]> Fundamental Solutions to Pell's Equation

# Fundamental Solutions to Pell's Equation

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## N = 2..1000

The fundamental solutions to Pell's equation (also known as "minimal solutions") presented below were computed in 2012 using a Python program that implements the chakravala method (attributed to Bhaskara II). N is skipped if it is not square-free (i.e., if it is a perfect square or a multiple of a square).

 N x y Fundamental solution 2 3 2 $3 2 -$2 . 2 2 = 1 3 2 1 $2 2 -$3 . 1 2 = 1 5 9 4 $9 2 -$5 . 4 2 = 1 6 5 2 $5 2 -$6 . 2 2 = 1 7 8 3 $8 2 -$7 . 3 2 = 1 10 19 6 $19 2 -$10 . 6 2 = 1 11 10 3 $10 2 -$11 . 3 2 = 1 13 649 180 $649 2 -$13 . 180 2 = 1 14 15 4 $15 2 -$14 . 4 2 = 1 15 4 1 $4 2 -$15 . 1 2 = 1 17 33 8 $33 2 -$17 . 8 2 = 1 19 170 39 $170 2 -$19 . 39 2 = 1 21 55 12 $55 2 -$21 . 12 2 = 1 22 197 42 $197 2 -$22 . 42 2 = 1 23 24 5 $24 2 -$23 . 5 2 = 1 26 51 10 $51 2 -$26 . 10 2 = 1 29 9801 1820 $9801 2 -$29 . 1820 2 = 1 30 11 2 $11 2 -$30 . 2 2 = 1 31 1520 273 $1520 2 -$31 . 273 2 = 1 33 23 4 $23 2 -$33 . 4 2 = 1 34 35 6 $35 2 -$34 . 6 2 = 1 35 6 1 $6 2 -$35 . 1 2 = 1 37 73 12 $73 2 -$37 . 12 2 = 1 38 37 6 $37 2 -$38 . 6 2 = 1 39 25 4 $25 2 -$39 . 4 2 = 1 41 2049 320 $2049 2 -$41 . 320 2 = 1 42 13 2 $13 2 -$42 . 2 2 = 1 43 3482 531 $3482 2 -$43 . 531 2 = 1 46 24335 3588 $24335 2 -$46 . 3588 2 = 1 47 48 7 $48 2 -$47 . 7 2 = 1 51 50 7 $50 2 -$51 . 7 2 = 1 53 66249 9100 $66249 2 -$53 . 9100 2 = 1 55 89 12 $89 2 -$55 . 12 2 = 1 57 151 20 $151 2 -$57 . 20 2 = 1 58 19603 2574 $19603 2 -$58 . 2574 2 = 1 59 530 69 $530 2 -$59 . 69 2 = 1 61 1766319049 226153980 $1766319049 2 -$61 . 226153980 2 = 1 62 63 8 $63 2 -$62 . 8 2 = 1 65 129 16 $129 2 -$65 . 16 2 = 1 66 65 8 $65 2 -$66 . 8 2 = 1 67 48842 5967 $48842 2 -$67 . 5967 2 = 1 69 7775 936 $7775 2 -$69 . 936 2 = 1 70 251 30 $251 2 -$70 . 30 2 = 1 71 3480 413 $3480 2 -$71 . 413 2 = 1 73 2281249 267000 $2281249 2 -$73 . 267000 2 = 1 74 3699 430 $3699 2 -$74 . 430 2 = 1 77 351 40 $351 2 -$77 . 40 2 = 1 78 53 6 $53 2 -$78 . 6 2 = 1 79 80 9 $80 2 -$79 . 9 2 = 1 82 163 18 $163 2 -$82 . 18 2 = 1 83 82 9 $82 2 -$83 . 9 2 = 1 85 285769 30996 $285769 2 -$85 . 30996 2 = 1 86 10405 1122 $10405 2 -$86 . 1122 2 = 1 87 28 3 $28 2 -$87 . 3 2 = 1 89 500001 53000 $500001 2 -$89 . 53000 2 = 1 91 1574 165 $1574 2 -$91 . 165 2 = 1 93 12151 1260 $12151 2 -$93 . 1260 2 = 1 94 2143295 221064 $2143295 2 -$94 . 221064 2 = 1 95 39 4 $39 2 -$95 . 4 2 = 1 97 62809633 6377352 $62809633 2 -$97 . 6377352 2 = 1 101 201 20 $201 2 -$101 . 20 2 = 1 102 101 10 $101 2 -$102 . 10 2 = 1 103 227528 22419 $227528 2 -$103 . 22419 2 = 1 105 41 4 $41 2 -$105 . 4 2 = 1 106 32080051 3115890 $32080051 2 -$106 . 3115890 2 = 1 107 962 93 $962 2 -$107 . 93 2 = 1 109 158070671986249 15140424455100 $158070671986249 2 -$109 . 15140424455100 2 = 1 110 21 2 $21 2 -$110 . 2 2 = 1 111 295 28 $295 2 -$111 . 28 2 = 1 113 1204353 113296 $1204353 2 -$113 . 113296 2 = 1 114 1025 96 $1025 2 -$114 . 96 2 = 1 115 1126 105 $1126 2 -$115 . 105 2 = 1 118 306917 28254 $306917 2 -$118 . 28254 2 = 1 119 120 11 $120 2 -$119 . 11 2 = 1 122 243 22 $243 2 -$122 . 22 2 = 1 123 122 11 $122 2 -$123 . 11 2 = 1 127 4730624 419775 $4730624 2 -$127 . 419775 2 = 1 129 16855 1484 $16855 2 -$129 . 1484 2 = 1 130 6499 570 $6499 2 -$130 . 570 2 = 1 131 10610 927 $10610 2 -$131 . 927 2 = 1 133 2588599 224460 $2588599 2 -$133 . 224460 2 = 1 134 145925 12606 $145925 2 -$134 . 12606 2 = 1 137 6083073 519712 $6083073 2 -$137 . 519712 2 = 1 138 47 4 $47 2 -$138 . 4 2 = 1 139 77563250 6578829 $77563250 2 -$139 . 6578829 2 = 1 141 95 8 $95 2 -$141 . 8 2 = 1 142 143 12 $143 2 -$142 . 12 2 = 1 143 12 1 $12 2 -$143 . 1 2 = 1 145 289 24 $289 2 -$145 . 24 2 = 1 146 145 12 $145 2 -$146 . 12 2 = 1 149 25801741449 2113761020 $25801741449 2 -$149 . 2113761020 2 = 1 151 1728148040 140634693 $1728148040 2 -$151 . 140634693 2 = 1 154 21295 1716 $21295 2 -$154 . 1716 2 = 1 155 249 20 $249 2 -$155 . 20 2 = 1 157 46698728731849 3726964292220 $46698728731849 2 -$157 . 3726964292220 2 = 1 158 7743 616 $7743 2 -$158 . 616 2 = 1 159 1324 105 $1324 2 -$159 . 