yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
838031	139 6029	[ "838031 139 6029", "6029 6029 1" ]
4354793	107 40699	[ "4354793 107 40699", "40699 40699 1" ]
4094901	3 3 3 37 4099	[ "4094901 3 1364967", "1364967 3 454989", "454989 3 151663", "151663 37 4099", "4099 4099 1" ]
2127967	2127967	[ "2127967 2127967 1" ]
1614617	109 14813	[ "1614617 109 14813", "14813 14813 1" ]
2350033	7 335719	[ "2350033 7 335719", "335719 335719 1" ]
3905649	3 3 11 39451	[ "3905649 3 1301883", "1301883 3 433961", "433961 11 39451", "39451 39451 1" ]
793195	5 13 12203	[ "793195 5 158639", "158639 13 12203", "12203 12203 1" ]
1204442	2 602221	[ "1204442 2 602221", "602221 602221 1" ]
1162116	2 2 3 3 19 1699	[ "1162116 2 581058", "581058 2 290529", "290529 3 96843", "96843 3 32281", "32281 19 1699", "1699 1699 1" ]
3036310	2 5 113 2687	[ "3036310 2 1518155", "1518155 5 303631", "303631 113 2687", "2687 2687 1" ]
1898532	2 2 3 3 3 17579	[ "1898532 2 949266", "949266 2 474633", "474633 3 158211", "158211 3 52737", "52737 3 17579", "17579 17579 1" ]
389738	2 194869	[ "389738 2 194869", "194869 194869 1" ]
966960	2 2 2 2 3 3 5 17 79	[ "966960 2 483480", "483480 2 241740", "241740 2 120870", "120870 2 60435", "60435 3 20145", "20145 3 6715", "6715 5 1343", "1343 17 79", "79 79 1" ]
2610013	7 372859	[ "2610013 7 372859", "372859 372859 1" ]
3883642	2 7 7 23 1723	[ "3883642 2 1941821", "1941821 7 277403", "277403 7 39629", "39629 23 1723", "1723 1723 1" ]
1619795	5 29 11171	[ "1619795 5 323959", "323959 29 11171", "11171 11171 1" ]
3762652	2 2 41 22943	[ "3762652 2 1881326", "1881326 2 940663", "940663 41 22943", "22943 22943 1" ]
4814126	2 139 17317	[ "4814126 2 2407063", "2407063 139 17317", "17317 17317 1" ]
302477	7 7 6173	[ "302477 7 43211", "43211 7 6173", "6173 6173 1" ]
1021931	29 131 269	[ "1021931 29 35239", "35239 131 269", "269 269 1" ]
3334263	3 43 25847	[ "3334263 3 1111421", "1111421 43 25847", "25847 25847 1" ]
2787307	2787307	[ "2787307 2787307 1" ]
637537	23 53 523	[ "637537 23 27719", "27719 53 523", "523 523 1" ]
350022	2 3 58337	[ "350022 2 175011", "175011 3 58337", "58337 58337 1" ]
1446042	2 3 13 18539	[ "1446042 2 723021", "723021 3 241007", "241007 13 18539", "18539 18539 1" ]
2440949	7 19 18353	[ "2440949 7 348707", "348707 19 18353", "18353 18353 1" ]
2918857	2918857	[ "2918857 2918857 1" ]
1735529	1735529	[ "1735529 1735529 1" ]
1082081	7 11 13 23 47	[ "1082081 7 154583", "154583 11 14053", "14053 13 1081", "1081 23 47", "47 47 1" ]
3830653	397 9649	[ "3830653 397 9649", "9649 9649 1" ]
1438096	2 2 2 2 11 8171	[ "1438096 2 719048", "719048 2 359524", "359524 2 179762", "179762 2 89881", "89881 11 8171", "8171 8171 1" ]
4534797	3 1511599	[ "4534797 3 1511599", "1511599 1511599 1" ]
2069764	2 2 67 7723	[ "2069764 2 1034882", "1034882 2 517441", "517441 67 7723", "7723 7723 1" ]
102526	2 51263	[ "102526 2 51263", "51263 51263 1" ]
