Pol[13, 1] with [h, u]=[10, 3] has ratio=0.006425372194022875325 at X, ratio=1.9452471776406031896 E-128 at Y, witness=3.
Pol[14, 1] with [h, u]=[12, 4] has ratio=0.06029735074378729325 at X, ratio=5.180515559966328901 E-436 at Y, witness=23.
Pol[15, 1] with [h, u]=[12, 4] has ratio=0.031062195077335407468 at X, ratio=1.2592346069151459749 E-317 at Y, witness=41.
Pol[16, 1] with [h, u]=[12, 4] has ratio=0.014023617861144365667 at X, ratio=2.1533956464646983162 E-231 at Y, witness=17.
Pol[17, 1] with [h, u]=[12, 4] has ratio=0.018656234159858234630 at X, ratio=1.3036618315876714276 E-168 at Y, witness=23.
Pol[18, 1] with [h, u]=[12, 4] has ratio=0.07549475558162524251 at X, ratio=5.476128569393355387 E-123 at Y, witness=11.
Pol[19, 1] with [h, u]=[12, 4] has ratio=0.04412487657439915197 at X, ratio=6.549768755796236838 E-90 at Y, witness=3.
Pol[20, 1] with [h, u]=[12, 4] has ratio=0.05926879398492343023 at X, ratio=7.690468385982878830 E-66 at Y, witness=2.
Pol[21, 1] with [h, u]=[14, 5] has ratio=0.04275644016572644676 at X, ratio=1.6385375108411909915 E-340 at Y, witness=13.
Pol[22, 1] with [h, u]=[14, 5] has ratio=0.010521501299430111277 at X, ratio=2.673519436605233099 E-262 at Y, witness=2.
Pol[23, 1] with [h, u]=[14, 5] has ratio=0.005395749912146242982 at X, ratio=3.494605480458498324 E-202 at Y, witness=5.
Pol[24, 1] with [h, u]=[14, 5] has ratio=0.020130442809267221406 at X, ratio=4.448856930103149219 E-156 at Y, witness=2.
Pol[25, 1] with [h, u]=[14, 5] has ratio=0.018901120848355271120 at X, ratio=2.8387171982855997382 E-120 at Y, witness=3.
Pol[26, 1] with [h, u]=[14, 5] has ratio=0.014481703266007614324 at X, ratio=5.683992373614082359 E-93 at Y, witness=2.
Pol[27, 1] with [h, u]=[16, 6] has ratio=1.0044917764098621020 E-19 at X, ratio=2.0596506462821662182 E-346 at Y, witness=3.
Pol[28, 1] with [h, u]=[16, 6] has ratio=3.3729667041457837244 E-49 at X, ratio=3.501265610716543332 E-266 at Y, witness=11.
Pol[29, 1] with [h, u]=[16, 6] has ratio=0.009520402426904854453 at X, ratio=4.752801926289262271 E-211 at Y, witness=5.
Pol[30, 1] with [h, u]=[16, 6] has ratio=0.010994444384675299508 at X, ratio=3.530711721741477838 E-169 at Y, witness=23.
Pol[31, 1] with [h, u]=[16, 6] has ratio=0.007130170887690954187 at X, ratio=8.051860909107558150 E-136 at Y, witness=3.
Pol[32, 1] with [h, u]=[18, 7] has ratio=0.028966832121098961620 at X, ratio=2.5648983766295833386 E-341 at Y, witness=2.
Pol[33, 1] with [h, u]=[18, 7] has ratio=0.000000002738466548953419205 at X, ratio=1.9751250835820866032 E-287 at Y, witness=5.
Pol[34, 1] with [h, u]=[18, 7] has ratio=1.8472749962918657714 E-47 at X, ratio=5.872492502785885959 E-244 at Y, witness=3.
Pol[35, 1] with [h, u]=[18, 7] has ratio=0.024470359902938498420 at X, ratio=1.5328577573852920081 E-191 at Y, witness=7.
Pol[36, 1] with [h, u]=[18, 7] has ratio=0.015224407038577154572 at X, ratio=4.915499335938285564 E-158 at Y, witness=17.
Pol[37, 1] with [h, u]=[18, 7] has ratio=0.008937728765548854249 at X, ratio=1.4278508052126397108 E-130 at Y, witness=5.
Pol[38, 1] with [h, u]=[18, 7] has ratio=0.013363652847668813203 at X, ratio=7.592272540136632490 E-108 at Y, witness=11.
Pol[39, 1] with [h, u]=[20, 8] has ratio=0.0018865125884841537286 at X, ratio=2.345724690394899538 E-302 at Y, witness=2.
Pol[40, 1] with [h, u]=[20, 8] has ratio=0.00000003293071594864430048 at X, ratio=2.4381145248558048430 E-259 at Y, witness=2.
Pol[41, 1] with [h, u]=[20, 8] has ratio=2.351379764130405858 E-41 at X, ratio=5.033854159081013856 E-227 at Y, witness=2.
Pol[42, 1] with [h, u]=[20, 8] has ratio=3.410689118927177622 E-26 at X, ratio=3.773177258247776275 E-182 at Y, witness=3.