105 2 = 1 161 11775 928 $11775 2 -$161 . 928 2 = 1 163 64080026 5019135 $64080026 2 -$163 . 5019135 2 = 1 165 1079 84 $1079 2 -$165 . 84 2 = 1 166 1700902565 132015642 $1700902565 2 -$166 . 132015642 2 = 1 167 168 13 $168 2 -$167 . 13 2 = 1 170 339 26 $339 2 -$170 . 26 2 = 1 173 2499849 190060 $2499849 2 -$173 . 190060 2 = 1 174 1451 110 $1451 2 -$174 . 110 2 = 1 177 62423 4692 $62423 2 -$177 . 4692 2 = 1 178 1601 120 $1601 2 -$178 . 120 2 = 1 179 4190210 313191 $4190210 2 -$179 . 313191 2 = 1 181 2469645423824185801 183567298683461940 $2469645423824185801 2 -$181 . 183567298683461940 2 = 1 182 27 2 $27 2 -$182 . 2 2 = 1 183 487 36 $487 2 -$183 . 36 2 = 1 185 9249 680 $9249 2 -$185 . 680 2 = 1 186 7501 550 $7501 2 -$186 . 550 2 = 1 187 1682 123 $1682 2 -$187 . 123 2 = 1 190 52021 3774 $52021 2 -$190 . 3774 2 = 1 191 8994000 650783 $8994000 2 -$191 . 650783 2 = 1 193 6224323426849 448036604040 $6224323426849 2 -$193 . 448036604040 2 = 1 194 195 14 $195 2 -$194 . 14 2 = 1 195 14 1 $14 2 -$195 . 1 2 = 1 197 393 28 $393 2 -$197 . 28 2 = 1 199 16266196520 1153080099 $16266196520 2 -$199 . 1153080099 2 = 1 201 515095 36332 $515095 2 -$201 . 36332 2 = 1 202 19731763 1388322 $19731763 2 -$202 . 1388322 2 = 1 203 57 4 $57 2 -$203 . 4 2 = 1 205 39689 2772 $39689 2 -$205 . 2772 2 = 1 206 59535 4148 $59535 2 -$206 . 4148 2 = 1 209 46551 3220 $46551 2 -$209 . 3220 2 = 1 210 29 2 $29 2 -$210 . 2 2 = 1 211 278354373650 19162705353 $278354373650 2 -$211 . 19162705353 2 = 1 213 194399 13320 $194399 2 -$213 . 13320 2 = 1 214 695359189925 47533775646 $695359189925 2 -$214 . 47533775646 2 = 1 215 44 3 $44 2 -$215 . 3 2 = 1 217 3844063 260952 $3844063 2 -$217 . 260952 2 = 1 218 126003 8534 $126003 2 -$218 . 8534 2 = 1 219 74 5 $74 2 -$219 . 5 2 = 1 221 1665 112 $1665 2 -$221 . 112 2 = 1 222 149 10 $149 2 -$222 . 10 2 = 1 223 224 15 $224 2 -$223 . 15 2 = 1 226 451 30 $451 2 -$226 . 30 2 = 1 227 226 15 $226 2 -$227 . 15 2 = 1 229 5848201 386460 $5848201 2 -$229 . 386460 2 = 1 230 91 6 $91 2 -$230 . 6 2 = 1 231 76 5 $76 2 -$231 . 5 2 = 1 233 1072400673 70255304 $1072400673 2 -$233 . 70255304 2 = 1 235 46 3 $46 2 -$235 . 3 2 = 1 237 228151 14820 $228151 2 -$237 . 14820 2 = 1 238 11663 756 $11663 2 -$238 . 756 2 = 1 239 6195120 400729 $6195120 2 -$239 . 400729 2 = 1 241 10085143557001249 649641205044600 $10085143557001249 2 -$241 . 649641205044600 2 = 1 246 88805 5662 $88805 2 -$246 . 5662 2 = 1 247 85292 5427 $85292 2 -$247 . 5427 2 = 1 249 8553815 542076 $8553815 2 -$249 . 542076 2 = 1 251 3674890 231957 $3674890 2 -$251 . 231957 2 = 1 253 3222617399 202604220 $3222617399 2 -$253 . 202604220 2 = 1 254 255 16 $255 2 -$254 . 16 2 = 1 255 16 1 $16 2 -$255 . 1 2 = 1 257 513 32 $513 2 -$257 . 32 2 = 1 258 257 16 $257 2 -$258 . 16 2 = 1 259 847225 52644 $847225 2 -$259 . 52644 2 = 1 262 104980517 6485718 $104980517 2 -$262 . 6485718 2 = 1 263 139128 8579 $139128 2 -$263 . 8579 2 = 1 265 73738369 4529712 $73738369 2 -$265 . 4529712 2 = 1 266 685 42 $685 2 -$266 . 42 2 = 1 267 2402 147 $2402 2 -$267 . 147 2 = 1 269 13449 820 $13449 2 -$269 . 820 2 = 1 271 115974983600 7044978537 $115974983600 2 -$271 . 7044978537 2 = 1 273 727 44 $727 2 -$273 . 44 2 = 1 274 3959299 239190 $3959299 2 -$274 . 239190 2 = 1 277 159150073798980475849 9562401173878027020 $159150073798980475849 2 -$277 . 9562401173878027020 2 = 1 278 2501 150 $2501 2 -$278 . 150 2 = 1 281 2262200630049 134951575480 $2262200630049 2 -$281 . 134951575480 2 = 1 282 2351 140 $2351 2 -$282 . 140 2 = 1 283 138274082 8219541 $138274082 2 -$283 . 8219541 2 = 1 285 2431 144 $2431 2 -$285 . 144 2 = 1 286 561835 33222 $561835 2 -$286 . 33222 2 = 1 287 288 17 $288 2 -$287 . 17 2 = 1 290 579 34 $579 2 -$290 . 34 2 = 1 291 290 17 $290 2 -$291 . 17 2 = 1 293 12320649 719780 $12320649 2 -$293 . 719780 2 = 1 295 2024999 117900 $2024999 2 -$295 . 117900 2 = 1 298 335473872499 19433479650 $335473872499 2 -$298 . 19433479650 2 = 1 299 415 24 $415 2 -$299 . 24 2 = 1 301 5883392537695 339113108232 $5883392537695 2 -$301 . 339113108232 2 = 1 302 4276623 246092 $4276623 2 -$302 . 246092 2 = 1 303 2524 145 $2524 2 -$303 . 145 2 = 1 305 489 28 $489 2 -$305 . 