3286208	2 2 2 2 2 2 51347	[ "3286208 2 1643104", "1643104 2 821552", "821552 2 410776", "410776 2 205388", "205388 2 102694", "102694 2 51347", "51347 51347 1" ]
2108788	2 2 11 11 4357	[ "2108788 2 1054394", "1054394 2 527197", "527197 11 47927", "47927 11 4357", "4357 4357 1" ]
546951	3 337 541	[ "546951 3 182317", "182317 337 541", "541 541 1" ]
3303111	3 7 157291	[ "3303111 3 1101037", "1101037 7 157291", "157291 157291 1" ]
1909255	5 383 997	[ "1909255 5 381851", "381851 383 997", "997 997 1" ]
2473518	2 3 412253	[ "2473518 2 1236759", "1236759 3 412253", "412253 412253 1" ]
4305784	2 2 2 7 23 3343	[ "4305784 2 2152892", "2152892 2 1076446", "1076446 2 538223", "538223 7 76889", "76889 23 3343", "3343 3343 1" ]
4308645	3 5 11 26113	[ "4308645 3 1436215", "1436215 5 287243", "287243 11 26113", "26113 26113 1" ]
3473613	3 3 11 13 2699	[ "3473613 3 1157871", "1157871 3 385957", "385957 11 35087", "35087 13 2699", "2699 2699 1" ]
4588207	13 352939	[ "4588207 13 352939", "352939 352939 1" ]
2014779	3 13 19 2719	[ "2014779 3 671593", "671593 13 51661", "51661 19 2719", "2719 2719 1" ]
4986043	347 14369	[ "4986043 347 14369", "14369 14369 1" ]
1395742	2 487 1433	[ "1395742 2 697871", "697871 487 1433", "1433 1433 1" ]
2899091	13 223007	[ "2899091 13 223007", "223007 223007 1" ]
885092	2 2 13 17021	[ "885092 2 442546", "442546 2 221273", "221273 13 17021", "17021 17021 1" ]
3499581	3 1166527	[ "3499581 3 1166527", "1166527 1166527 1" ]
2317143	3 772381	[ "2317143 3 772381", "772381 772381 1" ]
93591	3 3 10399	[ "93591 3 31197", "31197 3 10399", "10399 10399 1" ]
4867014	2 3 67 12107	[ "4867014 2 2433507", "2433507 3 811169", "811169 67 12107", "12107 12107 1" ]
2026539	3 3 3 3 127 197	[ "2026539 3 675513", "675513 3 225171", "225171 3 75057", "75057 3 25019", "25019 127 197", "197 197 1" ]
81790	2 5 8179	[ "81790 2 40895", "40895 5 8179", "8179 8179 1" ]
68064	2 2 2 2 2 3 709	[ "68064 2 34032", "34032 2 17016", "17016 2 8508", "8508 2 4254", "4254 2 2127", "2127 3 709", "709 709 1" ]
3811128	2 2 2 3 17 9341	[ "3811128 2 1905564", "1905564 2 952782", "952782 2 476391", "476391 3 158797", "158797 17 9341", "9341 9341 1" ]
570383	11 51853	[ "570383 11 51853", "51853 51853 1" ]
2913098	2 383 3803	[ "2913098 2 1456549", "1456549 383 3803", "3803 3803 1" ]
734868	2 2 3 3 137 149	[ "734868 2 367434", "367434 2 183717", "183717 3 61239", "61239 3 20413", "20413 137 149", "149 149 1" ]
2079361	23 90407	[ "2079361 23 90407", "90407 90407 1" ]
1679137	181 9277	[ "1679137 181 9277", "9277 9277 1" ]
2717882	2 89 15269	[ "2717882 2 1358941", "1358941 89 15269", "15269 15269 1" ]
86398	2 13 3323	[ "86398 2 43199", "43199 13 3323", "3323 3323 1" ]
250008	2 2 2 3 11 947	[ "250008 2 125004", "125004 2 62502", "62502 2 31251", "31251 3 10417", "10417 11 947", "947 947 1" ]
1777367	17 104551	[ "1777367 17 104551", "104551 104551 1" ]
1814226	2 3 67 4513	[ "1814226 2 907113", "907113 3 302371", "302371 67 4513", "4513 4513 1" ]
3326050	2 5 5 7 13 17 43	[ "3326050 2 1663025", "1663025 5 332605", "332605 5 66521", "66521 7 9503", "9503 13 731", "731 17 43", "43 43 1" ]