Pol[43, 1] with [h, u]=[20, 8] has ratio=0.006033549074866833069 at X, ratio=3.946781257899565279 E-153 at Y, witness=5.
Pol[44, 1] with [h, u]=[20, 8] has ratio=0.004243679116731171488 at X, ratio=3.248534267365035408 E-129 at Y, witness=11.
Pol[45, 1] with [h, u]=[20, 8] has ratio=0.009894866317976053096 at X, ratio=3.769017160804530110 E-109 at Y, witness=3.
Pol[46, 1] with [h, u]=[22, 9] has ratio=0.005635787545490764204 at X, ratio=7.332033060087717510 E-292 at Y, witness=2.
Pol[47, 1] with [h, u]=[22, 9] has ratio=0.0000005165081434198607371 at X, ratio=3.593888166685927838 E-254 at Y, witness=2.
Pol[48, 1] with [h, u]=[22, 9] has ratio=5.308975355639646608 E-31 at X, ratio=2.3713833938198221660 E-219 at Y, witness=5.
Pol[49, 1] with [h, u]=[22, 9] has ratio=0.005059077158136013320 at X, ratio=1.1845406394944774886 E-184 at Y, witness=5.
Pol[50, 1] with [h, u]=[22, 9] has ratio=0.0016423923974045304505 at X, ratio=1.8472836132208817118 E-158 at Y, witness=13.
Pol[51, 1] with [h, u]=[22, 9] has ratio=0.009055024219570831969 at X, ratio=3.2619626106356878506 E-136 at Y, witness=3.
Pol[52, 1] with [h, u]=[22, 9] has ratio=0.004647129934131368677 at X, ratio=5.049784450359435853 E-117 at Y, witness=2.
Pol[53, 1] with [h, u]=[24, 10] has ratio=0.003047444377089020044 at X, ratio=6.592288989283257818 E-290 at Y, witness=3.
Pol[54, 1] with [h, u]=[24, 10] has ratio=5.392390251169559946 E-32 at X, ratio=9.787814286746890017 E-256 at Y, witness=5.
Pol[55, 1] with [h, u]=[24, 10] has ratio=0.003230742971688473532 at X, ratio=8.724170721980619669 E-220 at Y, witness=2.
Pol[56, 1] with [h, u]=[24, 10] has ratio=0.0015557169550691808953 at X, ratio=1.8187836491891629538 E-191 at Y, witness=7.
Pol[57, 1] with [h, u]=[24, 10] has ratio=0.0005719430869901876436 at X, ratio=8.809111403261108604 E-167 at Y, witness=2.
Pol[58, 1] with [h, u]=[24, 10] has ratio=0.008977791313096007233 at X, ratio=2.5917037203024959542 E-145 at Y, witness=5.
Pol[59, 1] with [h, u]=[24, 10] has ratio=0.0006694335728647698654 at X, ratio=1.1324037349418568702 E-126 at Y, witness=2.
Pol[60, 1] with [h, u]=[24, 10] has ratio=0.002641203198990552462 at X, ratio=2.1746084436553956538 E-110 at Y, witness=2.
Pol[61, 1] with [h, u]=[26, 11] has ratio=0.00020798113962055914126 at X, ratio=1.9737660448764857532 E-277 at Y, witness=7.
Pol[62, 1] with [h, u]=[26, 11] has ratio=0.003138938761807508699 at X, ratio=2.1985478407233729076 E-244 at Y, witness=2.
Pol[63, 1] with [h, u]=[26, 11] has ratio=0.007948119488190152803 at X, ratio=2.1228244717462204382 E-215 at Y, witness=7.
Pol[64, 1] with [h, u]=[26, 11] has ratio=0.00013791134503642840243 at X, ratio=6.351791911019870258 E-190 at Y, witness=3.
Pol[65, 1] with [h, u]=[26, 11] has ratio=0.0005136889835895516449 at X, ratio=2.6031189201012115606 E-167 at Y, witness=5.
Pol[66, 1] with [h, u]=[26, 11] has ratio=0.0013690905676982764609 at X, ratio=1.4525976836239388647 E-147 at Y, witness=5.
Pol[67, 1] with [h, u]=[26, 11] has ratio=0.003488363339603510274 at X, ratio=3.5450039175765900696 E-130 at Y, witness=13.
Pol[68, 1] with [h, u]=[28, 12] has ratio=0.004389541807621766736 at X, ratio=9.983267688454385407 E-290 at Y, witness=11.
Pol[69, 1] with [h, u]=[28, 12] has ratio=0.005423857411261762377 at X, ratio=7.691847381323838084 E-258 at Y, witness=11.
Pol[70, 1] with [h, u]=[28, 12] has ratio=0.0019320284056895448522 at X, ratio=1.8531154001532246280 E-229 at Y, witness=3.
Pol[71, 1] with [h, u]=[28, 12] has ratio=0.002267579472360143454 at X, ratio=2.9920437847275829408 E-204 at Y, witness=3.
Pol[72, 1] with [h, u]=[28, 12] has ratio=0.0012286677095846652768 at X, ratio=8.259975480913048622 E-182 at Y, witness=5.