28 2 = 1 307 88529282 5052633 $88529282 2 -$307 . 5052633 2 = 1 309 64202725495 3652365444 $64202725495 2 -$309 . 3652365444 2 = 1 310 848719 48204 $848719 2 -$310 . 48204 2 = 1 311 16883880 957397 $16883880 2 -$311 . 957397 2 = 1 313 32188120829134849 1819380158564160 $32188120829134849 2 -$313 . 1819380158564160 2 = 1 314 392499 22150 $392499 2 -$314 . 22150 2 = 1 317 248678907849 13967198980 $248678907849 2 -$317 . 13967198980 2 = 1 318 107 6 $107 2 -$318 . 6 2 = 1 319 12901780 722361 $12901780 2 -$319 . 722361 2 = 1 321 215 12 $215 2 -$321 . 12 2 = 1 322 323 18 $323 2 -$322 . 18 2 = 1 323 18 1 $18 2 -$323 . 1 2 = 1 326 325 18 $325 2 -$326 . 18 2 = 1 327 217 12 $217 2 -$327 . 12 2 = 1 329 2376415 131016 $2376415 2 -$329 . 131016 2 = 1 330 109 6 $109 2 -$330 . 6 2 = 1 331 2785589801443970 153109862634573 $2785589801443970 2 -$331 . 153109862634573 2 = 1 334 63804373719695 3491219999244 $63804373719695 2 -$334 . 3491219999244 2 = 1 335 604 33 $604 2 -$335 . 33 2 = 1 337 2063810353129713793 112422913565764752 $2063810353129713793 2 -$337 . 112422913565764752 2 = 1 339 97970 5321 $97970 2 -$339 . 5321 2 = 1 341 10626551 575460 $10626551 2 -$341 . 575460 2 = 1 345 6761 364 $6761 2 -$345 . 364 2 = 1 346 17299 930 $17299 2 -$346 . 930 2 = 1 347 641602 34443 $641602 2 -$347 . 34443 2 = 1 349 169648201 9081060 $169648201 2 -$349 . 9081060 2 = 1 353 10157115393 540608704 $10157115393 2 -$353 . 540608704 2 = 1 354 258065 13716 $258065 2 -$354 . 13716 2 = 1 355 954809 50676 $954809 2 -$355 . 50676 2 = 1 357 3401 180 $3401 2 -$357 . 180 2 = 1 358 176579805797 9332532726 $176579805797 2 -$358 . 9332532726 2 = 1 359 360 19 $360 2 -$359 . 19 2 = 1 362 723 38 $723 2 -$362 . 38 2 = 1 365 23915529 1251796 $23915529 2 -$365 . 1251796 2 = 1 366 907925 47458 $907925 2 -$366 . 47458 2 = 1 367 19019995568 992835687 $19019995568 2 -$367 . 992835687 2 = 1 370 213859 11118 $213859 2 -$370 . 11118 2 = 1 371 1695 88 $1695 2 -$371 . 88 2 = 1 373 52387849 2712540 $52387849 2 -$373 . 2712540 2 = 1 374 3365 174 $3365 2 -$374 . 174 2 = 1 377 233 12 $233 2 -$377 . 12 2 = 1 379 12941197220540690 664744650125541 $12941197220540690 2 -$379 . 664744650125541 2 = 1 381 1015 52 $1015 2 -$381 . 52 2 = 1 382 164998439999 8442054600 $164998439999 2 -$382 . 8442054600 2 = 1 383 18768 959 $18768 2 -$383 . 959 2 = 1 385 95831 4884 $95831 2 -$385 . 4884 2 = 1 386 111555 5678 $111555 2 -$386 . 5678 2 = 1 389 3287049 166660 $3287049 2 -$389 . 166660 2 = 1 390 79 4 $79 2 -$390 . 4 2 = 1 391 7338680 371133 $7338680 2 -$391 . 371133 2 = 1 393 46437143 2342444 $46437143 2 -$393 . 2342444 2 = 1 394 312086396361222451 15722685507826110 $312086396361222451 2 -$394 . 15722685507826110 2 = 1 395 159 8 $159 2 -$395 . 8 2 = 1 397 838721786045180184649 42094239791738433660 $838721786045180184649 2 -$397 . 42094239791738433660 2 = 1 398 399 20 $399 2 -$398 . 20 2 = 1 399 20 1 $20 2 -$399 . 1 2 = 1 401 801 40 $801 2 -$401 . 40 2 = 1 402 401 20 $401 2 -$402 . 20 2 = 1 403 669878 33369 $669878 2 -$403 . 33369 2 = 1 406 59468095 2951352 $59468095 2 -$406 . 2951352 2 = 1 407 2663 132 $2663 2 -$407 . 132 2 = 1 409 25052977273092427986049 1238789998647218582160 $25052977273092427986049 2 -$409 . 1238789998647218582160 2 = 1 410 81 4 $81 2 -$410 . 4 2 = 1 411 49730 2453 $49730 2 -$411 . 2453 2 = 1 413 113399 5580 $113399 2 -$413 . 5580 2 = 1 415 18412804 903849 $18412804 2 -$415 . 903849 2 = 1 417 85322647 4178268 $85322647 2 -$417 . 4178268 2 = 1 418 33857 1656 $33857 2 -$418 . 1656 2 = 1 419 270174970 13198911 $270174970 2 -$419 . 13198911 2 = 1 421 3879474045914926879468217167061449 189073995951839020880499780706260 $3879474045914926879468217167061449 2 -$421 . 189073995951839020880499780706260 2 = 1 422 7022501 341850 $7022501 2 -$422 . 341850 2 = 1 426 88751 4300 $88751 2 -$426 . 4300 2 = 1 427 62 3 $62 2 -$427 . 3 2 = 1 429 1524095 73584 $1524095 2 -$429 . 73584 2 = 1 430 2862251 138030 $2862251 2 -$430 . 138030 2 = 1 431 151560720 7300423 $151560720 2 -$431 . 7300423 2 = 1 433 104564907854286695713 5025068784834899736 $104564907854286695713 2 -$433 . 5025068784834899736 2 = 1 434 125 6 $125 2 -$434 . 6 2 = 1 435 146 7 $146 2 -$435 . 