174560	2 2 2 2 2 5 1091	[ "174560 2 87280", "87280 2 43640", "43640 2 21820", "21820 2 10910", "10910 2 5455", "5455 5 1091", "1091 1091 1" ]
4509427	13 13 26683	[ "4509427 13 346879", "346879 13 26683", "26683 26683 1" ]
2881047	3 13 31 2383	[ "2881047 3 960349", "960349 13 73873", "73873 31 2383", "2383 2383 1" ]
1902218	2 951109	[ "1902218 2 951109", "951109 951109 1" ]
381888	2 2 2 2 2 2 3 3 3 13 17	[ "381888 2 190944", "190944 2 95472", "95472 2 47736", "47736 2 23868", "23868 2 11934", "11934 2 5967", "5967 3 1989", "1989 3 663", "663 3 221", "221 13 17", "17 17 1" ]
2250792	2 2 2 3 3 43 727	[ "2250792 2 1125396", "1125396 2 562698", "562698 2 281349", "281349 3 93783", "93783 3 31261", "31261 43 727", "727 727 1" ]
95134	2 13 3659	[ "95134 2 47567", "47567 13 3659", "3659 3659 1" ]
3221227	61 52807	[ "3221227 61 52807", "52807 52807 1" ]
1638098	2 7 11 11 967	[ "1638098 2 819049", "819049 7 117007", "117007 11 10637", "10637 11 967", "967 967 1" ]
4576114	2 2288057	[ "4576114 2 2288057", "2288057 2288057 1" ]
4064987	307 13241	[ "4064987 307 13241", "13241 13241 1" ]
4053763	7 73 7933	[ "4053763 7 579109", "579109 73 7933", "7933 7933 1" ]
1287133	1287133	[ "1287133 1287133 1" ]
2616975	3 3 3 5 5 3877	[ "2616975 3 872325", "872325 3 290775", "290775 3 96925", "96925 5 19385", "19385 5 3877", "3877 3877 1" ]
2004349	2004349	[ "2004349 2004349 1" ]
704389	7 47 2141	[ "704389 7 100627", "100627 47 2141", "2141 2141 1" ]
2264646	2 3 587 643	[ "2264646 2 1132323", "1132323 3 377441", "377441 587 643", "643 643 1" ]
4522460	2 2 5 226123	[ "4522460 2 2261230", "2261230 2 1130615", "1130615 5 226123", "226123 226123 1" ]
1393876	2 2 11 79 401	[ "1393876 2 696938", "696938 2 348469", "348469 11 31679", "31679 79 401", "401 401 1" ]
2946664	2 2 2 7 7 7517	[ "2946664 2 1473332", "1473332 2 736666", "736666 2 368333", "368333 7 52619", "52619 7 7517", "7517 7517 1" ]
1987225	5 5 29 2741	[ "1987225 5 397445", "397445 5 79489", "79489 29 2741", "2741 2741 1" ]
4038135	3 5 269209	[ "4038135 3 1346045", "1346045 5 269209", "269209 269209 1" ]
1792699	31 57829	[ "1792699 31 57829", "57829 57829 1" ]
4648287	3 7 7 103 307	[ "4648287 3 1549429", "1549429 7 221347", "221347 7 31621", "31621 103 307", "307 307 1" ]
4526327	13 13 26783	[ "4526327 13 348179", "348179 13 26783", "26783 26783 1" ]
852850	2 5 5 37 461	[ "852850 2 426425", "426425 5 85285", "85285 5 17057", "17057 37 461", "461 461 1" ]
2668750	2 5 5 5 5 5 7 61	[ "2668750 2 1334375", "1334375 5 266875", "266875 5 53375", "53375 5 10675", "10675 5 2135", "2135 5 427", "427 7 61", "61 61 1" ]
3293436	2 2 3 274453	[ "3293436 2 1646718", "1646718 2 823359", "823359 3 274453", "274453 274453 1" ]
3215537	13 31 79 101	[ "3215537 13 247349", "247349 31 7979", "7979 79 101", "101 101 1" ]
222861	3 74287	[ "222861 3 74287", "74287 74287 1" ]
3545909	43 82463	[ "3545909 43 82463", "82463 82463 1" ]