Pol[73, 1] with [h, u]=[28, 12] has ratio=0.0019523677576583151774 at X, ratio=6.876575677144189470 E-162 at Y, witness=2.
Pol[74, 1] with [h, u]=[28, 12] has ratio=0.002051744331403218318 at X, ratio=3.101866080339884609 E-144 at Y, witness=2.
Pol[75, 1] with [h, u]=[28, 12] has ratio=0.002145478174936056384 at X, ratio=1.9534478437141147936 E-128 at Y, witness=3.
Pol[76, 1] with [h, u]=[30, 13] has ratio=0.00012276957345443855666 at X, ratio=3.667126531850749579 E-284 at Y, witness=11.
Pol[77, 1] with [h, u]=[30, 13] has ratio=0.0012139011625846783258 at X, ratio=4.705046417461607167 E-255 at Y, witness=7.
Pol[78, 1] with [h, u]=[30, 13] has ratio=0.002647882502215198224 at X, ratio=5.045275240995317865 E-229 at Y, witness=3.
Pol[79, 1] with [h, u]=[30, 13] has ratio=0.0009059343653436167298 at X, ratio=1.4095002921662590175 E-205 at Y, witness=7.
Pol[80, 1] with [h, u]=[30, 13] has ratio=0.00010892039701777421098 at X, ratio=1.4424419657714780425 E-184 at Y, witness=2.
Pol[81, 1] with [h, u]=[30, 13] has ratio=0.0008028638782677508766 at X, ratio=7.979476657245497191 E-166 at Y, witness=11.
Pol[82, 1] with [h, u]=[32, 14] has ratio=0.002274366543036394997 at X, ratio=1.2242398780855267939 E-314 at Y, witness=11.
Pol[83, 1] with [h, u]=[32, 14] has ratio=0.0014636178979897380883 at X, ratio=1.7196174633944631394 E-284 at Y, witness=5.
Pol[84, 1] with [h, u]=[32, 14] has ratio=0.0016239403874699741789 at X, ratio=3.342632277625964061 E-257 at Y, witness=3.
Pol[85, 1] with [h, u]=[32, 14] has ratio=0.00009931383332292316773 at X, ratio=1.2379162159682105447 E-232 at Y, witness=7.
Pol[86, 1] with [h, u]=[32, 14] has ratio=0.0009278614380103042762 at X, ratio=2.1160019500470980590 E-210 at Y, witness=17.
Pol[87, 1] with [h, u]=[32, 14] has ratio=0.0007087945642483584760 at X, ratio=3.182570966153472366 E-190 at Y, witness=5.
Pol[88, 1] with [h, u]=[32, 14] has ratio=0.0004586992409835414024 at X, ratio=3.585890573526609502 E-172 at Y, witness=3.
Pol[89, 1] with [h, u]=[32, 14] has ratio=0.0009599106344541700404 at X, ratio=9.447878793036796741 E-156 at Y, witness=11.
Pol[90, 1] with [h, u]=[33, 15] has ratio=0.0013377550825489219756 at X, ratio=3.3731043844043367688 E-251 at Y, witness=2.
Pol[91, 1] with [h, u]=[33, 15] has ratio=0.0012857558272870154296 at X, ratio=9.114028318484550374 E-236 at Y, witness=3.
Pol[92, 1] with [h, u]=[33, 15] has ratio=0.00008685263246395346870 at X, ratio=3.720165523899478095 E-221 at Y, witness=2.
Pol[93, 1] with [h, u]=[33, 15] has ratio=0.0015743883699213131013 at X, ratio=1.2627380553973041351 E-207 at Y, witness=2.
Pol[94, 1] with [h, u]=[33, 15] has ratio=0.002771850039464203299 at X, ratio=8.763918927795434279 E-195 at Y, witness=2.
Pol[95, 1] with [h, u]=[33, 15] has ratio=0.00000006655788269874119266 at X, ratio=7.964792007803510998 E-186 at Y, witness=3.
Pol[96, 1] with [h, u]=[33, 15] has ratio=0.0003975567172111904546 at X, ratio=1.5268274959831044357 E-171 at Y, witness=7.
Pol[97, 1] with [h, u]=[33, 15] has ratio=0.0015762989482820899205 at X, ratio=5.782444239907268822 E-161 at Y, witness=13.
Pol[98, 1] with [h, u]=[33, 15] has ratio=0.0004067186599929795793 at X, ratio=4.501732638887416572 E-151 at Y, witness=2.
Pol[99, 1] with [h, u]=[35, 16] has ratio=0.0006492847484329344247 at X, ratio=2.3102380789621843418 E-287 at Y, witness=5.
Pol[100, 1] with [h, u]=[35, 16] has ratio=0.00017585760887693384918 at X, ratio=1.2182614845816564955 E-270 at Y, witness=3.
Pol[101, 1] with [h, u]=[35, 16] has ratio=0.0011379061048909982239 at X, ratio=7.437576225132424533 E-255 at Y, witness=2.
Pol[102, 1] with [h, u]=[35, 16] has ratio=0.0006964175788046930726 at X, ratio=4.781609078379819557 E-240 at Y, witness=2.
Pol[103, 1] with [h, u]=[35, 16] has ratio=0.0007951644470434305769 at X, ratio=4.538053241263834439 E-226 at Y, witness=5.