7 2 = 1 437 4599 220 $4599 2 -$437 . 220 2 = 1 438 293 14 $293 2 -$438 . 14 2 = 1 439 440 21 $440 2 -$439 . 21 2 = 1 442 883 42 $883 2 -$442 . 42 2 = 1 443 442 21 $442 2 -$443 . 21 2 = 1 445 43468489 2060604 $43468489 2 -$445 . 2060604 2 = 1 446 110166015 5216512 $110166015 2 -$446 . 5216512 2 = 1 447 148 7 $148 2 -$447 . 7 2 = 1 449 71798771299708449 3388393513402120 $71798771299708449 2 -$449 . 3388393513402120 2 = 1 451 46471490 2188257 $46471490 2 -$451 . 2188257 2 = 1 453 1653751 77700 $1653751 2 -$453 . 77700 2 = 1 454 16916040084175685 793909098494766 $16916040084175685 2 -$454 . 793909098494766 2 = 1 455 64 3 $64 2 -$455 . 3 2 = 1 457 6983244756398928218113 326662411570389853632 $6983244756398928218113 2 -$457 . 326662411570389853632 2 = 1 458 22899 1070 $22899 2 -$458 . 1070 2 = 1 461 1182351890184201 55067617520620 $1182351890184201 2 -$461 . 55067617520620 2 = 1 462 43 2 $43 2 -$462 . 2 2 = 1 463 247512720456368 11502891625161 $247512720456368 2 -$463 . 11502891625161 2 = 1 465 15871 736 $15871 2 -$465 . 736 2 = 1 466 938319425 43466808 $938319425 2 -$466 . 43466808 2 = 1 467 1625626 75225 $1625626 2 -$467 . 75225 2 = 1 469 137215 6336 $137215 2 -$469 . 6336 2 = 1 470 1691 78 $1691 2 -$470 . 78 2 = 1 471 7838695 361188 $7838695 2 -$471 . 361188 2 = 1 473 87 4 $87 2 -$473 . 4 2 = 1 474 193549 8890 $193549 2 -$474 . 8890 2 = 1 478 1617319577991743 73974475657896 $1617319577991743 2 -$478 . 73974475657896 2 = 1 479 2989440 136591 $2989440 2 -$479 . 136591 2 = 1 481 1859131879201 84769117080 $1859131879201 2 -$481 . 84769117080 2 = 1 482 483 22 $483 2 -$482 . 22 2 = 1 483 22 1 $22 2 -$483 . 1 2 = 1 485 969 44 $969 2 -$485 . 44 2 = 1 487 51906073840568 2352088722477 $51906073840568 2 -$487 . 2352088722477 2 = 1 489 7592629975 343350596 $7592629975 2 -$489 . 343350596 2 = 1 491 93628044170 4225374483 $93628044170 2 -$491 . 4225374483 2 = 1 493 935662752649 42140131020 $935662752649 2 -$493 . 42140131020 2 = 1 494 73035 3286 $73035 2 -$494 . 3286 2 = 1 497 1201887 53912 $1201887 2 -$497 . 53912 2 = 1 498 179777 8056 $179777 2 -$498 . 8056 2 = 1 499 4490 201 $4490 2 -$499 . 201 2 = 1 501 11242731902975 502288218432 $11242731902975 2 -$501 . 502288218432 2 = 1 502 3832352837 171046278 $3832352837 2 -$502 . 171046278 2 = 1 503 24648 1099 $24648 2 -$503 . 1099 2 = 1 505 809 36 $809 2 -$505 . 36 2 = 1 506 45 2 $45 2 -$506 . 2 2 = 1 509 313201220822405001 13882400040814700 $313201220822405001 2 -$509 . 13882400040814700 2 = 1 510 271 12 $271 2 -$510 . 12 2 = 1 511 4188548960 185290497 $4188548960 2 -$511 . 185290497 2 = 1 514 4625 204 $4625 2 -$514 . 204 2 = 1 515 17406 767 $17406 2 -$515 . 767 2 = 1 517 590968985399 25990786260 $590968985399 2 -$517 . 25990786260 2 = 1 518 2367 104 $2367 2 -$518 . 104 2 = 1 519 14851876 651925 $14851876 2 -$519 . 651925 2 = 1 521 32961431500035201 1444066532654320 $32961431500035201 2 -$521 . 1444066532654320 2 = 1 523 81810300626 3577314675 $81810300626 2 -$523 . 3577314675 2 = 1 526 84056091546952933775 3665019757324295532 $84056091546952933775 2 -$526 . 3665019757324295532 2 = 1 527 528 23 $528 2 -$527 . 23 2 = 1 530 1059 46 $1059 2 -$530 . 46 2 = 1 533 74859849 3242540 $74859849 2 -$533 . 3242540 2 = 1 534 3678725 159194 $3678725 2 -$534 . 159194 2 = 1 535 1618804 69987 $1618804 2 -$535 . 69987 2 = 1 537 192349463 8300492 $192349463 2 -$537 . 8300492 2 = 1 538 9536081203 411129654 $9536081203 2 -$538 . 411129654 2 = 1 541 3707453360023867028800645599667005001 159395869721270110077187138775196900 $3707453360023867028800645599667005001 2 -$541 . 159395869721270110077187138775196900 2 = 1 542 4293183 184408 $4293183 2 -$542 . 184408 2 = 1 543 669337 28724 $669337 2 -$543 . 28724 2 = 1 545 1961 84 $1961 2 -$545 . 84 2 = 1 546 701 30 $701 2 -$546 . 30 2 = 1 547 160177601264642 6848699678673 $160177601264642 2 -$547 . 6848699678673 2 = 1 551 8380 357 $8380 2 -$551 . 357 2 = 1 553 624635837407 26562217704 $624635837407 2 -$553 . 26562217704 2 = 1 554 60756099699 2581279330 $60756099699 2 -$554 . 2581279330 2 = 1 555 1814 77 $1814 2 -$555 . 77 2 = 1 557 27849 1180 $27849 2 -$557 . 1180 2 = 1 559 506568295 21425556 $506568295 2 -$559 . 