838031

139 6029

[ "838031 139 6029", "6029 6029 1" ]

4354793

107 40699

[ "4354793 107 40699", "40699 40699 1" ]

4094901

3 3 3 37 4099

[ "4094901 3 1364967", "1364967 3 454989", "454989 3 151663", "151663 37 4099", "4099 4099 1" ]

2127967

[ "2127967 2127967 1" ]

1614617

109 14813

[ "1614617 109 14813", "14813 14813 1" ]

2350033

7 335719

[ "2350033 7 335719", "335719 335719 1" ]

3905649

3 3 11 39451

[ "3905649 3 1301883", "1301883 3 433961", "433961 11 39451", "39451 39451 1" ]

793195

5 13 12203

[ "793195 5 158639", "158639 13 12203", "12203 12203 1" ]

1204442

2 602221

[ "1204442 2 602221", "602221 602221 1" ]

1162116

2 2 3 3 19 1699

[ "1162116 2 581058", "581058 2 290529", "290529 3 96843", "96843 3 32281", "32281 19 1699", "1699 1699 1" ]

3036310

2 5 113 2687

[ "3036310 2 1518155", "1518155 5 303631", "303631 113 2687", "2687 2687 1" ]

1898532

2 2 3 3 3 17579

[ "1898532 2 949266", "949266 2 474633", "474633 3 158211", "158211 3 52737", "52737 3 17579", "17579 17579 1" ]

389738

2 194869

[ "389738 2 194869", "194869 194869 1" ]

966960

2 2 2 2 3 3 5 17 79

[ "966960 2 483480", "483480 2 241740", "241740 2 120870", "120870 2 60435", "60435 3 20145", "20145 3 6715", "6715 5 1343", "1343 17 79", "79 79 1" ]

2610013

7 372859

[ "2610013 7 372859", "372859 372859 1" ]

3883642

2 7 7 23 1723

[ "3883642 2 1941821", "1941821 7 277403", "277403 7 39629", "39629 23 1723", "1723 1723 1" ]

1619795

5 29 11171

[ "1619795 5 323959", "323959 29 11171", "11171 11171 1" ]

3762652

2 2 41 22943

[ "3762652 2 1881326", "1881326 2 940663", "940663 41 22943", "22943 22943 1" ]

4814126

2 139 17317

[ "4814126 2 2407063", "2407063 139 17317", "17317 17317 1" ]

302477

7 7 6173

[ "302477 7 43211", "43211 7 6173", "6173 6173 1" ]

1021931

29 131 269

[ "1021931 29 35239", "35239 131 269", "269 269 1" ]

3334263

3 43 25847

[ "3334263 3 1111421", "1111421 43 25847", "25847 25847 1" ]

2787307

[ "2787307 2787307 1" ]

637537

23 53 523

[ "637537 23 27719", "27719 53 523", "523 523 1" ]

350022

2 3 58337

[ "350022 2 175011", "175011 3 58337", "58337 58337 1" ]

1446042

2 3 13 18539

[ "1446042 2 723021", "723021 3 241007", "241007 13 18539", "18539 18539 1" ]

2440949

7 19 18353

[ "2440949 7 348707", "348707 19 18353", "18353 18353 1" ]

2918857

[ "2918857 2918857 1" ]

1735529

[ "1735529 1735529 1" ]

1082081

7 11 13 23 47

[ "1082081 7 154583", "154583 11 14053", "14053 13 1081", "1081 23 47", "47 47 1" ]

3830653

397 9649

[ "3830653 397 9649", "9649 9649 1" ]

1438096

2 2 2 2 11 8171

[ "1438096 2 719048", "719048 2 359524", "359524 2 179762", "179762 2 89881", "89881 11 8171", "8171 8171 1" ]

4534797

3 1511599

[ "4534797 3 1511599", "1511599 1511599 1" ]

2069764

2 2 67 7723

[ "2069764 2 1034882", "1034882 2 517441", "517441 67 7723", "7723 7723 1" ]

102526

2 51263

[ "102526 2 51263", "51263 51263 1" ]

3286208

2 2 2 2 2 2 51347

[ "3286208 2 1643104", "1643104 2 821552", "821552 2 410776", "410776 2 205388", "205388 2 102694", "102694 2 51347", "51347 51347 1" ]