Pol[104, 1] with [h, u]=[35, 16] has ratio=0.0008481819455029248960 at X, ratio=5.663121353039384037 E-213 at Y, witness=7.
Pol[105, 1] with [h, u]=[35, 16] has ratio=0.00007511217621685174254 at X, ratio=1.2247157239112729756 E-200 at Y, witness=3.
Pol[106, 1] with [h, u]=[35, 16] has ratio=0.0012098495801032517763 at X, ratio=5.172538009459724465 E-189 at Y, witness=2.
Pol[107, 1] with [h, u]=[37, 17] has ratio=0.0006409014541936101787 at X, ratio=7.185021509309146101 E-323 at Y, witness=17.
Pol[108, 1] with [h, u]=[37, 17] has ratio=0.0003682577196827168262 at X, ratio=4.608056258852145277 E-305 at Y, witness=2.
Pol[109, 1] with [h, u]=[37, 17] has ratio=0.00007456034438224983181 at X, ratio=2.6729271244775637642 E-288 at Y, witness=11.
Pol[110, 1] with [h, u]=[37, 17] has ratio=0.0003107368173040306530 at X, ratio=1.7581095400267579677 E-272 at Y, witness=3.
Pol[111, 1] with [h, u]=[37, 17] has ratio=0.0012650842538948183826 at X, ratio=1.7487369351718756924 E-257 at Y, witness=7.
Pol[112, 1] with [h, u]=[37, 17] has ratio=0.00013657858834588336590 at X, ratio=2.1447691862857651282 E-243 at Y, witness=11.
Pol[113, 1] with [h, u]=[37, 17] has ratio=0.000017941269743444139524 at X, ratio=4.970318070291182874 E-230 at Y, witness=2.
Pol[114, 1] with [h, u]=[38, 18] has ratio=0.0002634571837595395498 at X, ratio=5.611358598932960127 E-313 at Y, witness=3.
Pol[115, 1] with [h, u]=[38, 18] has ratio=0.0004447623589759570370 at X, ratio=1.2827100850794017310 E-304 at Y, witness=11.
Pol[116, 1] with [h, u]=[38, 18] has ratio=0.00004957747605048773925 at X, ratio=1.6262494417870197596 E-296 at Y, witness=2.
Pol[117, 1] with [h, u]=[38, 18] has ratio=0.0002882389972140281049 at X, ratio=1.3394574813631763132 E-288 at Y, witness=2.
Pol[118, 1] with [h, u]=[38, 18] has ratio=0.00013136853323905641883 at X, ratio=7.094615110469183373 E-281 at Y, witness=7.
Pol[119, 1] with [h, u]=[39, 18] has ratio=0.00015816279687904192882 at X, ratio=2.6215059091485652872 E-284 at Y, witness=17.
Pol[1, 2] with [h, u]=[5, 1] has ratio=2.6472682919221417818 E-92 at X, ratio=1.9812782779660817134 E-610 at Y, witness=2.
Pol[2, 2] with [h, u]=[5, 1] has ratio=0.3118603676420890070 at X, ratio=1.2823612894674562268 E-305 at Y, witness=2.
Pol[3, 2] with [h, u]=[4, 1] has ratio=1.0707224351694644668 E-36 at X, ratio=8.276971074156408249 E-189 at Y, witness=13.
Pol[4, 2] with [h, u]=[7, 2] has ratio=1.6582073327255326578 E-46 at X, ratio=4.602112524970760664 E-522 at Y, witness=5.
Pol[5, 2] with [h, u]=[7, 2] has ratio=8.604228537859183714 E-125 at X, ratio=2.3426433939666300016 E-442 at Y, witness=5.
Pol[6, 2] with [h, u]=[8, 2] has ratio=0.12185060742132660947 at X, ratio=2.329064520436286704 E-395 at Y, witness=11.
Pol[7, 2] with [h, u]=[8, 2] has ratio=0.08695616356107126446 at X, ratio=1.1031745816274247545 E-226 at Y, witness=2.
Pol[8, 2] with [h, u]=[8, 2] has ratio=0.10766962573023621909 at X, ratio=5.847503154967885704 E-130 at Y, witness=3.
Pol[9, 2] with [h, u]=[9, 3] has ratio=0.013214640672595065608 at X, ratio=4.681593755404041712 E-242 at Y, witness=2.
Pol[10, 2] with [h, u]=[10, 3] has ratio=0.12052174222094126739 at X, ratio=2.903804830708472714 E-430 at Y, witness=17.
Pol[11, 2] with [h, u]=[10, 3] has ratio=0.04953638111851802955 at X, ratio=2.1654359632441423260 E-287 at Y, witness=7.
Pol[12, 2] with [h, u]=[10, 3] has ratio=0.06495753323177111648 at X, ratio=5.434478255547404323 E-192 at Y, witness=3.
Pol[13, 2] with [h, u]=[10, 3] has ratio=0.08149858860397122348 at X, ratio=1.7439229147103593409 E-128 at Y, witness=13.
Pol[14, 2] with [h, u]=[12, 4] has ratio=0.009581406117622745123 at X, ratio=4.918193727812691826 E-436 at Y, witness=5.