21425556 2 = 1 561 522785 22072 $522785 2 -$561 . 22072 2 = 1 562 220938497 9319728 $220938497 2 -$562 . 9319728 2 = 1 563 68122 2871 $68122 2 -$563 . 2871 2 = 1 565 435259412378569 18311501103948 $435259412378569 2 -$565 . 18311501103948 2 = 1 566 95609285 4018758 $95609285 2 -$566 . 4018758 2 = 1 569 16760473211643448449 702635588524014320 $16760473211643448449 2 -$569 . 702635588524014320 2 = 1 570 191 8 $191 2 -$570 . 8 2 = 1 571 181124355061630786130 7579818350628982587 $181124355061630786130 2 -$571 . 7579818350628982587 2 = 1 573 383 16 $383 2 -$573 . 16 2 = 1 574 575 24 $575 2 -$574 . 24 2 = 1 577 1153 48 $1153 2 -$577 . 48 2 = 1 579 385 16 $385 2 -$579 . 16 2 = 1 581 152071153975 6308974548 $152071153975 2 -$581 . 6308974548 2 = 1 582 193 8 $193 2 -$582 . 8 2 = 1 583 8429543 349116 $8429543 2 -$583 . 349116 2 = 1 586 33867877212256207699 1399069112058008310 $33867877212256207699 2 -$586 . 1399069112058008310 2 = 1 587 1907162 78717 $1907162 2 -$587 . 78717 2 = 1 589 41423166067036218751 1706811823063746000 $41423166067036218751 2 -$589 . 1706811823063746000 2 = 1 590 5781 238 $5781 2 -$590 . 238 2 = 1 591 165676 6815 $165676 2 -$591 . 6815 2 = 1 593 721517598849 29629176560 $721517598849 2 -$593 . 29629176560 2 = 1 595 18514 759 $18514 2 -$595 . 759 2 = 1 597 463287093751 18961078500 $463287093751 2 -$597 . 18961078500 2 = 1 598 1574351 64380 $1574351 2 -$598 . 64380 2 = 1 599 24686379794520 1008658133851 $24686379794520 2 -$599 . 1008658133851 2 = 1 601 38902815462492318420311478049 1586878942101888360258625080 $38902815462492318420311478049 2 -$601 . 1586878942101888360258625080 2 = 1 602 687 28 $687 2 -$602 . 28 2 = 1 606 42187499 1713750 $42187499 2 -$606 . 1713750 2 = 1 607 164076033968 6659640783 $164076033968 2 -$607 . 6659640783 2 = 1 609 605695 24544 $605695 2 -$609 . 24544 2 = 1 610 10323982819 418005846 $10323982819 2 -$610 . 418005846 2 = 1 611 236926 9585 $236926 2 -$611 . 9585 2 = 1 613 464018873584078278910994299849 18741545784831997880308784340 $464018873584078278910994299849 2 -$613 . 18741545784831997880308784340 2 = 1 614 348291186245 14055888354 $348291186245 2 -$614 . 14055888354 2 = 1 615 124 5 $124 2 -$615 . 5 2 = 1 617 3363593612801313 135413180018248 $3363593612801313 2 -$617 . 135413180018248 2 = 1 618 10093 406 $10093 2 -$618 . 406 2 = 1 619 517213510553282930 20788566180548739 $517213510553282930 2 -$619 . 20788566180548739 2 = 1 622 13804370063 553504812 $13804370063 2 -$622 . 553504812 2 = 1 623 624 25 $624 2 -$623 . 25 2 = 1 626 1251 50 $1251 2 -$626 . 50 2 = 1 627 626 25 $626 2 -$627 . 25 2 = 1 629 123245001 4914100 $123245001 2 -$629 . 4914100 2 = 1 631 48961575312998650035560 1949129537575151036427 $48961575312998650035560 2 -$631 . 1949129537575151036427 2 = 1 633 440772247 17519124 $440772247 2 -$633 . 17519124 2 = 1 634 8711856945587257031251 345992039259400361250 $8711856945587257031251 2 -$634 . 345992039259400361250 2 = 1 635 126 5 $126 2 -$635 . 5 2 = 1 638 42283 1674 $42283 2 -$638 . 1674 2 = 1 641 2609429220845977814049 103066257550962737720 $2609429220845977814049 2 -$641 . 103066257550962737720 2 = 1 642 5777 228 $5777 2 -$642 . 228 2 = 1 643 1988960193026 78436933185 $1988960193026 2 -$643 . 78436933185 2 = 1 645 1024001 40320 $1024001 2 -$645 . 40320 2 = 1 646 305 12 $305 2 -$646 . 12 2 = 1 647 120187368 4725053 $120187368 2 -$647 . 4725053 2 = 1 649 1123593226162199 44104892095380 $1123593226162199 2 -$649 . 44104892095380 2 = 1 651 1735 68 $1735 2 -$651 . 68 2 = 1 653 10499986568677299849 410896226494013260 $10499986568677299849 2 -$653 . 410896226494013260 2 = 1 654 8915765 348634 $8915765 2 -$654 . 348634 2 = 1 655 737709209 28824684 $737709209 2 -$655 . 28824684 2 = 1 658 1693 66 $1693 2 -$658 . 66 2 = 1 659 5930 231 $5930 2 -$659 . 231 2 = 1 661 16421658242965910275055840472270471049 638728478116949861246791167518480580 $16421658242965910275055840472270471049 2 -$661 . 638728478116949861246791167518480580 2 = 1 662 1718102501 66775950 $1718102501 2 -$662 . 66775950 2 = 1 663 103 4 $103 2 -$663 . 4 2 = 1 665 13719 532 $13719 2 -$665 . 532 2 = 1 667 107119097 4147668 $107119097 2 -$667 . 