2108788

2 2 11 11 4357

[ "2108788 2 1054394", "1054394 2 527197", "527197 11 47927", "47927 11 4357", "4357 4357 1" ]

546951

3 337 541

[ "546951 3 182317", "182317 337 541", "541 541 1" ]

3303111

3 7 157291

[ "3303111 3 1101037", "1101037 7 157291", "157291 157291 1" ]

1909255

5 383 997

[ "1909255 5 381851", "381851 383 997", "997 997 1" ]

2473518

2 3 412253

[ "2473518 2 1236759", "1236759 3 412253", "412253 412253 1" ]

4305784

2 2 2 7 23 3343

[ "4305784 2 2152892", "2152892 2 1076446", "1076446 2 538223", "538223 7 76889", "76889 23 3343", "3343 3343 1" ]

4308645

3 5 11 26113

[ "4308645 3 1436215", "1436215 5 287243", "287243 11 26113", "26113 26113 1" ]

3473613

3 3 11 13 2699

[ "3473613 3 1157871", "1157871 3 385957", "385957 11 35087", "35087 13 2699", "2699 2699 1" ]

4588207

13 352939

[ "4588207 13 352939", "352939 352939 1" ]

2014779

3 13 19 2719

[ "2014779 3 671593", "671593 13 51661", "51661 19 2719", "2719 2719 1" ]

4986043

347 14369

[ "4986043 347 14369", "14369 14369 1" ]

1395742

2 487 1433

[ "1395742 2 697871", "697871 487 1433", "1433 1433 1" ]

2899091

13 223007

[ "2899091 13 223007", "223007 223007 1" ]

885092

2 2 13 17021

[ "885092 2 442546", "442546 2 221273", "221273 13 17021", "17021 17021 1" ]

3499581

3 1166527

[ "3499581 3 1166527", "1166527 1166527 1" ]

2317143

3 772381

[ "2317143 3 772381", "772381 772381 1" ]

93591

3 3 10399

[ "93591 3 31197", "31197 3 10399", "10399 10399 1" ]

4867014

2 3 67 12107

[ "4867014 2 2433507", "2433507 3 811169", "811169 67 12107", "12107 12107 1" ]

2026539

3 3 3 3 127 197

[ "2026539 3 675513", "675513 3 225171", "225171 3 75057", "75057 3 25019", "25019 127 197", "197 197 1" ]

81790

2 5 8179

[ "81790 2 40895", "40895 5 8179", "8179 8179 1" ]

68064

2 2 2 2 2 3 709

[ "68064 2 34032", "34032 2 17016", "17016 2 8508", "8508 2 4254", "4254 2 2127", "2127 3 709", "709 709 1" ]

3811128

2 2 2 3 17 9341

[ "3811128 2 1905564", "1905564 2 952782", "952782 2 476391", "476391 3 158797", "158797 17 9341", "9341 9341 1" ]

570383

11 51853

[ "570383 11 51853", "51853 51853 1" ]

2913098

2 383 3803

[ "2913098 2 1456549", "1456549 383 3803", "3803 3803 1" ]

734868

2 2 3 3 137 149

[ "734868 2 367434", "367434 2 183717", "183717 3 61239", "61239 3 20413", "20413 137 149", "149 149 1" ]

2079361

23 90407

[ "2079361 23 90407", "90407 90407 1" ]

1679137

181 9277

[ "1679137 181 9277", "9277 9277 1" ]

2717882

2 89 15269

[ "2717882 2 1358941", "1358941 89 15269", "15269 15269 1" ]

86398

2 13 3323

[ "86398 2 43199", "43199 13 3323", "3323 3323 1" ]

250008

2 2 2 3 11 947

[ "250008 2 125004", "125004 2 62502", "62502 2 31251", "31251 3 10417", "10417 11 947", "947 947 1" ]

1777367

17 104551

[ "1777367 17 104551", "104551 104551 1" ]

1814226

2 3 67 4513

[ "1814226 2 907113", "907113 3 302371", "302371 67 4513", "4513 4513 1" ]

3326050

2 5 5 7 13 17 43

[ "3326050 2 1663025", "1663025 5 332605", "332605 5 66521", "66521 7 9503", "9503 13 731", "731 17 43", "43 43 1" ]