Pol[15, 2] with [h, u]=[12, 4] has ratio=0.08026327040081208634 at X, ratio=1.6606619015698015494 E-317 at Y, witness=2.
Pol[16, 2] with [h, u]=[12, 4] has ratio=0.06476600218631137645 at X, ratio=2.881951498938862984 E-231 at Y, witness=5.
Pol[17, 2] with [h, u]=[12, 4] has ratio=0.03750304510442442684 at X, ratio=1.1124006834848515863 E-168 at Y, witness=11.
Pol[18, 2] with [h, u]=[12, 4] has ratio=0.013336928626112565059 at X, ratio=3.930089871633141191 E-123 at Y, witness=5.
Pol[19, 2] with [h, u]=[12, 4] has ratio=0.05435810616618902033 at X, ratio=6.118567494895827371 E-90 at Y, witness=5.
Pol[20, 2] with [h, u]=[12, 4] has ratio=0.005698228131541914662 at X, ratio=8.054525628160744115 E-66 at Y, witness=5.
Pol[21, 2] with [h, u]=[14, 5] has ratio=0.04706993182118334068 at X, ratio=1.8338234193770295751 E-340 at Y, witness=2.
Pol[22, 2] with [h, u]=[14, 5] has ratio=0.008872178876614117132 at X, ratio=2.704814482387543210 E-262 at Y, witness=3.
Pol[23, 2] with [h, u]=[14, 5] has ratio=0.009455917633211032620 at X, ratio=3.162966024482787531 E-202 at Y, witness=2.
Pol[24, 2] with [h, u]=[14, 5] has ratio=0.03865645000769795377 at X, ratio=6.566856452951808101 E-156 at Y, witness=3.
Pol[25, 2] with [h, u]=[14, 5] has ratio=0.019615028276055299642 at X, ratio=2.7391065560090035462 E-120 at Y, witness=3.
Pol[26, 2] with [h, u]=[14, 5] has ratio=0.030395341290516595992 at X, ratio=6.555400117537629322 E-93 at Y, witness=2.
Pol[27, 2] with [h, u]=[16, 6] has ratio=5.217802862505312695 E-19 at X, ratio=5.526614513457249011 E-345 at Y, witness=2.
Pol[28, 2] with [h, u]=[16, 6] has ratio=1.7463141480125156185 E-47 at X, ratio=8.490833485573989011 E-265 at Y, witness=2.
Pol[29, 2] with [h, u]=[16, 6] has ratio=0.003550958300987718983 at X, ratio=5.083598046525325901 E-211 at Y, witness=5.
Pol[30, 2] with [h, u]=[16, 6] has ratio=0.016545743798595541732 at X, ratio=3.475609922879971050 E-169 at Y, witness=2.
Pol[31, 2] with [h, u]=[16, 6] has ratio=0.013512982956691120988 at X, ratio=1.0061012022085011308 E-135 at Y, witness=2.
Pol[32, 2] with [h, u]=[18, 7] has ratio=0.028447536425207984816 at X, ratio=2.9158880801966180430 E-341 at Y, witness=3.
Pol[33, 2] with [h, u]=[18, 7] has ratio=0.0000000002542789684015583870 at X, ratio=1.0747537600929137990 E-288 at Y, witness=2.
Pol[34, 2] with [h, u]=[18, 7] has ratio=2.3129555262394810242 E-48 at X, ratio=3.3306232974071418618 E-245 at Y, witness=7.
Pol[35, 2] with [h, u]=[18, 7] has ratio=0.019002966318233053980 at X, ratio=2.0515261505971904260 E-191 at Y, witness=2.
Pol[36, 2] with [h, u]=[18, 7] has ratio=0.011161079970101753796 at X, ratio=4.997420870512407553 E-158 at Y, witness=2.
Pol[37, 2] with [h, u]=[18, 7] has ratio=0.005161507142814602630 at X, ratio=1.7543209975563068748 E-130 at Y, witness=5.
Pol[38, 2] with [h, u]=[18, 7] has ratio=0.021249171832716360424 at X, ratio=8.190737625935173692 E-108 at Y, witness=2.
Pol[39, 2] with [h, u]=[20, 8] has ratio=0.013918156095417468104 at X, ratio=2.2311359845156002864 E-302 at Y, witness=17.
Pol[40, 2] with [h, u]=[20, 8] has ratio=0.0000003037478433420876292 at X, ratio=3.045061278267109955 E-258 at Y, witness=5.
Pol[41, 2] with [h, u]=[20, 8] has ratio=2.1717700680023355260 E-40 at X, ratio=5.864839633782745043 E-226 at Y, witness=5.
Pol[42, 2] with [h, u]=[20, 8] has ratio=0.018780536865287908714 at X, ratio=2.3413748908733494966 E-181 at Y, witness=11.
Pol[43, 2] with [h, u]=[20, 8] has ratio=0.003396674242799857632 at X, ratio=3.882567892659051257 E-153 at Y, witness=5.
Pol[44, 2] with [h, u]=[20, 8] has ratio=0.002017365734229508753 at X, ratio=2.7911650208051192572 E-129 at Y, witness=31.