4147668 2 = 1 669 14226117859054135 550013492618436 $14226117859054135 2 -$669 . 550013492618436 2 = 1 670 5791211 223734 $5791211 2 -$670 . 223734 2 = 1 671 58620 2263 $58620 2 -$671 . 2263 2 = 1 673 4765506835465395993032041249 183696788896587421699032600 $4765506835465395993032041249 2 -$673 . 183696788896587421699032600 2 = 1 674 675 26 $675 2 -$674 . 26 2 = 1 677 1353 52 $1353 2 -$677 . 52 2 = 1 678 677 26 $677 2 -$678 . 26 2 = 1 679 17792625320 682818291 $17792625320 2 -$679 . 682818291 2 = 1 681 10743166003415 411679015748 $10743166003415 2 -$681 . 411679015748 2 = 1 682 1197901 45870 $1197901 2 -$682 . 45870 2 = 1 683 170067682 6507459 $170067682 2 -$683 . 6507459 2 = 1 685 95592800063517769 3652413145693884 $95592800063517769 2 -$685 . 3652413145693884 2 = 1 687 165337 6308 $165337 2 -$687 . 6308 2 = 1 689 105 4 $105 2 -$689 . 4 2 = 1 690 1471 56 $1471 2 -$690 . 56 2 = 1 691 31138100617500578690 1184549173291009383 $31138100617500578690 2 -$691 . 1184549173291009383 2 = 1 694 38782105445014642382885 1472148590903997672114 $38782105445014642382885 2 -$694 . 1472148590903997672114 2 = 1 695 33639 1276 $33639 2 -$695 . 1276 2 = 1 697 34849 1320 $34849 2 -$697 . 1320 2 = 1 698 51999603 1968214 $51999603 2 -$698 . 1968214 2 = 1 699 2271050 85899 $2271050 2 -$699 . 85899 2 = 1 701 277631049 10485980 $277631049 2 -$701 . 10485980 2 = 1 703 1159172 43719 $1159172 2 -$703 . 43719 2 = 1 705 237161 8932 $237161 2 -$705 . 8932 2 = 1 706 34595 1302 $34595 2 -$706 . 1302 2 = 1 707 2526 95 $2526 2 -$707 . 95 2 = 1 709 665782673992201 25003993164540 $665782673992201 2 -$709 . 25003993164540 2 = 1 710 1279 48 $1279 2 -$710 . 48 2 = 1 713 5286367 197976 $5286367 2 -$713 . 197976 2 = 1 714 4115 154 $4115 2 -$714 . 154 2 = 1 715 75646 2829 $75646 2 -$715 . 2829 2 = 1 717 6998399 261360 $6998399 2 -$717 . 261360 2 = 1 718 8933399183036079503 333391496474140716 $8933399183036079503 2 -$718 . 333391496474140716 2 = 1 719 403480310400 15047276489 $403480310400 2 -$719 . 15047276489 2 = 1 721 18632176943292415 693898530122112 $18632176943292415 2 -$721 . 693898530122112 2 = 1 723 242 9 $242 2 -$723 . 9 2 = 1 727 728 27 $728 2 -$727 . 27 2 = 1 730 1459 54 $1459 2 -$730 . 54 2 = 1 731 730 27 $730 2 -$731 . 27 2 = 1 733 195307849 7213860 $195307849 2 -$733 . 7213860 2 = 1 734 10394175 383656 $10394175 2 -$734 . 383656 2 = 1 737 252975383 9318468 $252975383 2 -$737 . 9318468 2 = 1 739 98015661073616742153890 3605564376516452758671 $98015661073616742153890 2 -$739 . 3605564376516452758671 2 = 1 741 7352695 270108 $7352695 2 -$741 . 270108 2 = 1 742 263091151 9658380 $263091151 2 -$742 . 9658380 2 = 1 743 714024 26195 $714024 2 -$743 . 26195 2 = 1 745 12769001 467820 $12769001 2 -$745 . 467820 2 = 1 746 61268974069299 2243216519470 $61268974069299 2 -$746 . 2243216519470 2 = 1 749 1084616384895 39631020176 $1084616384895 2 -$749 . 39631020176 2 = 1 751 7293318466794882424418960 266136970677206024456793 $7293318466794882424418960 2 -$751 . 266136970677206024456793 2 = 1 753 308526027863 11243313484 $308526027863 2 -$753 . 11243313484 2 = 1 754 836977699 30480930 $836977699 2 -$754 . 30480930 2 = 1 755 1209 44 $1209 2 -$755 . 44 2 = 1 757 3750107388553 136299971388 $3750107388553 2 -$757 . 136299971388 2 = 1 758 413959717 15035694 $413959717 2 -$758 . 15035694 2 = 1 759 551 20 $551 2 -$759 . 20 2 = 1 761 1280001 46400 $1280001 2 -$761 . 46400 2 = 1 762 6349 230 $6349 2 -$762 . 230 2 = 1 763 719724601 26055780 $719724601 2 -$763 . 26055780 2 = 1 766 145933611945744638015 5272795728865625208 $145933611945744638015 2 -$766 . 5272795728865625208 2 = 1 767 31212 1127 $31212 2 -$767 . 1127 2 = 1 769 535781868388881310859702308423201 19320788325040337217824455505160 $535781868388881310859702308423201 2 -$769 . 19320788325040337217824455505160 2 = 1 770 111 4 $111 2 -$770 . 4 2 = 1 771 2989136930 107651137 $2989136930 2 -$771 . 107651137 2 = 1 773 3607394696649 129748968980 $3607394696649 2 -$773 . 129748968980 2 = 1 777 223 8 $223 2 -$777 . 8 2 = 1 778 5964562960504723 213839942395674 $5964562960504723 2 -$778 . 213839942395674 2 = 1 779 11785490 422259 $11785490 2 -$779 . 