174560

2 2 2 2 2 5 1091

[ "174560 2 87280", "87280 2 43640", "43640 2 21820", "21820 2 10910", "10910 2 5455", "5455 5 1091", "1091 1091 1" ]

4509427

13 13 26683

[ "4509427 13 346879", "346879 13 26683", "26683 26683 1" ]

2881047

3 13 31 2383

[ "2881047 3 960349", "960349 13 73873", "73873 31 2383", "2383 2383 1" ]

1902218

2 951109

[ "1902218 2 951109", "951109 951109 1" ]

381888

2 2 2 2 2 2 3 3 3 13 17

[ "381888 2 190944", "190944 2 95472", "95472 2 47736", "47736 2 23868", "23868 2 11934", "11934 2 5967", "5967 3 1989", "1989 3 663", "663 3 221", "221 13 17", "17 17 1" ]

2250792

2 2 2 3 3 43 727

[ "2250792 2 1125396", "1125396 2 562698", "562698 2 281349", "281349 3 93783", "93783 3 31261", "31261 43 727", "727 727 1" ]

95134

2 13 3659

[ "95134 2 47567", "47567 13 3659", "3659 3659 1" ]

3221227

61 52807

[ "3221227 61 52807", "52807 52807 1" ]

1638098

2 7 11 11 967

[ "1638098 2 819049", "819049 7 117007", "117007 11 10637", "10637 11 967", "967 967 1" ]

4576114

2 2288057

[ "4576114 2 2288057", "2288057 2288057 1" ]

4064987

307 13241

[ "4064987 307 13241", "13241 13241 1" ]

4053763

7 73 7933

[ "4053763 7 579109", "579109 73 7933", "7933 7933 1" ]

1287133

[ "1287133 1287133 1" ]

2616975

3 3 3 5 5 3877

[ "2616975 3 872325", "872325 3 290775", "290775 3 96925", "96925 5 19385", "19385 5 3877", "3877 3877 1" ]

2004349

[ "2004349 2004349 1" ]

704389

7 47 2141

[ "704389 7 100627", "100627 47 2141", "2141 2141 1" ]

2264646

2 3 587 643

[ "2264646 2 1132323", "1132323 3 377441", "377441 587 643", "643 643 1" ]

4522460

2 2 5 226123

[ "4522460 2 2261230", "2261230 2 1130615", "1130615 5 226123", "226123 226123 1" ]

1393876

2 2 11 79 401

[ "1393876 2 696938", "696938 2 348469", "348469 11 31679", "31679 79 401", "401 401 1" ]

2946664

2 2 2 7 7 7517

[ "2946664 2 1473332", "1473332 2 736666", "736666 2 368333", "368333 7 52619", "52619 7 7517", "7517 7517 1" ]

1987225

5 5 29 2741

[ "1987225 5 397445", "397445 5 79489", "79489 29 2741", "2741 2741 1" ]

4038135

3 5 269209

[ "4038135 3 1346045", "1346045 5 269209", "269209 269209 1" ]

1792699

31 57829

[ "1792699 31 57829", "57829 57829 1" ]

4648287

3 7 7 103 307

[ "4648287 3 1549429", "1549429 7 221347", "221347 7 31621", "31621 103 307", "307 307 1" ]

4526327

13 13 26783

[ "4526327 13 348179", "348179 13 26783", "26783 26783 1" ]

852850

2 5 5 37 461

[ "852850 2 426425", "426425 5 85285", "85285 5 17057", "17057 37 461", "461 461 1" ]

2668750

2 5 5 5 5 5 7 61

[ "2668750 2 1334375", "1334375 5 266875", "266875 5 53375", "53375 5 10675", "10675 5 2135", "2135 5 427", "427 7 61", "61 61 1" ]

3293436

2 2 3 274453

[ "3293436 2 1646718", "1646718 2 823359", "823359 3 274453", "274453 274453 1" ]

3215537

13 31 79 101

[ "3215537 13 247349", "247349 31 7979", "7979 79 101", "101 101 1" ]

222861

3 74287

[ "222861 3 74287", "74287 74287 1" ]

3545909

43 82463

[ "3545909 43 82463", "82463 82463 1" ]