Pol[45, 2] with [h, u]=[20, 8] has ratio=0.002178183708745952554 at X, ratio=3.630293939348200859 E-109 at Y, witness=7.
Pol[46, 2] with [h, u]=[22, 9] has ratio=0.0002666654637289916440 at X, ratio=7.260815086448130198 E-292 at Y, witness=3.
Pol[47, 2] with [h, u]=[22, 9] has ratio=0.00000007210187500923848329 at X, ratio=3.216652643737226930 E-255 at Y, witness=5.
Pol[48, 2] with [h, u]=[22, 9] has ratio=1.1793549256009580722 E-31 at X, ratio=2.1343512018198952756 E-220 at Y, witness=13.
Pol[49, 2] with [h, u]=[22, 9] has ratio=0.005893921012220443789 at X, ratio=1.4058056064006747201 E-184 at Y, witness=5.
Pol[50, 2] with [h, u]=[22, 9] has ratio=0.010488482002613283131 at X, ratio=1.5574718724815415900 E-158 at Y, witness=11.
Pol[51, 2] with [h, u]=[22, 9] has ratio=0.006048308438680552990 at X, ratio=2.9746634285019259678 E-136 at Y, witness=2.
Pol[52, 2] with [h, u]=[22, 9] has ratio=0.004366775454888862645 at X, ratio=3.597315906140718457 E-117 at Y, witness=3.
Pol[53, 2] with [h, u]=[24, 10] has ratio=0.005155520829759219670 at X, ratio=6.168709505898470751 E-290 at Y, witness=11.
Pol[54, 2] with [h, u]=[24, 10] has ratio=1.7025549387690871606 E-30 at X, ratio=6.839202290393201940 E-255 at Y, witness=3.
Pol[55, 2] with [h, u]=[24, 10] has ratio=0.0013786742693281378474 at X, ratio=8.758840074638740973 E-220 at Y, witness=3.
Pol[56, 2] with [h, u]=[24, 10] has ratio=0.002798721480274214202 at X, ratio=2.1759968386280328142 E-191 at Y, witness=11.
Pol[57, 2] with [h, u]=[24, 10] has ratio=0.0015015208449820861780 at X, ratio=8.754689360894958494 E-167 at Y, witness=7.
Pol[58, 2] with [h, u]=[24, 10] has ratio=0.006664534611832155717 at X, ratio=2.3055740520154835476 E-145 at Y, witness=3.
Pol[59, 2] with [h, u]=[24, 10] has ratio=0.008175224568117162392 at X, ratio=9.889302303736992411 E-127 at Y, witness=5.
Pol[60, 2] with [h, u]=[24, 10] has ratio=0.001978869916982060947 at X, ratio=2.0777030428570122970 E-110 at Y, witness=19.
Pol[61, 2] with [h, u]=[26, 11] has ratio=0.0016404644737566138516 at X, ratio=2.2025500022558459702 E-277 at Y, witness=13.
Pol[62, 2] with [h, u]=[26, 11] has ratio=0.003880964358729263940 at X, ratio=2.0637124832973860714 E-244 at Y, witness=3.
Pol[63, 2] with [h, u]=[26, 11] has ratio=0.0005465924209232715892 at X, ratio=2.1308154859129042666 E-215 at Y, witness=2.
Pol[64, 2] with [h, u]=[26, 11] has ratio=0.00023097397955367076614 at X, ratio=8.196498759708888536 E-190 at Y, witness=3.
Pol[65, 2] with [h, u]=[26, 11] has ratio=0.003040396556699033229 at X, ratio=2.6712122698495232644 E-167 at Y, witness=2.
Pol[66, 2] with [h, u]=[26, 11] has ratio=0.002333671091541807989 at X, ratio=1.5339405753887053625 E-147 at Y, witness=3.
Pol[67, 2] with [h, u]=[26, 11] has ratio=0.005613476755086232130 at X, ratio=3.832779358589626994 E-130 at Y, witness=11.
Pol[68, 2] with [h, u]=[28, 12] has ratio=0.002523009606001020206 at X, ratio=9.364006734907515086 E-290 at Y, witness=13.
Pol[69, 2] with [h, u]=[28, 12] has ratio=0.0002967591192213954100 at X, ratio=8.989397752911496861 E-258 at Y, witness=3.
Pol[70, 2] with [h, u]=[28, 12] has ratio=0.0017488002829989465096 at X, ratio=1.9097750963315676104 E-229 at Y, witness=2.
Pol[71, 2] with [h, u]=[28, 12] has ratio=0.0008342656993317404149 at X, ratio=3.1653367334193572470 E-204 at Y, witness=3.
Pol[72, 2] with [h, u]=[28, 12] has ratio=0.003179726922625323899 at X, ratio=8.292179817691606480 E-182 at Y, witness=2.
Pol[73, 2] with [h, u]=[28, 12] has ratio=0.004752874616577052476 at X, ratio=6.421336567770804349 E-162 at Y, witness=3.
Pol[74, 2] with [h, u]=[28, 12] has ratio=0.002256054968730210402 at X, ratio=3.437142828509000755 E-144 at Y, witness=2.