422259 2 = 1 781 67606199 2419140 $67606199 2 -$781 . 2419140 2 = 1 782 783 28 $783 2 -$782 . 28 2 = 1 785 1569 56 $1569 2 -$785 . 56 2 = 1 786 785 28 $785 2 -$786 . 28 2 = 1 787 34625394242 1234262007 $34625394242 2 -$787 . 1234262007 2 = 1 789 16116667272575 573768548496 $16116667272575 2 -$789 . 573768548496 2 = 1 790 6616066879 235389096 $6616066879 2 -$790 . 235389096 2 = 1 791 225 8 $225 2 -$791 . 8 2 = 1 793 4393 156 $4393 2 -$793 . 156 2 = 1 794 1828310451 64884310 $1828310451 2 -$794 . 64884310 2 = 1 795 6626 235 $6626 2 -$795 . 235 2 = 1 797 1221759532448649 43276943002540 $1221759532448649 2 -$797 . 43276943002540 2 = 1 798 113 4 $113 2 -$798 . 4 2 = 1 799 424 15 $424 2 -$799 . 15 2 = 1 802 295496099 10434330 $295496099 2 -$802 . 10434330 2 = 1 803 7226 255 $7226 2 -$803 . 255 2 = 1 805 1514868641 53392104 $1514868641 2 -$805 . 53392104 2 = 1 806 6166395 217202 $6166395 2 -$806 . 217202 2 = 1 807 51841948 1824923 $51841948 2 -$807 . 1824923 2 = 1 809 376455160998025676163201 13235458622462202510640 $376455160998025676163201 2 -$809 . 13235458622462202510640 2 = 1 811 1382072163578616410 48531117622921197 $1382072163578616410 2 -$811 . 48531117622921197 2 = 1 813 2167 76 $2167 2 -$813 . 76 2 = 1 814 4206992174549 147454999410 $4206992174549 2 -$814 . 147454999410 2 = 1 815 156644 5487 $156644 2 -$815 . 5487 2 = 1 817 343 12 $343 2 -$817 . 12 2 = 1 818 40899 1430 $40899 2 -$818 . 1430 2 = 1 821 9000987377460935993101449 314136625452886403879740 $9000987377460935993101449 2 -$821 . 314136625452886403879740 2 = 1 822 7397 258 $7397 2 -$822 . 258 2 = 1 823 235170474903644006168 8197527430497636651 $235170474903644006168 2 -$823 . 8197527430497636651 2 = 1 826 222239304685 7732694382 $222239304685 2 -$826 . 7732694382 2 = 1 827 900602 31317 $900602 2 -$827 . 31317 2 = 1 829 479835713751049 16665383182260 $479835713751049 2 -$829 . 16665383182260 2 = 1 830 146411 5082 $146411 2 -$830 . 5082 2 = 1 831 9799705 339948 $9799705 2 -$831 . 339948 2 = 1 834 6552578705 226897244 $6552578705 2 -$834 . 226897244 2 = 1 835 34336355806 1188258591 $34336355806 2 -$835 . 1188258591 2 = 1 838 42112785797 1454762046 $42112785797 2 -$838 . 1454762046 2 = 1 839 840 29 $840 2 -$839 . 29 2 = 1 842 1683 58 $1683 2 -$842 . 58 2 = 1 843 842 29 $842 2 -$843 . 29 2 = 1 849 1501654712948695 51536656330476 $1501654712948695 2 -$849 . 51536656330476 2 = 1 851 8418574 288585 $8418574 2 -$851 . 288585 2 = 1 853 215454135724113414336120649 7377009103065498851032020 $215454135724113414336120649 2 -$853 . 7377009103065498851032020 2 = 1 854 1294299 44290 $1294299 2 -$854 . 44290 2 = 1 857 131822292741249 4502963741200 $131822292741249 2 -$857 . 4502963741200 2 = 1 858 703 24 $703 2 -$858 . 24 2 = 1 859 2058844771979643060124010 70246877103894937291269 $2058844771979643060124010 2 -$859 . 70246877103894937291269 2 = 1 861 541601801 18457740 $541601801 2 -$861 . 18457740 2 = 1 862 358022566147312125503 12194296994921665128 $358022566147312125503 2 -$862 . 12194296994921665128 2 = 1 863 18524026608 630565199 $18524026608 2 -$863 . 630565199 2 = 1 865 242688628535063329 8251660923733224 $242688628535063329 2 -$865 . 8251660923733224 2 = 1 866 42435 1442 $42435 2 -$866 . 1442 2 = 1 869 60192738698751 2041898807200 $60192738698751 2 -$869 . 2041898807200 2 = 1 870 59 2 $59 2 -$870 . 2 2 = 1 871 19442812076 658794555 $19442812076 2 -$871 . 658794555 2 = 1 874 3725 126 $3725 2 -$874 . 126 2 = 1 877 116476476553 3933131148 $116476476553 2 -$877 . 3933131148 2 = 1 878 9314703 314356 $9314703 2 -$878 . 314356 2 = 1 879 107245324 3617295 $107245324 2 -$879 . 3617295 2 = 1 881 22606256615916825861249 761624136944072910800 $22606256615916825861249 2 -$881 . 761624136944072910800 2 = 1 883 34878475759617272473442 1173754162936357802169 $34878475759617272473442 2 -$883 . 1173754162936357802169 2 = 1 885 119 4 $119 2 -$885 . 4 2 = 1 886 7743524593057655851637765 260148796464024194850378 $7743524593057655851637765 2 -$886 . 260148796464024194850378 2 = 1 887 469224 15755 $469224 2 -$887 . 15755 2 = 1 889 13231974717803657215 443786188413453504 $13231974717803657215 2 -$889 . 443786188413453504 2 = 1 890 179 6 $179 2 -$890 . 