Pol[75, 2] with [h, u]=[28, 12] has ratio=0.00012815023532577810108 at X, ratio=1.6411073262970631665 E-128 at Y, witness=3.
Pol[76, 2] with [h, u]=[30, 13] has ratio=0.0012478476810952471432 at X, ratio=3.301296923325334042 E-284 at Y, witness=3.
Pol[77, 2] with [h, u]=[30, 13] has ratio=0.002717074415451345550 at X, ratio=3.940917111889697839 E-255 at Y, witness=13.
Pol[78, 2] with [h, u]=[30, 13] has ratio=0.003603632348180245386 at X, ratio=5.929816934372924000 E-229 at Y, witness=7.
Pol[79, 2] with [h, u]=[30, 13] has ratio=0.0006513127411731702920 at X, ratio=1.2067406945069641354 E-205 at Y, witness=5.
Pol[80, 2] with [h, u]=[30, 13] has ratio=0.0008204090381797653189 at X, ratio=1.4907640956054708626 E-184 at Y, witness=17.
Pol[81, 2] with [h, u]=[30, 13] has ratio=0.0004521940544799664330 at X, ratio=9.143827765019758625 E-166 at Y, witness=2.
Pol[82, 2] with [h, u]=[32, 14] has ratio=0.002724836401011643074 at X, ratio=1.1159903602653339716 E-314 at Y, witness=7.
Pol[83, 2] with [h, u]=[32, 14] has ratio=0.0004576400152276781373 at X, ratio=1.8532103378099884756 E-284 at Y, witness=5.
Pol[84, 2] with [h, u]=[32, 14] has ratio=0.00012609616333258694271 at X, ratio=3.2198344742547805892 E-257 at Y, witness=5.
Pol[85, 2] with [h, u]=[32, 14] has ratio=0.0013895433978522436751 at X, ratio=1.1681179835453740588 E-232 at Y, witness=2.
Pol[86, 2] with [h, u]=[32, 14] has ratio=0.0003344292593501345377 at X, ratio=2.0510106807414103798 E-210 at Y, witness=11.
Pol[87, 2] with [h, u]=[32, 14] has ratio=0.0016165170124913736929 at X, ratio=2.786564537188892866 E-190 at Y, witness=11.
Pol[88, 2] with [h, u]=[32, 14] has ratio=0.0010183512943819093258 at X, ratio=3.625813145285486260 E-172 at Y, witness=11.
Pol[89, 2] with [h, u]=[32, 14] has ratio=0.0004129363302789461732 at X, ratio=9.152450243328056536 E-156 at Y, witness=5.
Pol[90, 2] with [h, u]=[33, 15] has ratio=0.0010618928353669273047 at X, ratio=2.9292008629873258046 E-251 at Y, witness=2.
Pol[91, 2] with [h, u]=[33, 15] has ratio=0.00021727624220244723822 at X, ratio=1.0915652067013756172 E-235 at Y, witness=5.
Pol[92, 2] with [h, u]=[33, 15] has ratio=0.0006503217194555898882 at X, ratio=3.526378047458974874 E-221 at Y, witness=5.
Pol[93, 2] with [h, u]=[33, 15] has ratio=0.0011375428740415222079 at X, ratio=1.5849316637259333553 E-207 at Y, witness=5.
Pol[94, 2] with [h, u]=[33, 15] has ratio=0.00005369674889761943256 at X, ratio=1.1023492615081643149 E-194 at Y, witness=2.
Pol[95, 2] with [h, u]=[33, 15] has ratio=0.00000018365948138203206001 at X, ratio=6.311312853396514901 E-186 at Y, witness=7.
Pol[96, 2] with [h, u]=[33, 15] has ratio=0.00014156999729408392785 at X, ratio=1.3858886715664818987 E-171 at Y, witness=5.
Pol[97, 2] with [h, u]=[33, 15] has ratio=0.002519126997143722247 at X, ratio=6.281573427983222625 E-161 at Y, witness=3.
Pol[98, 2] with [h, u]=[33, 15] has ratio=0.002182365604794483299 at X, ratio=4.313450970932463557 E-151 at Y, witness=5.
Pol[99, 2] with [h, u]=[35, 16] has ratio=0.0010232097136515567621 at X, ratio=2.5449872488766613388 E-287 at Y, witness=5.
Pol[100, 2] with [h, u]=[35, 16] has ratio=0.00017146621037612813319 at X, ratio=1.3116670134326241755 E-270 at Y, witness=13.
Pol[101, 2] with [h, u]=[35, 16] has ratio=0.0007533144060047454964 at X, ratio=7.745997185619946488 E-255 at Y, witness=7.
Pol[102, 2] with [h, u]=[35, 16] has ratio=0.0011422617566161832096 at X, ratio=4.618137283286696088 E-240 at Y, witness=5.
Pol[103, 2] with [h, u]=[35, 16] has ratio=0.0003054840598844430556 at X, ratio=3.800165882691409149 E-226 at Y, witness=17.
Pol[104, 2] with [h, u]=[35, 16] has ratio=0.0007783721326227616785 at X, ratio=5.164619168357201184 E-213 at Y, witness=11.
Pol[105, 2] with [h, u]=[35, 16] has ratio=0.0012152880182337601379 at X, ratio=1.2584587022169153210 E-200 at Y, witness=7.
Pol[106, 2] with [h, u]=[35, 16] has ratio=0.00016961188909939167904 at X, ratio=5.945903571000782551 E-189 at Y, witness=3.
Pol[107, 2] with [h, u]=[37, 17] has ratio=0.0003758721077689724902 at X, ratio=8.357966838409287174 E-323 at Y, witness=3.
Pol[108, 2] with [h, u]=[37, 17] has ratio=0.0007758411220059142668 at X, ratio=4.143095574807120185 E-305 at Y, witness=2.
Pol[109, 2] with [h, u]=[37, 17] has ratio=0.0003991397805403785475 at X, ratio=3.1460942056510170916 E-288 at Y, witness=2.
Pol[110, 2] with [h, u]=[37, 17] has ratio=0.00003464573314808448584 at X, ratio=1.6915683914475704769 E-272 at Y, witness=13.
Pol[111, 2] with [h, u]=[37, 17] has ratio=0.00005691258406326150873 at X, ratio=1.7783330112098770417 E-257 at Y, witness=11.
Pol[112, 2] with [h, u]=[37, 17] has ratio=0.0004852859975539075566 at X, ratio=2.1050028936606355798 E-243 at Y, witness=11.
Pol[113, 2] with [h, u]=[37, 17] has ratio=0.0003219098950974758332 at X, ratio=5.193284518985897533 E-230 at Y, witness=2.
Pol[114, 2] with [h, u]=[38, 18] has ratio=0.0007879255406878326406 at X, ratio=4.850621451435856238 E-313 at Y, witness=5.
Pol[115, 2] with [h, u]=[38, 18] has ratio=0.0004519203011730788759 at X, ratio=1.3106261727473621482 E-304 at Y, witness=7.
Pol[116, 2] with [h, u]=[38, 18] has ratio=0.0004606560219913678560 at X, ratio=1.6319566982115494994 E-296 at Y, witness=3.
Pol[117, 2] with [h, u]=[38, 18] has ratio=0.0009261636186990189291 at X, ratio=1.4228924981614968793 E-288 at Y, witness=2.
Pol[118, 2] with [h, u]=[38, 18] has ratio=0.00020813352011578722988 at X, ratio=7.402125409769907960 E-281 at Y, witness=2.
Pol[119, 2] with [h, u]=[39, 18] has ratio=0.00011587826262264041251 at X, ratio=2.4440634432476833936 E-284 at Y, witness=3.

Validated in 1856 sec.

Goodbye!
```
A copy of the CHG certificate `9473_4969.out` (312MB) is included in: `9473_4969.zip` and can be verified by running the Pari-GP script `verify.gp`.

## Helper File

Based on factorization of N-1 and N+1:
```Phi(2484,9473)/(4969*12421*56920064266370917)
Phi(276,9473)/(4078196149*21076115072967628669*5868411029542058847037*312340887712771025632933)
790578391644824305704095933668494322391702207992644117439348583296937373447043952812273607125071276632631368384796696388294063
48238600824143466690629821931569982924209904378253126423067498663038548511913
125792403951832429666582190562096368653205568376633314259131899118754219
454116213229883576821395708231824748457006974519898793066012728117
6153802444099194197172163246356699598983542344586491218411613
10518357415550938091666737844077546199697408551419227017509
5673572348997578174866203989768318738865408868732938557
13838679075694115139419776418017538480189346833119
2885173089464494158993207873643480978115924893
131947473383237809379236333393902922169707777
6504897024500732032535854457543958709
1525755501002914055912854011211331761
69833511292590478889935763948193241
682908818115657803529289808225593
670190822656157947508137927161289
26180666624035769943202015321
10889645257590586215851795599
2276488939138219124696392409
1187165404047152983009948051
760310289351036399286573069
198303481065921840216568313
12826485649338855075211313
8442915788075527408047709
312340887712771025632933
5868411029542058847037
145582911518144307139
21076115072967628669
14192306557614508699
94208551283625809
86328297063284401
56920064266370917
3912576759594721
2526820026506011
1145831626392961
674471077906877
196654321398011
120677507224633
37281273697741
16798507911253
8632773367651
534257275681
396151522981
339587330041
104867802001
101490434377
12193657921
4078196149
3888651313
1655808871
596043529
463773637
260910343
167265757
29909419
24578713
24180361
21241513
9772057
7725241
6469579
6455539
4703593
1476199
1349687
880993
527869
212383
177929
166393
153871
80317
51907
26083
15073
12421
12007
9473
7489
5521
4969
3313
1657
1579
1033
967
829
487
433
409
277
271
193
181
139
127
109
97
73
47
19
17
13
7
5
3
3
3
3
2
2
2
180975869
3899941
1567
569
2
```

## Prime Factor Certification

Signed Primo certificates for `Phi(2484,9473)/(4969*12421*56920064266370917)` (3125 digits) and `Phi(276,9473)/(4078196149*21076115072967628669*5868411029542058847037*312340887712771025632933)` (276 digits) are included in: `9473_4969.zip`

Tom Wu