6 2 = 1 893 6091434999 203842100 $6091434999 2 -$893 . 203842100 2 = 1 894 299 10 $299 2 -$894 . 10 2 = 1 895 359 12 $359 2 -$895 . 12 2 = 1 897 599 20 $599 2 -$897 . 20 2 = 1 898 899 30 $899 2 -$898 . 30 2 = 1 899 30 1 $30 2 -$899 . 1 2 = 1 901 1801 60 $1801 2 -$901 . 60 2 = 1 902 901 30 $901 2 -$902 . 30 2 = 1 903 601 20 $601 2 -$903 . 20 2 = 1 905 361 12 $361 2 -$905 . 12 2 = 1 906 301 10 $301 2 -$906 . 10 2 = 1 907 123823410343073497682 4111488857741309517 $123823410343073497682 2 -$907 . 4111488857741309517 2 = 1 910 181 6 $181 2 -$910 . 6 2 = 1 911 371832584927520 12319363142953 $371832584927520 2 -$911 . 12319363142953 2 = 1 913 515734243080407 17068312251564 $515734243080407 2 -$913 . 17068312251564 2 = 1 914 62563299 2069410 $62563299 2 -$914 . 2069410 2 = 1 915 121 4 $121 2 -$915 . 4 2 = 1 917 823604599 27197820 $823604599 2 -$917 . 27197820 2 = 1 919 4481603010937119451551263720 147834442396536759781499589 $4481603010937119451551263720 2 -$919 . 147834442396536759781499589 2 = 1 921 2522057712835735 83104627139412 $2522057712835735 2 -$921 . 83104627139412 2 = 1 922 351605368773852499 11579506138834350 $351605368773852499 2 -$922 . 11579506138834350 2 = 1 923 638 21 $638 2 -$923 . 21 2 = 1 926 304560297142335 10008472361032 $304560297142335 2 -$926 . 10008472361032 2 = 1 929 13224937103288377430049 433896111669844912840 $13224937103288377430049 2 -$929 . 433896111669844912840 2 = 1 930 61 2 $61 2 -$930 . 2 2 = 1 933 75263 2464 $75263 2 -$933 . 2464 2 = 1 934 3034565 99294 $3034565 2 -$934 . 99294 2 = 1 935 1376 45 $1376 2 -$935 . 45 2 = 1 937 480644425002415999597113107233 15701968936415353889062192632 $480644425002415999597113107233 2 -$937 . 15701968936415353889062192632 2 = 1 938 17151 560 $17151 2 -$938 . 560 2 = 1 939 122695 4004 $122695 2 -$939 . 4004 2 = 1 941 1068924905989944201 34845956052079180 $1068924905989944201 2 -$941 . 34845956052079180 2 = 1 942 106133 3458 $106133 2 -$942 . 3458 2 = 1 943 737 24 $737 2 -$943 . 24 2 = 1 946 45225786400145 1470417148788 $45225786400145 2 -$946 . 1470417148788 2 = 1 947 13509645362 439004487 $13509645362 2 -$947 . 439004487 2 = 1 949 609622436806639069525576201 19789181711517243032971740 $609622436806639069525576201 2 -$949 . 19789181711517243032971740 2 = 1 951 224208076 7270445 $224208076 2 -$951 . 7270445 2 = 1 953 15090531843660371073 488830275367615376 $15090531843660371073 2 -$953 . 488830275367615376 2 = 1 955 2095256249 67800900 $2095256249 2 -$955 . 67800900 2 = 1 957 14849 480 $14849 2 -$957 . 480 2 = 1 958 16762522330425599 541572514048560 $16762522330425599 2 -$958 . 541572514048560 2 = 1 959 960 31 $960 2 -$959 . 31 2 = 1 962 1923 62 $1923 2 -$962 . 62 2 = 1 965 446526729 14374204 $446526729 2 -$965 . 14374204 2 = 1 966 57499 1850 $57499 2 -$966 . 1850 2 = 1 967 4649532557817485528 149518887194649693 $4649532557817485528 2 -$967 . 149518887194649693 2 = 1 969 13588951 436540 $13588951 2 -$969 . 436540 2 = 1 970 215395035859 6915917802 $215395035859 2 -$970 . 6915917802 2 = 1 971 12479806786330 400496058813 $12479806786330 2 -$971 . 400496058813 2 = 1 973 903223 28956 $903223 2 -$973 . 28956 2 = 1 974 488825745235215 15662987185124 $488825745235215 2 -$974 . 15662987185124 2 = 1 977 108832847723078562849 3481871275306470280 $108832847723078562849 2 -$977 . 3481871275306470280 2 = 1 978 118337 3784 $118337 2 -$978 . 3784 2 = 1 979 360449 11520 $360449 2 -$979 . 11520 2 = 1 982 8837 282 $8837 2 -$982 . 282 2 = 1 983 284088 9061 $284088 2 -$983 . 9061 2 = 1 985 332929 10608 $332929 2 -$985 . 10608 2 = 1 986 49299 1570 $49299 2 -$986 . 1570 2 = 1 987 377 12 $377 2 -$987 . 12 2 = 1 989 550271588560695 17497618534396 $550271588560695 2 -$989 . 17497618534396 2 = 1 991 379516400906811930638014896080 12055735790331359447442538767 $379516400906811930638014896080 2 -$991 . 12055735790331359447442538767 2 = 1 993 2647 84 $2647 2 -$993 . 84 2 = 1 994 1135 36 $1135 2 -$994 . 36 2 = 1 995 8835999 280120 $8835999 2 -$995 . 280120 2 = 1 997 14418057673 456624468 $14418057673 2 -$997 . 456624468 2 = 1 998 984076901 31150410 $984076901 2 -$998 . 31150410 2 = 1

J.P. Martin-Flatin